Online Curve Fitting and Surface Fitting at ZunZunSite3

2D Functions		3D Functions		Characterizers		Site Related

Welcome to ZunZunSite3

Here you can curve fit and surface fit your 2D and 3D data online with
a rich set of error histograms, error plots, curve plots, surface plots,
contour plots, auto-generated source code, and PDF file output.

If you're looking for high quality curve fitting and surface fitting, this is
the site for you! Source code is available at the Bitbucket Code Repository.

To begin, select an equation family from the drop-down menus above or try
the "Function Finders" to help determine the best curve fit for your data.


Powered by Debian Linux	Written in Python	Using the Django Web Framework


Coded with Wingware	Plotted by Matplotlib	PDF Generation by Report Lab


		ZunZunSite3's Google discussion group

Historical Note

Prior to the invention of electronic calculation, only manual methods were available,
of course - meaning that creating mathematical models from experimental data was
done by hand. Even Napier's invention of logarithms did not help much in reducing
the tediousness of this task. Linear regression techniques worked, but how to then
compare models? - and so the F-statistic was created for the purpose of model
selection, since graphing models and their confidence intervals was practically out
of the question. Forward and backward regression techniques used linear methods,
requiring less calculation than nonlinear methods, but limited the possible mathematical
models to linear combinations of functions.

With the advent of computerized calculations, nonlinear methods which were
impractical in the past could be automated and made practical. However, the
nonlinear fitting methods all required starting points for their solvers - meaning in
practice you had to have a good idea of the final equation parameters to begin with!

If however a genetic or monte carlo algorithm searched error space for initial parameters
prior to running the nonlinear solvers, this problem could be strongly mitigated. This
meant that instead of hit-or-miss forward and backward regression, large numbers of
known linear *and* nonlinear equations could be fitted to an experimental data set and
then ranked by a fit statistic such as AIC or SSQ errors.

This technique is captured in the pyeq3 open source fitting code. Note that for an initial
guesstimate of parameter values, not all data need be used. A reduced size data set with
min, max, and (hopefully) evenly spaced additional data points in between are used. The
total number of data points required is the number of equation parameters plus a few
extra points.

Reducing the data set size used by the code's genetic algorithm greatly reduces total
processing time. No secrets here, it's in the open source code. I tested many different
methods before choosing the one in the code, a genetic algorithm named "Differential Evolution".

Dedication

This site is dedicated to Jesus of Nazareth, son of the living God.


Ephesians 4:28

Let him that stole steal no more:
but rather let him labour,
working with his hands the thing which is good,
that he may have to give to him that needeth.

King 14 2D		f(x) = k * [1/sqrt(1 + (x/r_c) 2) - 1/sqrt(1 + (r_t/r_c) 2)] ** 2 [web citation]
King 14 With Offset 2D		f(x) = k * [1/sqrt(1 + (x/r_c) 2) - 1/sqrt(1 + (r_t/r_c) 2)] ** 2 + Offset [web citation]

Aphid Population Growth 2D		N(t) = a * exp(bt) * (1 + c * exp(bt))^-2 [web citation]
Beverton-Holt A 2D		y = r / (1 + ((r-1)/K) * x)
Beverton-Holt B 2D		y = rx / (1 + ((r-1)/K) * x)
BioScience A 2D		y = a * (1.0 - (b * c^x))
BioScience B 2D		y = a * (1.0 -(1.0 + (x/b)^c)^{-1.0 * d})
Cellular Conductance 2D		g = p3/(1+exp((v-p1)/p2)) + p4*exp((v-45)/p5) [web citation]
Derek Duncan Custom Equation 2D		y = a / (1 + exp(-1/b*(x-c)))^d
Dose-Response A 2D		y = b + (a-b) / (1 + 10^x-c)
Dose-Response B 2D		y = b + (a-b) / (1 + 10^c-x)
Dose-Response C 2D		y = b + (a-b) / (1 + 10^d*(x-c))
Dose-Response D 2D		y = b + (a-b) / (1 + 10^d*(c-x))
Dose-Response E 2D		y = b + (a-b) / (1 + (x/c)^d)
Generalized Negative Exponential 2D		y = a * (1.0 - exp(-bx))^c
Generalized Product Accumulation 2D		y = a(b-x) / (c + (b-x)) + d(b-x) + f
Generalized Substrate Depletion 2D		y = ax / (b + x) - cx - d
High-Low Affinity 2D		y = abx / (1+bx)
High-Low Affinity Double 2D		y = abx / (1+bx) + cdx / (1+dx)
High-Low Affinity Double Isotope Displacement ([Hot] subsumed) 2D		y = ab / (1+bx) + cd / (1+dx)
High-Low Affinity Isotope Displacement ([Hot] subsumed) 2D		y = ab / (1+bx)
Hyperbolic A 2D		y = (a + x) / (b + x)
Hyperbolic B 2D		y = (a + bx) / (c + x)
Hyperbolic C 2D		y = (a + x) / (b + cx)
Hyperbolic D 2D		y = (a + bx) / (c + dx)
Hyperbolic E 2D		y = ax / (b + x)
Hyperbolic F 2D		y = ax / (b + x) + cx
Hyperbolic G 2D		y = ax / (b + x) + cx / (d + x)
Hyperbolic H 2D		y = ax / (b + x) + cx / (d + x) + fx
Hyperbolic I 2D		y = ab / (b + x)
Hyperbolic J 2D		y = x / (a + bx)
Hyperbolic Logistic 2D		y = ax^b / (c + x^b)
Jorge Rabinovich Population Growth 2D		Y = (P1CC) / (P1 + (CC-P1)exp(-R*X))
Membrane Transport 2D		y = a(x-b) / (x² + cx + d)
Michaelis-Menten 2D		y = ax / (b + x)
Michaelis-Menten Double 2D		y = ax / (b + x) + cx / (d + x)
Michaelis-Menten Isotope Displacement ([Hot] subsumed) 2D		y = a / (b + x)
Michaelis-Menten Isotope Displacement Double ([Hot] subsumed) 2D		y = a / (b + x) + c / (d + x)
Michaelis-Menten Product Accumulation 2D		y = a(b-x) / (c + (b-x))
Negative Exponential 2D		y = a * (1.0 - exp(-bx))
New Zealand Ecology Logistic 1 2D		n = B0 + ((B1 - B0) / (1.0 + exp((B2 - D) * B3)))
New Zealand Ecology Logistic 2 2D		n = B0 + ((B1 - B0) / (1.0 + exp((B2 - D + (B4D²)) B3)))
Plant Disease Exponential Model 2D		Incidence = y0 * exp(r * time) [web citation]
Plant Disease Gompertz Model 2D		Incidence = exp(ln(y0) * exp(-r * time)) [web citation]
Plant Disease Logistic Model 2D		Incidence = 1 / (1 + (1 - y0) / (y0 * exp(-r * time))) [web citation]
Plant Disease Monomolecular Model 2D		Incidence = 1 - ((1 - y0) * exp(-r * time)) [web citation]
Plant Disease Weibull Model 2D		Incidence = 1 - exp(-1.0 * ((time - a) / b)^c) [web citation]
Plant Disease Weibull Model Scaled 2D		y = Scale * (1 - exp(-1.0 * ((time - a) / b)^c)) [web citation]
Preece And Baines Growth 2D		y = a - 2(a-b) / (exp(c(x-d)) + exp(f(x-d)))
Scaled Log 2D		y = a * log(x)
Scaled Log Transform 2D		y = a * log(bx + c)
Scaled Power 2D		y = a * x^b
Scaled Power Transform 2D		y = a * (cx + d)^b
Standard 3-Parameter Logistic Equation 2D		y = d + (a - d) / (1 + (x / c))
Standard 4-Parameter Logistic Equation 2D		y = d + (a - d) / (1 + (x / c)^b)
Standard 5-Parameter Logistic Equation 2D		y = d + (a - d) / (1 + (x / c)^b )^f
Weibull 2D		y = a * (1.0 - exp(-b * (x - c)^d))
Xiaogang Peng Immunoassay 2D		y = K / (1.0 + exp(-1.0 * (a + blog(x) + cx)))
von Bertalanffy Growth 2D		L(t) = L_inf * (1.0 - exp(-K * (t-t_zero)))



Aphid Population Growth With Offset 2D		N(t) = a * exp(bt) * (1 + c * exp(bt))^-2 + Offset [web citation]
Beverton-Holt A With Offset 2D		y = r / (1 + ((r-1)/K) * x) + Offset
Beverton-Holt B With Offset 2D		y = rx / (1 + ((r-1)/K) * x) + Offset
BioScience A With Offset 2D		y = a * (1.0 - (b * c^x)) + Offset
BioScience B With Offset 2D		y = a * (1.0 -(1.0 + (x/b)^c)^{-1.0 * d}) + Offset
Cellular Conductance With Offset 2D		g = p3/(1+exp((v-p1)/p2)) + p4*exp((v-45)/p5) + Offset [web citation]
Derek Duncan Custom Equation With Offset 2D		y = a / (1 + exp(-1/b*(x-c)))^d + Offset
Generalized Negative Exponential With Offset 2D		y = a * (1.0 - exp(-bx))^c + Offset
High-Low Affinity Double Isotope Displacement ([Hot] subsumed) With Offset 2D		y = ab / (1+bx) + cd / (1+dx) + Offset
High-Low Affinity Double With Offset 2D		y = abx / (1+bx) + cdx / (1+dx) + Offset
High-Low Affinity Isotope Displacement ([Hot] subsumed) With Offset 2D		y = ab / (1+bx) + Offset
High-Low Affinity With Offset 2D		y = abx / (1+bx) + Offset
Hyperbolic A With Offset 2D		y = (a + x) / (b + x) + Offset
Hyperbolic B With Offset 2D		y = (a + bx) / (c + x) + Offset
Hyperbolic C With Offset 2D		y = (a + x) / (b + cx) + Offset
Hyperbolic D With Offset 2D		y = (a + bx) / (c + dx) + Offset
Hyperbolic E With Offset 2D		y = ax / (b + x) + Offset
Hyperbolic F With Offset 2D		y = ax / (b + x) + cx + Offset
Hyperbolic G With Offset 2D		y = ax / (b + x) + cx / (d + x) + Offset
Hyperbolic H With Offset 2D		y = ax / (b + x) + cx / (d + x) + fx + Offset
Hyperbolic I With Offset 2D		y = ab / (b + x) + Offset
Hyperbolic J With Offset 2D		y = x / (a + bx) + Offset
Hyperbolic Logistic With Offset 2D		y = ax^b / (c + x^b) + Offset
Jorge Rabinovich Population Growth With Offset 2D		Y = (P1CC) / (P1 + (CC-P1)exp(-R*X)) + Offset
Membrane Transport With Offset 2D		y = a(x-b) / (x² + cx + d) + Offset
Michaelis-Menten Double With Offset 2D		y = ax / (b + x) + cx / (d + x) + Offset
Michaelis-Menten Isotope Displacement ([Hot] subsumed) With Offset 2D		y = a / (b + x) + Offset
Michaelis-Menten Isotope Displacement Double ([Hot] subsumed) With Offset 2D		y = a / (b + x) + c / (d + x) + Offset
Michaelis-Menten Product Accumulation With Offset 2D		y = a(b-x) / (c + (b-x)) + Offset
Michaelis-Menten With Offset 2D		y = ax / (b + x) + Offset
Negative Exponential With Offset 2D		y = a * (1.0 - exp(-bx)) + Offset
Plant Disease Exponential Model With Offset 2D		Incidence = y0 * exp(r * time) + Offset [web citation]
Plant Disease Gompertz Model With Offset 2D		Incidence = exp(ln(y0) * exp(-r * time)) + Offset [web citation]
Plant Disease Logistic Model With Offset 2D		Incidence = 1 / (1 + (1 - y0) / (y0 * exp(-r * time))) + Offset [web citation]
Plant Disease Monomolecular Model With Offset 2D		Incidence = 1 - ((1 - y0) * exp(-r * time)) + Offset [web citation]
Plant Disease Weibull Model Scaled With Offset 2D		y = Scale * (1 - exp(-1.0 * ((time - a) / b)^c)) + Offset [web citation]
Plant Disease Weibull Model With Offset 2D		Incidence = 1 - exp(-1.0 * ((time - a) / b)^c) + Offset [web citation]
Scaled Log Transform With Offset 2D		y = a * log(bx + c) + Offset
Scaled Log With Offset 2D		y = a * log(x) + Offset
Scaled Power Transform With Offset 2D		y = a * (cx + d)^b + Offset
Scaled Power With Offset 2D		y = a * x^b + Offset
Weibull With Offset 2D		y = a * (1.0 - exp(-b * (x - c)^d)) + Offset
Xiaogang Peng Immunoassay With Offset 2D		y = K / (1.0 + exp(-1.0 * (a + blog(x) + cx))) + Offset
von Bertalanffy Growth With Offset 2D		L(t) = L_inf * (1.0 - exp(-K * (t-t_zero))) + Offset

Arcsin CDF Based 2D		y = a * asin( (bx+c) / d) [web citation]
Arcsin PDF Based 2D		y = a / sqrt( b² - x²) [web citation]
Bradford CDF Based A 2D		y = ln(1.0+c*(x-a)/(b-a)) / ln(c+1.0) [web citation]
Bradford CDF Based B 2D		y = d * ln(1.0+c*(x-a)/(b-a)) / ln(c+1.0) [web citation]
Bradford PDF Based 2D		y = c / (( c * (x-a) + b-a) * ln(c + 1.0)) [web citation]
Burr CDF Based A 2D		y = 1.0 / ( 1.0 + ( b / ( x-a ))^c)^d [web citation]
Burr CDF Based B 2D		y = f / ( 1.0 + ( b / ( x-a ))^c)^d [web citation]
Burr PDF Based 2D		y = (cd/b) ((x-a)/b)^(-c-1.0) * (1.0+((x-a)/b)^(-c))^(-d-1.0) [web citation]
Dipole CDF Based 2D		y = a * arctan(x) + b/x [web citation]
Exponential PDF Based 2D		y = (1.0/b) * exp((a-x)/b) [web citation]
Exponential PDF Based Scaled 2D		y = Scale * (1.0/b) * exp((a-x)/b) [web citation]
Extreme Values CDF Based A 2D		y = exp(-exp(-((x-a)/b))) [web citation]
Extreme Values CDF Based B 2D		y = c * exp(-exp(-((x-a)/b))) [web citation]
Extreme Values PDF Based 2D		y = (1.0/b) * exp(((a-x)/b)-exp((a-x)/b)) [web citation]
Fisk CDF Based A 2D		y = 1.0 / (1.0+(b/(x-a))^c) [web citation]
Fisk CDF Based B 2D		y = d / (1.0+(b/(x-a))^c) [web citation]
Fisk PDF Based 2D		y = (c/b) * ((x-a)/b)^(c-1.0) / (1.0 + ((x-a)/b)^c)² [web citation]
Folded Normal PDF Based 2D		y = c * (1/b) * cosh(ax/b²) exp(-0.5 * (x² + a²)/b²) [web citation]
Frechet CDF Based A 2D		y = exp(-1.0 / x^a) [web citation]
Frechet CDF Based B 2D		y = b * exp(-1.0 / x^a) [web citation]
Frechet PDF Based A 2D		y = exp(- 1.0 / x^a) / x^{( a + 1.0)} [web citation]
Frechet PDF Based B 2D		y = b * exp(- 1.0 / x^a) / x^{( a + 1.0)} [web citation]
Genlogistic CDF Based A 2D		y = (1.0/(1.0+exp(-(x-a)/b)))^c [web citation]
Genlogistic CDF Based B 2D		y = (d/(1.0+exp(-(x-a)/b)))^c [web citation]
Genlogistic PDF Based 2D		y = (c/b) * exp(-((x-a)/b)) / (1.0+exp(-((x-a)/b)))^(c+1.0) [web citation]
Gompertz CDF Based 2D		y = 1.0 - exp(-b * (a^x-1.0) / ln(a)) [web citation]
Gompertz CDF Based Scaled 2D		y = Scale * (1.0 - exp(-b * (a^x-1.0) / ln(a))) [web citation]
Gumbel CDF Based 2D		y = a * exp(-exp(-x)) [web citation]
Gumbel PDF Based 2D		y = a * exp(-x-exp(-x)) [web citation]
Half Normal PDF Based 2D		y = c * ( 1.0/b) * exp(-0.5((x-a)/b)((x-a)/b)) [web citation]
Inverse_gaussian PDF Based A 2D		y = sqrt(b/(cx³))exp(-b(x-a)² / (2.0a²*x)) [web citation]
Inverse_gaussian PDF Based B 2D		y = sqrt(b/(cx³))exp(-b(x-a)² / (2.0a²*x)) [web citation]
Levy PDF Based 2D		y = b^0.5 * exp(-b/(2.0*(x-a)))/sqrt((x-a)³) [web citation]
Levy PDF Based Scaled 2D		y = Scale * b^0.5 * exp(-b/(2.0*(x-a)))/sqrt((x-a)³) [web citation]
Log Normal PDF Based 2D		y = exp(-0.5((ln(x)-a)/b)²) / (bx) [web citation]
Logistic PDF Based 2D		y = exp((a-x)/b) / (b*(1.0+exp((a-x)/b))²) [web citation]
Pareto PDF Based 2D		y = b * a^b / x^(b+1.0) [web citation]
Power PDF Based 2D		y = (a/b) * (x/b)^(a-1.0) [web citation]
Rayleigh CDF Based A 2D		y = 1.0 - exp(-x²/(2.0*a²)) [web citation]
Rayleigh CDF Based B 2D		y = b * exp(-x²/(2.0*a²)) [web citation]
Rayleigh PDF Based 2D		y = (x/a²) * exp(-x²/(2.0*a²)) [web citation]
Rayleigh PDF Based Scaled 2D		y = Scale * (x/a²) * exp(-x²/(2.0*a²)) [web citation]
Reciprocal CDF Based 2D		y = ln(a/x) / ln(a/b) [web citation]
Sech CDF Based 2D		y = c * atan(exp((x-a)/b)) [web citation]
Weibull CDF Based A 2D		y = 1.0 / exp(((x-a)/b)^c) [web citation]
Weibull CDF Based B 2D		y = d / exp(((x-a)/b)^c) [web citation]
Weibull PDF Based 2D		y = (c/b) * ((x-a)/b)^(c-1.0) / exp(((x-a)/b)^c) [web citation]



Arcsin CDF Based With Offset 2D		y = a * asin( (bx+c) / d) + Offset [web citation]
Arcsin PDF Based With Offset 2D		y = a / sqrt( b² - x²) + Offset [web citation]
Bradford CDF Based A With Offset 2D		y = ln(1.0+c*(x-a)/(b-a)) / ln(c+1.0) + Offset [web citation]
Bradford CDF Based B With Offset 2D		y = d * ln(1.0+c*(x-a)/(b-a)) / ln(c+1.0) + Offset [web citation]
Bradford PDF Based With Offset 2D		y = c / (( c * (x-a) + b-a) * ln(c + 1.0)) + Offset [web citation]
Burr CDF Based A With Offset 2D		y = 1.0 / ( 1.0 + ( b / ( x-a ))^c)^d + Offset [web citation]
Burr CDF Based B With Offset 2D		y = f / ( 1.0 + ( b / ( x-a ))^c)^d + Offset [web citation]
Burr PDF Based With Offset 2D		y = (cd/b) ((x-a)/b)^(-c-1.0) * (1.0+((x-a)/b)^(-c))^(-d-1.0) + Offset [web citation]
Dipole CDF Based With Offset 2D		y = a * arctan(x) + b/x + Offset [web citation]
Exponential PDF Based Scaled With Offset 2D		y = Scale * (1.0/b) * exp((a-x)/b) + Offset [web citation]
Exponential PDF Based With Offset 2D		y = (1.0/b) * exp((a-x)/b) + Offset [web citation]
Extreme Values CDF Based A With Offset 2D		y = exp(-exp(-((x-a)/b))) + Offset [web citation]
Extreme Values CDF Based B With Offset 2D		y = c * exp(-exp(-((x-a)/b))) + Offset [web citation]
Extreme Values PDF Based With Offset 2D		y = (1.0/b) * exp(((a-x)/b)-exp((a-x)/b)) + Offset [web citation]
Fisk CDF Based A With Offset 2D		y = 1.0 / (1.0+(b/(x-a))^c) + Offset [web citation]
Fisk CDF Based B With Offset 2D		y = d / (1.0+(b/(x-a))^c) + Offset [web citation]
Fisk PDF Based With Offset 2D		y = (c/b) * ((x-a)/b)^(c-1.0) / (1.0 + ((x-a)/b)^c)² + Offset [web citation]
Folded Normal PDF Based With Offset 2D		y = c * (1/b) * cosh(ax/b²) exp(-0.5 * (x² + a²)/b²) + Offset [web citation]
Frechet CDF Based A With Offset 2D		y = exp(-1.0 / x^a) + Offset [web citation]
Frechet CDF Based B With Offset 2D		y = b * exp(-1.0 / x^a) + Offset [web citation]
Frechet PDF Based A With Offset 2D		y = exp(- 1.0 / x^a) / x^{( a + 1.0)} + Offset [web citation]
Frechet PDF Based B With Offset 2D		y = b * exp(- 1.0 / x^a) / x^{( a + 1.0)} + Offset [web citation]
Genlogistic CDF Based A With Offset 2D		y = (1.0/(1.0+exp(-(x-a)/b)))^c + Offset [web citation]
Genlogistic CDF Based B With Offset 2D		y = (d/(1.0+exp(-(x-a)/b)))^c + Offset [web citation]
Genlogistic PDF Based With Offset 2D		y = (c/b) * exp(-((x-a)/b)) / (1.0+exp(-((x-a)/b)))^(c+1.0) + Offset [web citation]
Gompertz CDF Based Scaled With Offset 2D		y = Scale * (1.0 - exp(-b * (a^x-1.0) / ln(a))) + Offset [web citation]
Gompertz CDF Based With Offset 2D		y = 1.0 - exp(-b * (a^x-1.0) / ln(a)) + Offset [web citation]
Gumbel CDF Based With Offset 2D		y = a * exp(-exp(-x)) + Offset [web citation]
Gumbel PDF Based With Offset 2D		y = a * exp(-x-exp(-x)) + Offset [web citation]
Half Normal PDF Based With Offset 2D		y = c * ( 1.0/b) * exp(-0.5((x-a)/b)((x-a)/b)) + Offset [web citation]
Inverse_gaussian PDF Based A With Offset 2D		y = sqrt(b/(cx³))exp(-b(x-a)² / (2.0a²*x)) + Offset [web citation]
Inverse_gaussian PDF Based B With Offset 2D		y = sqrt(b/(cx³))exp(-b(x-a)² / (2.0a²*x)) + Offset [web citation]
Levy PDF Based Scaled With Offset 2D		y = Scale * b^0.5 * exp(-b/(2.0*(x-a)))/sqrt((x-a)³) + Offset [web citation]
Levy PDF Based With Offset 2D		y = b^0.5 * exp(-b/(2.0*(x-a)))/sqrt((x-a)³) + Offset [web citation]
Log Normal PDF Based With Offset 2D		y = exp(-0.5((ln(x)-a)/b)²) / (bx) + Offset [web citation]
Logistic PDF Based With Offset 2D		y = exp((a-x)/b) / (b*(1.0+exp((a-x)/b))²) + Offset [web citation]
Pareto PDF Based With Offset 2D		y = b * a^b / x^(b+1.0) + Offset [web citation]
Power PDF Based With Offset 2D		y = (a/b) * (x/b)^(a-1.0) + Offset [web citation]
Rayleigh CDF Based A With Offset 2D		y = 1.0 - exp(-x²/(2.0*a²)) + Offset [web citation]
Rayleigh CDF Based B With Offset 2D		y = b * exp(-x²/(2.0*a²)) + Offset [web citation]
Rayleigh PDF Based Scaled With Offset 2D		y = Scale * (x/a²) * exp(-x²/(2.0*a²)) + Offset [web citation]
Rayleigh PDF Based With Offset 2D		y = (x/a²) * exp(-x²/(2.0*a²)) + Offset [web citation]
Reciprocal CDF Based With Offset 2D		y = ln(a/x) / ln(a/b) + Offset [web citation]
Sech CDF Based With Offset 2D		y = c * atan(exp((x-a)/b)) + Offset [web citation]
Weibull CDF Based A With Offset 2D		y = 1.0 / exp(((x-a)/b)^c) + Offset [web citation]
Weibull CDF Based B With Offset 2D		y = d / exp(((x-a)/b)^c) + Offset [web citation]
Weibull PDF Based With Offset 2D		y = (c/b) * ((x-a)/b)^(c-1.0) / exp(((x-a)/b)^c) + Offset [web citation]

Dispersion Optical 2D		n²(x) = A1 + A2*x² + A3/x² + A4/x⁴
Dispersion Optical Square Root 2D		n = (A1 + A2*x² + A3/x² + A4/x⁴)^0.5
Electron Beam Lithography Point Spread 2D		y = aexp(-bx) + cexp(-(x-d)² / f²) + gexp(-(x-h)² / i²) + j*exp(-(x-k)² / l²)
Extended Steinhart-Hart 2D		1/T = A + Bln(R) + C(ln(R))² + D(ln(R))³
Graeme Paterson Electric Motor 2D		y = Aexp(-bt)cos(omegat + phi) + A2exp(-b2t)
Klimpel Kinetics Flotation A 2D		y = a * (1 - (1 - exp(-bx)) / (bx))
Maxwell - Wiechert 1 2D		y = a1*exp(-X/Tau1) [web citation]
Maxwell - Wiechert 2 2D		y = a1exp(-X/Tau1) + a2exp(-X/Tau2) [web citation]
Maxwell - Wiechert 3 2D		y = a1exp(-X/Tau1) + a2exp(-X/Tau2) + a3*exp(-X/Tau3) [web citation]
Maxwell - Wiechert 4 2D		y = a1exp(-X/Tau1) + a2exp(-X/Tau2) + a3exp(-X/Tau3) + a4exp(-X/Tau4) [web citation]
Ramberg-Osgood 2D		y = (Stress / Youngs_Modulus) + (Stress/K)^(1.0/n)
Reciprocal Extended Steinhart-Hart 2D		T = 1.0 / (A + Bln(R) + C(ln(R))² + D(ln(R))³)
Reciprocal Steinhart-Hart 2D		T = 1.0 / (A + Bln(R) + C(ln(R))³)
Sellmeier Optical 2D		n²(x) = 1 + (B1 x²)/(x²-C1) + (B2 x²)/(x²-C2) + (B3 x²)/(x²-C3)
Sellmeier Optical Square Root 2D		n = (1 + (B1 x²)/(x²-C1) + (B2 x²)/(x²-C2) + (B3 x²)/(x²-C3))^0.5
Steinhart-Hart 2D		1/T = A + Bln(R) + C(ln(R))³
VanDeemter Chromatography 2D		y = a + b/x + cx



Electron Beam Lithography Point Spread With Offset 2D		y = aexp(-bx) + cexp(-(x-d)² / f²) + gexp(-(x-h)² / i²) + j*exp(-(x-k)² / l²) + Offset
Graeme Paterson Electric Motor With Offset 2D		y = Aexp(-bt)cos(omegat + phi) + A2exp(-b2t) + Offset
Klimpel Kinetics Flotation A With Offset 2D		y = a * (1 - (1 - exp(-bx)) / (bx)) + Offset
Maxwell - Wiechert 1 With Offset 2D		y = a1*exp(-X/Tau1) + Offset [web citation]
Maxwell - Wiechert 2 With Offset 2D		y = a1exp(-X/Tau1) + a2exp(-X/Tau2) + Offset [web citation]
Maxwell - Wiechert 3 With Offset 2D		y = a1exp(-X/Tau1) + a2exp(-X/Tau2) + a3*exp(-X/Tau3) + Offset [web citation]
Maxwell - Wiechert 4 With Offset 2D		y = a1exp(-X/Tau1) + a2exp(-X/Tau2) + a3exp(-X/Tau3) + a4exp(-X/Tau4) + Offset [web citation]
Ramberg-Osgood With Offset 2D		y = (Stress / Youngs_Modulus) + (Stress/K)^(1.0/n) + Offset
Reciprocal Extended Steinhart-Hart With Offset 2D		T = 1.0 / (A + Bln(R) + C(ln(R))² + D(ln(R))³) + Offset
Reciprocal Steinhart-Hart With Offset 2D		T = 1.0 / (A + Bln(R) + C(ln(R))³) + Offset
Sellmeier Optical Square Root With Offset 2D		n = (1 + (B1 x²)/(x²-C1) + (B2 x²)/(x²-C2) + (B3 x²)/(x²-C3))^0.5 + Offset
Sellmeier Optical With Offset 2D		n²(x) = 1 + (B1 x²)/(x²-C1) + (B2 x²)/(x²-C2) + (B3 x²)/(x²-C3) + Offset

Asymptotic Exponential A 2D		y = 1.0 - a^x
Asymptotic Exponential A Transform 2D		y = 1.0 - a^{bx + c}
Asymptotic Exponential B 2D		y = a * (1.0 - exp(bx))
Bruno Torremans Quadruple Exponential 2D		y = Offset - R1 * exp(-x/T1) + R2 * exp(-x/T2) + R3 * exp(-x/T3) + R4 * exp(-x/T4)
Double Asymptotic Exponential B 2D		y = a * (1.0 - exp(bx)) + c * (1.0 - exp(dx))
Double Exponential 2D		y = a * exp(bx) + c * exp(dx)
Exponential 2D		y = a * exp(bx)
Hocket-Sherby 2D		y = b - (b-a) * exp(-c * (x^d))
Hoerl 2D		y = x^a * exp(x)
Hoerl Transform 2D		y = (bx + c)^a * exp(bx + c)
Inverted Exponential 2D		y = a * exp(b/x)
Inverted Offset Exponential 2D		y = a * exp(b/(x+c))
Jonathan Litz Custom Exponential 2D		y = a + b * x + c * exp(-d * x) - c * x * exp(-d * x) [web citation]
Offset Exponential 2D		y = a * exp(bx + c)
Scaled Exponential 2D		y = a * exp(x)
Shifted Exponential 2D		y = a * exp(x + b)
Simple Exponential 2D		y = a^x
Standard Vapor Pressure 2D		y = exp(a + (b/x) + c*ln(x))
Steve Battison Exponential A 2D		y = exp((a + bx) / (c + dx))
Steve Battison Exponential B 2D		y = a * exp((b + cx) / (d + fx))
Stirling 2D		y = a * (exp(bx) - 1.0) / b
Triple Exponential 2D		y = a * exp(bx) + c * exp(dx) + f * exp(gx)



Asymptotic Exponential A Transform With Offset 2D		y = 1.0 - a^{bx + c} + Offset
Asymptotic Exponential A With Offset 2D		y = 1.0 - a^x + Offset
Asymptotic Exponential B With Offset 2D		y = a * (1.0 - exp(bx)) + Offset
Double Asymptotic Exponential B With Offset 2D		y = a * (1.0 - exp(bx)) + c * (1.0 - exp(dx)) + Offset
Double Exponential With Offset 2D		y = a * exp(bx) + c * exp(dx) + Offset
Exponential With Offset 2D		y = a * exp(bx) + Offset
Hoerl Transform With Offset 2D		y = (bx + c)^a * exp(bx + c) + Offset
Hoerl With Offset 2D		y = x^a * exp(x) + Offset
Inverted Exponential With Offset 2D		y = a * exp(b/x) + Offset
Inverted Offset Exponential With Offset 2D		y = a * exp(b/(x+c)) + Offset
Offset Exponential With Offset 2D		y = a * exp(bx + c) + Offset
Scaled Exponential With Offset 2D		y = a * exp(x) + Offset
Shifted Exponential With Offset 2D		y = a * exp(x + b) + Offset
Simple Exponential With Offset 2D		y = a^x + Offset
Standard Vapor Pressure With Offset 2D		y = exp(a + (b/x) + c*ln(x)) + Offset
Steve Battison Exponential A With Offset 2D		y = exp((a + bx) / (c + dx)) + Offset
Steve Battison Exponential B With Offset 2D		y = a * exp((b + cx) / (d + fx)) + Offset
Stirling With Offset 2D		y = a * (exp(bx) - 1.0) / b + Offset
Triple Exponential With Offset 2D		y = a * exp(bx) + c * exp(dx) + f * exp(gx) + Offset

1 Term (Scaled X) 2D		y = a0 + a1sin(c1x)+b1cos(c1x) [web citation]
1 Term Standard 2D		y = a0 + a1sin(x)+b1cos(x) [web citation]
2 Term Standard 2D		y = a0 + a1sin(x)+b1cos(x) + a2sin(2x)+b2cos(2x) [web citation]
3 Term Standard 2D		y = a0 + a1sin(x)+b1cos(x) + a2sin(2x)+b2cos(2x) + a3sin(3x)+b3cos(3x) [web citation]
4 Term Standard 2D		y = a0 + a1sin(x)+b1cos(x) + a2sin(2x)+b2cos(2x) + a3sin(3x)+b3cos(3x) + a4sin(4x)+b4cos(4x) [web citation]

Gamma Ray Angular Distribution (degrees) A 2D		y = A0 + A2 * P₂(cos(theta))
Gamma Ray Angular Distribution (degrees) B 2D		y = A0 + A2 * P₂(cos(theta)) + A4 * P₄(cos(theta))
Gamma Ray Angular Distribution (radians) A 2D		y = A0 + A2 * P₂(cos(theta))
Gamma Ray Angular Distribution (radians) B 2D		y = A0 + A2 * P₂(cos(theta)) + A4 * P₄(cos(theta))
Legendre Polynomial A - Second Degree 2D		y = a + bx + cP₂ [web citation]
Legendre Polynomial B - Third Degree 2D		y = a + bx + cP₂ + dP₃ [web citation]
Legendre Polynomial C - Fourth Degree 2D		y = a + bx + cP₂ + dP₃ + fP₄ [web citation]
Legendre Polynomial D - Fifth Degree 2D		y = a + bx + cP₂ + dP₃ + fP₄ + gP₅ [web citation]
Legendre Polynomial E - Sixth Degree 2D		y = a + bx + cP₂ + dP₃ + fP₄ + gP₅ + hP₆ [web citation]
Legendre Polynomial F - Seventh Degree 2D		y = a + bx + cP₂ + dP₃ + fP₄ + gP₅ + hP₆ + iP₇ [web citation]
Legendre Polynomial G - Eighth Degree 2D		y = a + bx + cP₂ + dP₃ + fP₄ + gP₅ + hP₆ + iP₇ + jP₈ [web citation]
Legendre Polynomial H - Ninth Degree 2D		y = a + bx + cP₂ + dP₃ + fP₄ + gP₅ + hP₆ + iP₇ + jP₈ + kP₉ [web citation]
Legendre Polynomial I - Tenth Degree 2D		y = a + bx + cP₂ + dP₃ + fP₄ + gP₅ + hP₆ + iP₇ + jP₈ + kP₉ + mP₁₀ [web citation]

Base 10 Logarithmic 2D		y = a + b*log₁₀(x)
Bradley 2D		y = a * ln(-b * ln(x))
Bradley Transform 2D		y = a * ln(-b * ln(cx + d))
Crystal Resonator Ageing MIL-PRF-55310E 2D		y = A(ln(Bt + 1)) + f0
Cubic Logarithmic 2D		y = a + bln(x) + cln(x)² + d*ln(x)³
Cubic Logarithmic Scaled 2D		y = a + bln(fx) + cln(fx)² + dln(fx)³
Cubic Logarithmic Transform 2D		y = a + bln(fx+g) + cln(fx+g)² + dln(fx+g)³
Linear Logarithmic 2D		y = a + b*ln(x)
Linear Logarithmic Scaled 2D		y = a + b*ln(cx)
Linear Logarithmic Transform 2D		y = a + b*ln(cx+d)
Quadratic Logarithmic 2D		y = a + bln(x) + cln(x)²
Quadratic Logarithmic Scaled 2D		y = a + bln(dx) + cln(dx)²
Quadratic Logarithmic Transform 2D		y = a + bln(dx+f) + cln(dx+f)²
Quartic Logarithmic 2D		y = a + bln(x) + cln(x)² + dln(x)³ + fln(x)⁴
Quartic Logarithmic Scaled 2D		y = a + bln(hx) + cln(hx)² + dln(hx)³ + fln(hx)⁴
Quartic Logarithmic Transform 2D		y = a + bln(gx+h) + cln(gx+h)² + dln(gx+h)³ + fln(gx+h)⁴
Quintic Logarithmic 2D		y = a + bln(x) + cln(x)² + dln(x)³ + fln(x)⁴ + g*ln(x)⁵
Quintic Logarithmic Scaled 2D		y = a + bln(hx) + cln(hx)² + dln(hx)³ + fln(hx)⁴ + gln(hx)⁴
Quintic Logarithmic Transform 2D		y = a + bln(hx+i) + cln(hx+i)² + dln(hx+i)³ + fln(hx+i)⁴ + gln(hx+i)⁵



Bradley Transform With Offset 2D		y = a * ln(-b * ln(cx + d)) + Offset
Bradley With Offset 2D		y = a * ln(-b * ln(x)) + Offset

Arrhenius Rate Constant Law 2D		y = a * exp(-b/x)
Arrhenius Rate Constant Law Stretched 2D		y = a * exp(-pow(b/x, c))
Bleasdale-Nelder 2D		y = (a + bx)^-1/c
Bleasdale-Nelder Power 2D		y = (a + bx^c)^-1/d
Catenary 2D		y = a * cosh(x / a) [web citation]
Catenary Transform 2D		y = a * cosh((bx + c) / a) [web citation]
Cissoid Of Diocles 2D		y = a(x³ / (2b-x))^0.5 [web citation]
Cissoid Of Diocles Transform 2D		y = a((xc-d)³ / (2b-(xc-d)))^0.5 [web citation]
Combined Power And Exponential 2D		y = ax^b * exp(cx)
David Rodbard NIH 2D		y = d + (a - d) / (1.0 + (x/c)^b) [web citation]
Double Langmuir Probe Characteristic 2D		y = a * tanh(bx+c)
Double Rectangular Hyperbola A 2D		y = ax/(b+x) + cx/(d+x)
Double Rectangular Hyperbola B 2D		y = ax/(b+x) + cx/(d+x) + fx
Figure Eight Curve 2D		y = a(x² - (x⁴/b²))^0.5 [web citation]
Figure Eight Curve Transform 2D		y = a((cx+d)² - ((cx+d)⁴/b²))^0.5 [web citation]
Gunary 2D		y = x / (a + bx + cx^0.5)
Hyperbola A Modified 2D		y = ax/(1+bx)
Hyperbola B Modified 2D		y = x/(a+bx)
Hyperbolic Decay 2D		y = ab/(b+x)
Karplus NMR Spectroscopy 2D		J(da) = Acos²(da) + Bcos(da) + C [web citation]
Karplus NMR Spectroscopy Scaled 2D		J(da) = Acos²(s * da) + Bcos(s * da) + C [web citation]
Lame's Cubic 2D		y = (a³ - x³)^1/3 [web citation]
Lame's Cubic Transform 2D		y = (a³ - (bx + c)³)^1/3 [web citation]
Miscellaneous 1 2D		y = 1.0 + a(1.0 - exp(bx))
Morse Potential 2D		V = D(exp(-2m(x-u)) - 2exp(-m*(x-u))) + offset [web citation]
Nelson-Siegel 2D		y(m) = B0 + B1((1-exp(-m/t))/(m/t)) + B2(((1-exp(-m/t))/(m/t)) - exp(-m/t))) [web citation]
Nelson-Siegel-Svensson 2D		y(m) = B0 + B1((1-exp(-m/t))/(m/t)) + B2(((1-exp(-m/t))/(m/t)) - exp(-m/t)) + B3*(((1-exp(-m/t2))/(m/t2)) - exp(-m/t2)) [web citation]
Niele's Semi-cubical Parabola 2D		y = (ax²)^1.0/3.0 [web citation]
Niele's Semi-cubical Parabola Transform 2D		y = (a(b*x+c)²)^1.0/3.0 [web citation]
Pareto A 2D		y = 1 - x^-a
Pareto B 2D		y = a(1 - x^-b)
Pareto C 2D		y = 1.0 - (1.0 / (1 + ax)^b
Pareto D 2D		y = 1.0 - (1.0 / x^a)
Pear-shaped Quartic 2D		y = a(x³(b-x) / c²)^0.5 [web citation]
Pear-shaped Quartic Transform 2D		y = a((dx+f)³(b-(dx+f)) / c²)^0.5 [web citation]
Physicist Peter's Custom Equation 2D		y = A + B(X-C) + 0.5G(X-C)*2
Physicist Peter's Pendulum Traversal 2D		y = a*(x + b)^1/2
Polytrope 2D		y = a / x^b [web citation]
Polytrope Transform 2D		y = a / (cx + d)^b [web citation]
Pursuit Curve 2D		y = ax² - log(x)
Pursuit Curve Transform 2D		y = a(bx + c)² - log(bx + c)
Rectangular Hyperbola A 2D		y = ax/(b+x)
Rectangular Hyperbola B 2D		y = ax/(b+x) + cx
Serpentine 2D		y = ax / (1.0 + bx²)
Shifted Reciprocal 2D		y = 1.0 / (a - x)
Square Modified 2D		y = x² - ax
Square Modified Transform 2D		y = (bx + c)² - a(bx + c)
Timothy Strobel's Custom Equation 2D		y = (A-BXC)(1-(0.5+(arctan((X-D)/E))/pi))+(F-GXH)(0.5+(arctan((X-D)/E))/pi) [web citation]
Transition State Rate Constant Law 2D		y = ax^b * exp(-c/x)
Trisectrix Of Maclaurin 2D		y = a(x²(3b-x) / (b+x))^0.5 [web citation]
Trisectrix Of Maclaurin Transform 2D		y = a((cx+d)²(3b-(cx+d)) / (b+(cx+d)))^0.5 [web citation]
Witch Of Maria Agnesi A 2D		y = 8a³ / (x² + 4a²)
Witch Of Maria Agnesi B 2D		y = a³ / (x² + a²)
Witch Of Maria Agnesi C 2D		y = a³ / ((x * b + c)² + a²)



Arrhenius Rate Constant Law Stretched With Offset 2D		y = a * exp(-pow(b/x, c)) + Offset
Arrhenius Rate Constant Law With Offset 2D		y = a * exp(-b/x) + Offset
Bleasdale-Nelder Power With Offset 2D		y = (a + bx^c)^-1/d + Offset
Bleasdale-Nelder With Offset 2D		y = (a + bx)^-1/c + Offset
Catenary Transform With Offset 2D		y = a * cosh((bx + c) / a) + Offset [web citation]
Catenary With Offset 2D		y = a * cosh(x / a) + Offset [web citation]
Cissoid Of Diocles Transform With Offset 2D		y = a((xc-d)³ / (2b-(xc-d)))^0.5 + Offset [web citation]
Cissoid Of Diocles With Offset 2D		y = a(x³ / (2b-x))^0.5 + Offset [web citation]
Combined Power And Exponential With Offset 2D		y = ax^b * exp(cx) + Offset
Double Langmuir Probe Characteristic With Offset 2D		y = a * tanh(bx+c) + Offset
Double Rectangular Hyperbola A With Offset 2D		y = ax/(b+x) + cx/(d+x) + Offset
Double Rectangular Hyperbola B With Offset 2D		y = ax/(b+x) + cx/(d+x) + fx + Offset
Figure Eight Curve Transform With Offset 2D		y = a((cx+d)² - ((cx+d)⁴/b²))^0.5 + Offset [web citation]
Figure Eight Curve With Offset 2D		y = a(x² - (x⁴/b²))^0.5 + Offset [web citation]
Gunary With Offset 2D		y = x / (a + bx + cx^0.5) + Offset
Hyperbola A Modified With Offset 2D		y = ax/(1+bx) + Offset
Hyperbola B Modified With Offset 2D		y = x/(a+bx) + Offset
Hyperbolic Decay With Offset 2D		y = ab/(b+x) + Offset
Lame's Cubic Transform With Offset 2D		y = (a³ - (bx + c)³)^1/3 + Offset [web citation]
Lame's Cubic With Offset 2D		y = (a³ - x³)^1/3 + Offset [web citation]
Miscellaneous 1 With Offset 2D		y = 1.0 + a(1.0 - exp(bx)) + Offset
Niele's Semi-cubical Parabola Transform With Offset 2D		y = (a(b*x+c)²)^1.0/3.0 + Offset [web citation]
Niele's Semi-cubical Parabola With Offset 2D		y = (ax²)^1.0/3.0 + Offset [web citation]
Pareto A With Offset 2D		y = 1 - x^-a + Offset
Pareto B With Offset 2D		y = a(1 - x^-b) + Offset
Pareto C With Offset 2D		y = 1.0 - (1.0 / (1 + ax)^b + Offset
Pareto D With Offset 2D		y = 1.0 - (1.0 / x^a) + Offset
Pear-shaped Quartic Transform With Offset 2D		y = a((dx+f)³(b-(dx+f)) / c²)^0.5 + Offset [web citation]
Pear-shaped Quartic With Offset 2D		y = a(x³(b-x) / c²)^0.5 + Offset [web citation]
Physicist Peter's Pendulum Traversal With Offset 2D		y = a*(x + b)^1/2 + Offset
Polytrope Transform With Offset 2D		y = a / (cx + d)^b + Offset [web citation]
Polytrope With Offset 2D		y = a / x^b + Offset [web citation]
Pursuit Curve Transform With Offset 2D		y = a(bx + c)² - log(bx + c) + Offset
Pursuit Curve With Offset 2D		y = ax² - log(x) + Offset
Rectangular Hyperbola A With Offset 2D		y = ax/(b+x) + Offset
Rectangular Hyperbola B With Offset 2D		y = ax/(b+x) + cx + Offset
Serpentine With Offset 2D		y = ax / (1.0 + bx²) + Offset
Shifted Reciprocal With Offset 2D		y = 1.0 / (a - x) + Offset
Square Modified Transform With Offset 2D		y = (bx + c)² - a(bx + c) + Offset
Square Modified With Offset 2D		y = x² - ax + Offset
Timothy Strobel's Custom Equation With Offset 2D		y = (A-BXC)(1-(0.5+(arctan((X-D)/E))/pi))+(F-GXH)(0.5+(arctan((X-D)/E))/pi) + Offset [web citation]
Transition State Rate Constant Law With Offset 2D		y = ax^b * exp(-c/x) + Offset
Trisectrix Of Maclaurin Transform With Offset 2D		y = a((cx+d)²(3b-(cx+d)) / (b+(cx+d)))^0.5 + Offset [web citation]
Trisectrix Of Maclaurin With Offset 2D		y = a(x²(3b-x) / (b+x))^0.5 + Offset [web citation]
Witch Of Maria Agnesi A With Offset 2D		y = 8a³ / (x² + 4a²) + Offset
Witch Of Maria Agnesi B With Offset 2D		y = a³ / (x² + a²) + Offset
Witch Of Maria Agnesi C With Offset 2D		y = a³ / ((x * b + c)² + a²) + Offset

NIST Bennett5 2D		y = a * (b+x)^-1/c [web citation]
NIST BoxBOD 2D		y = a * (1.0-exp(-b*x)) [web citation]
NIST Chwirut 2D		y = exp(-ax) / (b + cx) [web citation]
NIST DanWood 2D		y = a*x^b [web citation]
NIST ENSO 2D		y = a + bcos(2pix/12) + csin(2pix/12) + fcos(2pix/d) + gsin(2pix/d) + icos(2pix/h) + jsin(2pix/h) [web citation]
NIST Eckerle4 2D		y = (a/b) * exp(-0.5*((x-c)/b)²) [web citation]
NIST Gauss 2D		y = aexp(-bx) + cexp(-(x-d)² / f²) + gexp(-(x-h)² / i²) [web citation]
NIST Hahn 2D		y = (a + bx + cx² + dx³) / (1.0 + fx + gx² + hx³) [web citation]
NIST Kirby 2D		y = (a + bx + cx²) / (1.0 + dx + fx²) [web citation]
NIST Lanczos 2D		y = aexp(-bx) + cexp(-dx) + fexp(-gx) [web citation]
NIST MGH09 2D		y = a * (x² + bx) / (x² + cx + d) [web citation]
NIST MGH10 2D		y = a * exp(b/(x+c)) [web citation]
NIST MGH17 2D		y = a + bexp(-xd) + cexp(-xf) [web citation]
NIST Misra1a 2D		y = a * (1.0 - exp(-b*x)) [web citation]
NIST Misra1b 2D		y = a * (1.0 - (1.0+b*x/2.0)^-2.0) [web citation]
NIST Misra1c 2D		y = a * (1.0 - (1.0 + 2.0bx)^-0.5) [web citation]
NIST Misra1d 2D		y = a * b * x * (1.0 + b*x)^-1.0 [web citation]
NIST Rat42 2D		y = a / (1.0 + exp(b - c*x)) [web citation]
NIST Rat43 2D		y = a / ((1.0 + exp(b - c*x))^(1.0/d)) [web citation]
NIST Roszman 2D		y = a - bx - (arctan(c/(x-d)) / pi) [web citation]
NIST Thurber 2D		y = (a + bx + cx² + dx³) / (1.0 + fx + gx² + hx³) [web citation]



NIST Bennett5 With Offset 2D		y = a * (b+x)^-1/c + Offset [web citation]
NIST BoxBOD With Offset 2D		y = a * (1.0-exp(-b*x)) + Offset [web citation]
NIST Chwirut With Offset 2D		y = exp(-ax) / (b + cx) + Offset [web citation]
NIST DanWood With Offset 2D		y = a*x^b + Offset [web citation]
NIST Eckerle4 With Offset 2D		y = (a/b) * exp(-0.5*((x-c)/b)²) + Offset [web citation]
NIST Gauss With Offset 2D		y = aexp(-bx) + cexp(-(x-d)² / f²) + gexp(-(x-h)² / i²) + Offset [web citation]
NIST Hahn With Offset 2D		y = (a + bx + cx² + dx³) / (1.0 + fx + gx² + hx³) + Offset [web citation]
NIST Kirby With Offset 2D		y = (a + bx + cx²) / (1.0 + dx + fx²) + Offset [web citation]
NIST Lanczos With Offset 2D		y = aexp(-bx) + cexp(-dx) + fexp(-gx) + Offset [web citation]
NIST MGH09 With Offset 2D		y = a * (x² + bx) / (x² + cx + d) + Offset [web citation]
NIST MGH10 With Offset 2D		y = a * exp(b/(x+c)) + Offset [web citation]
NIST Misra1a With Offset 2D		y = a * (1.0 - exp(-b*x)) + Offset [web citation]
NIST Misra1b With Offset 2D		y = a * (1.0 - (1.0+b*x/2.0)^-2.0) + Offset [web citation]
NIST Misra1c With Offset 2D		y = a * (1.0 - (1.0 + 2.0bx)^-0.5) + Offset [web citation]
NIST Misra1d With Offset 2D		y = a * b * x * (1.0 + b*x)^-1.0 + Offset [web citation]
NIST Rat42 With Offset 2D		y = a / (1.0 + exp(b - c*x)) + Offset [web citation]
NIST Rat43 With Offset 2D		y = a / ((1.0 + exp(b - c*x))^(1.0/d)) + Offset [web citation]
NIST Thurber With Offset 2D		y = (a + bx + cx² + dx³) / (1.0 + fx + gx² + hx³) + Offset [web citation]

CAUCHY 2D		n = A + B/x² + C/x⁴ [web citation]
CONRADY1 2D		n = A + B/x + C/x^3.5 [web citation]
CONRADY2 2D		n = A + B/x² + C/x^3.5 [web citation]
HARTMANN1 2D		n = A + B/(C - x) [web citation]
HARTMANN2 2D		n = A + B/(C - x)² [web citation]
HARTMANN3a 2D		n = A + B/(C - x)^1.2 [web citation]
HARTMANN3b 2D		n = A/(x - B)^1.2 [web citation]
HARTMANN4 2D		n = A + B/(C - x) + D/(E - x) [web citation]
HERZBRGR2X2 2D		n = A + Bx² + C / (x² - 0.028) + D / (x² - 0.028)² [web citation]
HERZBRGR3X2 2D		n = A + Bx² + Cx⁴ + D / (x² - 0.028) + E / (x² - 0.028)² [web citation]
HERZBRGR3X3 2D		n = A + Bx² + Cx⁴ + D / (x² - 0.028) + E / (x² - 0.028)² + F / (x² - 0.028)⁴ [web citation]
HERZBRGR4X2 2D		n = A + Bx² + Cx⁴ + Dx⁶ + E / (x² - 0.028) + F / (x² - 0.028)² [web citation]
HERZBRGR5X2 2D		n = A + Bx² + Cx⁴ + Dx⁶ + Ex⁸ + F / (x² - 0.028) + G / (x² - 0.028)² [web citation]
HERZBRGRJK 2D		n = A + Bx² + Cx⁴ + Dx⁶ + E / (x² - J) + F / (x² - K)² [web citation]
HoO1 2D		n² = A + Bx² + C / (x² - D²) [web citation]
HoO2 2D		n² = A + Bx² + Cx² / (x² - D²) [web citation]
KINGSLAKE1 2D		n² = A + B/(x²-C²) + D/(x²-E²) [web citation]
KINGSLAKE2 2D		n² = A + B/(x²-C²) + D/(x²-E²) + F/(x²-G²) [web citation]
MISC01 2D		n² = A + B/(x²-C²) [web citation]
MISC02 2D		n² = A + Bx² + C/(x²-D²) [web citation]
MISC03 2D		n² = A + B/x² + Cx²/(x²-D²) [web citation]
MISC04 2D		n² = A + Bx² + Cx⁴ + D/x² + Ex²/(x²-F+(Gx²/(x²-F))) [web citation]
SCHOTT2X3 2D		n² = A + Bx² + C/x² + D/x⁴ + E/x⁶ [web citation]
SCHOTT2X4 2D		n² = A + Bx² + C/x² + D/x⁴ + E/x⁶ + F/x⁸ [web citation]
SCHOTT2X5 2D		n² = A + Bx² + C/x² + D/x⁴ + E/x⁶ + F/x⁸ + G/x¹⁰ [web citation]
SCHOTT2X6 2D		n² = A + Bx² + C/x² + D/x⁴ + E/x⁶ + F/x⁸ + G/x¹⁰ + H/x¹² [web citation]
SCHOTT3X3 2D		n² = A + Bx² + Cx⁴ + D/x² + E/x⁴ + F/x⁶ [web citation]
SCHOTT3X4 2D		n² = A + Bx² + Cx⁴ + D/x² + E/x⁴ + F/x⁶ + G/x⁸ [web citation]
SCHOTT3X5 2D		n² = A + Bx² + Cx⁴ + D/x² + E/x⁴ + F/x⁶ + G/x⁸ + H/x¹⁰ [web citation]
SCHOTT4X4 2D		n² = A + Bx² + Cx⁴ + Dx⁶ + E/x² + F/x⁴ + G/x⁶ + H/x⁸ [web citation]
SCHOTT5X5 2D		n² = A + Bx² + Cx⁴ + Dx⁶ + Ex⁸ + F/x² + G/x⁴ + H/x⁶ + J/x⁸ + K/x¹⁰ [web citation]
SELL1T 2D		n² = 1 + Ax² / (x² - B²) [web citation]
SELL1TA 2D		n² = A + Bx² / (x² - C²) [web citation]
SELL2T 2D		n² = 1 + Ax²/(x²-B²) + Cx²/(x²-D²) [web citation]
SELL2TA 2D		n² = A + Bx²/(x²-C²) + Dx²/(x²-E²) [web citation]
SELL3T 2D		n² = 1 + Ax²/(x²-B²) + Cx²/(x²-D²) + Ex²/(x²-F²) [web citation]
SELL3TA 2D		n² = A + Bx²/(x²-C²) + Dx²/(x²-E²) + Fx²/(x²-G²) [web citation]
SELL4T 2D		n² = 1 + Ax²/(x²-B²) + Cx²/(x²-D²) + Ex²/(x²-F²) + Gx²/(x²-H²) [web citation]
SELL4TA 2D		n² = A + Bx²/(x²-C²) + Dx²/(x²-E²) + Fx²/(x²-G²) + Hx²/(x²-J²) [web citation]
SELL5T 2D		n² = 1 + Ax²/(x²-B²) + Cx²/(x²-D²) + Ex²/(x²-F²) + Gx²/(x²-H²) + Jx²/(x²-K²) [web citation]
SELL5TA 2D		n² = A + Bx²/(x²-C²) + Dx²/(x²-E²) + Fx²/(x²-G²) + Hx²/(x²-J²) + Kx²/(x²-M²) [web citation]
SELL6TA 2D		n² = A + Bx²/(x²-C²) + Dx²/(x²-E²) + Fx²/(x²-G²) + Hx²/(x²-J²) + Kx²/(x²-M²) + Nx²/(x²-P²) [web citation]
SELL7TA 2D		n² = A + Bx²/(x²-C²) + Dx²/(x²-E²) + Fx²/(x²-G²) + Hx²/(x²-J²) + Kx²/(x²-M²) + Nx²/(x²-P²) + Qx²/(x²-R²) [web citation]
SELLMOD1 2D		n² = A + Bx + Cx² + Dx²/(x²-E²) [web citation]
SELLMOD1A 2D		n² = A + Bx + Cx² + D/(x²-E²) [web citation]
SELLMOD2 2D		n² = A + Bx + Cx⁴ + Dx²/(x²-E²) [web citation]
SELLMOD2A 2D		n² = A + Bx + Cx⁴ + D/(x²-E²) [web citation]
SELLMOD3 2D		n² = (Ax²+B)/(x²-C²) + Dx²/(x²-E²) [web citation]
SELLMOD4 2D		n² = A + Bx² + C/x² + Dx²/(x²-E²) + Fx²/(x²-G²) [web citation]
SELLMOD4A 2D		n² = A + Bx² + C/x² + D/(x²-E²) + F/(x²-G²) [web citation]
SELLMOD5 2D		n² = A + Bx² + Cx²/(x²-D²) + Ex²/(x²-F²) [web citation]
SELLMOD6 2D		n² = A + Bx²/(x²-C²) + D/(x²-E²) [web citation]
SELLMOD7 2D		n² = A + Bx² + Cx⁴ + D/x⁶ + Ex²/(x²-F²) [web citation]
SELLMOD7A 2D		n² = A + Bx² + Cx⁴ + D/x⁶ + E/(x²-F²) [web citation]
SELLMOD8 2D		n² = A + Bx² + Cx⁴ + D/(x²-E²) + F/(x²-G²) [web citation]
SELLMOD9 2D		n² = A + B/x² + C/x⁴ + D/x⁶ + Ex²/(x²-F²) [web citation]



HARTMANN3b With Offset 2D		n = A/(x - B)^1.2 + Offset [web citation]
SELLMOD3 With Offset 2D		n² = (Ax²+B)/(x²-C²) + Dx²/(x²-E²) + Offset [web citation]

Arnold Cohen Log-Normal Peak Shifted 2D		y = a * (exp(-0.5 * ((ln(x-f)-b)/c)²)) / (d * (x-g))
Arnold Cohen Two-Parameter Log-Normal Peak Shifted 2D		y = exp(-0.5 * ((ln(x-d)-b)/c)²) / (sqrt(2pi) c * (x-f))
Box Lucas A 2D		y = a * (1.0 - b^x)
Box Lucas A Shifted 2D		y = a * (1.0 - b^x-c)
Box Lucas B 2D		y = a * (1.0 - exp(-bx))
Box Lucas B Shifted 2D		y = a * (1.0 - exp(-b(x-c)))
Box Lucas C 2D		y = (a / (a-b)) * (exp(-bx) - exp(-ax))
Box Lucas C shifted 2D		y = (a / (a-b)) * (exp(-b(x-c)) - exp(-a(x-c)))
Extreme Value 4 Parameter Peak 2D		y = a * exp(-x + b + c - cdexp(-1.0 * ((x + cln(d) - b) / c)) / (cd))
Extreme Value Area 2D		y = (a/c) * exp(-exp(-((x-b)/c))-((x-b)/c))
Extreme Value Peak 2D		y = a * exp(-exp(-((x-b)/c))-((x-b)/c)+1.0)
Gaussian Area 2D		y = (a / (pow(2pi, 0.5) c)) * exp(-0.5 * ((x-b)/c)²)
Gaussian Peak 2D		y = a * exp(-0.5 * ((x-b)/c)²)
Gaussian Peak Modified 2D		y = a * exp(-0.5 * ((x-b)/c)^d)
Hamilton 2D		Vb = Gb * (I/mu)^{ln(mu/I)/(BB)} + (Vb_max I)/(I + sigma_b)
Laplace Area 2D		y = (a / (pow(2.0, 0.5) * c)) * exp((-1.0 * pow(2.0, 0.5) * abs(x-b))/c)
Laplace Peak 2D		y = a * exp((-1.0 * pow(2.0, 0.5) * abs(x-b))/c)
Log-Normal 4 Parameter 2D		y = a * exp(-1.0 * (ln(2) * ln((((x-b) * (d²-1)) / (c*d)) + 1.0)²) / ln(d)²)
Log-Normal Peak A 2D		y = a * exp(-0.5 * ((ln(x)-b)/c)²)
Log-Normal Peak A Modified 2D		y = a * exp(-0.5 * ((ln(x)-b)/c)^d)
Log-Normal Peak A Modified Shifted 2D		y = a * exp(-0.5 * ((ln(x-f)-b)/c)^d)
Log-Normal Peak A Shifted 2D		y = a * exp(-0.5 * ((ln(x-d)-b)/c)²)
Log-Normal Peak B 2D		y = a * exp(-0.5 * (ln(x/b)/c)²)
Log-Normal Peak B Modified 2D		y = a * exp(-0.5 * (ln(x/b)/c)^d)
Log-Normal Peak B Modified Shifted 2D		y = a * exp(-0.5 * (ln((x-f)/b)/c)^d)
Log-Normal Peak B Shifted 2D		y = a * exp(-0.5 * (ln((x-d/b))/c)²)
Logistic Area 2D		y = a * exp(-1.0 * (x-b) / c) / (c * (1.0 + exp(-1.0 * (x-b) / c))²)
Logistic Peak 2D		y = 4a * exp(-1.0 * (x-b) / c) / (1.0 + exp(-1.0 * (x-b) / c))²
Lorentzian Modified Peak A 2D		y = 1.0 / (1.0 + (x-a)^b)
Lorentzian Modified Peak B 2D		y = 1.0 / (a + (x-b)^c)
Lorentzian Modified Peak C 2D		y = a / (b + (x-c)^d)
Lorentzian Modified Peak D 2D		y = 1.0 / (1.0 + ((x-a)/b)^c)
Lorentzian Modified Peak E 2D		y = 1.0 / (a + ((x-b)/c)^d)
Lorentzian Modified Peak F 2D		y = a / (b + ((x-c)/d)^f)
Lorentzian Modified Peak G 2D		y = a / (1.0 + ((x-b)/c)^d)
Lorentzian Peak A 2D		y = 1.0 / (1.0 + (x-a)²)
Lorentzian Peak B 2D		y = 1.0 / (a + (x-b)²)
Lorentzian Peak C 2D		y = a / (b + (x-c)²)
Lorentzian Peak D 2D		y = 1.0 / (1.0 + ((x-a)/b)²)
Lorentzian Peak E 2D		y = 1.0 / (a + ((x-b)/c)²)
Lorentzian Peak F 2D		y = a / (b + ((x-c)/d)²)
Lorentzian Peak G 2D		y = a / (1.0 + ((x-b)/c)²)
Pseudo-Voight Peak 2D		y = a * (d * (1/(1+((x-b)/c)²)) + (1-d) * exp(-0.5 * ((x-b)/c)²))
Pseudo-Voight Peak Modified 2D		y = a * (d * (1/(1+((x-b)/c)^f)) + (1-d) * exp(-0.5 * ((x-b)/c)^g))
Pulse Peak 2D		y = 4a * exp(-(x-b)/c) * (1.0 - exp(-(x-b)/c))
UVED Fruit Growth Rate 2D		y = ((t/5)^(a-1)(1-t/5)^(b-1))/(((a-1)/(a+b-2))^(a-1)((b-1)/(a+b-2))^(b-1)) [web citation]
UVED Fruit Growth Rate B 2D		y = c * ((t/5)^(a-1)(1-t/5)^(b-1))/(((a-1)/(a+b-2))^(a-1)((b-1)/(a+b-2))^(b-1)) [web citation]
UVED Fruit Growth Rate Scaled 2D		y = ((ct)^(a-1)(1-(ct)^(b-1))/(((a-1)/(a+b-2))^(a-1)((b-1)/(a+b-2))^(b-1)) [web citation]
UVED Fruit Growth Rate Scaled B 2D		y = d * ((ct)^(a-1)(1-(ct)^(b-1))/(((a-1)/(a+b-2))^(a-1)((b-1)/(a+b-2))^(b-1)) [web citation]
UVED Fruit Growth Rate Transform 2D		y = ((ct+d)^(a-1)(1-(ct+d)^(b-1))/(((a-1)/(a+b-2))^(a-1)((b-1)/(a+b-2))^(b-1)) [web citation]
UVED Fruit Growth Rate Transform B 2D		y = f * ((ct+d)^(a-1)(1-(ct+d)^(b-1))/(((a-1)/(a+b-2))^(a-1)((b-1)/(a+b-2))^(b-1)) [web citation]
Weibull Peak 2D		y = a * exp(-0.5 * (ln(x/b)/c)²)
Weibull Peak Modified 2D		y = a * exp(-0.5 * (ln(x/b)/c)^d)
Weibull Peak Modified Shifted 2D		y = a * exp(-0.5 * (ln((x-f)/b)/c)^d)
Weibull Peak Shifted 2D		y = a * exp(-0.5 * (ln((x-d)/b)/c)²)



Arnold Cohen Log-Normal Peak Shifted With Offset 2D		y = a * (exp(-0.5 * ((ln(x-f)-b)/c)²)) / (d * (x-g)) + Offset
Arnold Cohen Two-Parameter Log-Normal Peak Shifted With Offset 2D		y = exp(-0.5 * ((ln(x-d)-b)/c)²) / (sqrt(2pi) c * (x-f)) + Offset
Box Lucas A Shifted With Offset 2D		y = a * (1.0 - b^x-c) + Offset
Box Lucas A With Offset 2D		y = a * (1.0 - b^x) + Offset
Box Lucas B Shifted With Offset 2D		y = a * (1.0 - exp(-b(x-c))) + Offset
Box Lucas B With Offset 2D		y = a * (1.0 - exp(-bx)) + Offset
Box Lucas C With Offset 2D		y = (a / (a-b)) * (exp(-bx) - exp(-ax)) + Offset
Box Lucas C shifted With Offset 2D		y = (a / (a-b)) * (exp(-b(x-c)) - exp(-a(x-c))) + Offset
Extreme Value 4 Parameter Peak With Offset 2D		y = a * exp(-x + b + c - cdexp(-1.0 * ((x + cln(d) - b) / c)) / (cd)) + Offset
Extreme Value Area With Offset 2D		y = (a/c) * exp(-exp(-((x-b)/c))-((x-b)/c)) + Offset
Extreme Value Peak With Offset 2D		y = a * exp(-exp(-((x-b)/c))-((x-b)/c)+1.0) + Offset
Gaussian Area With Offset 2D		y = (a / (pow(2pi, 0.5) c)) * exp(-0.5 * ((x-b)/c)²) + Offset
Gaussian Peak Modified With Offset 2D		y = a * exp(-0.5 * ((x-b)/c)^d) + Offset
Gaussian Peak With Offset 2D		y = a * exp(-0.5 * ((x-b)/c)²) + Offset
Hamilton With Offset 2D		Vb = Gb * (I/mu)^{ln(mu/I)/(BB)} + (Vb_max I)/(I + sigma_b) + Offset
Laplace Area With Offset 2D		y = (a / (pow(2.0, 0.5) * c)) * exp((-1.0 * pow(2.0, 0.5) * abs(x-b))/c) + Offset
Laplace Peak With Offset 2D		y = a * exp((-1.0 * pow(2.0, 0.5) * abs(x-b))/c) + Offset
Log-Normal 4 Parameter With Offset 2D		y = a * exp(-1.0 * (ln(2) * ln((((x-b) * (d²-1)) / (c*d)) + 1.0)²) / ln(d)²) + Offset
Log-Normal Peak A Modified Shifted With Offset 2D		y = a * exp(-0.5 * ((ln(x-f)-b)/c)^d) + Offset
Log-Normal Peak A Modified With Offset 2D		y = a * exp(-0.5 * ((ln(x)-b)/c)^d) + Offset
Log-Normal Peak A Shifted With Offset 2D		y = a * exp(-0.5 * ((ln(x-d)-b)/c)²) + Offset
Log-Normal Peak A With Offset 2D		y = a * exp(-0.5 * ((ln(x)-b)/c)²) + Offset
Log-Normal Peak B Modified Shifted With Offset 2D		y = a * exp(-0.5 * (ln((x-f)/b)/c)^d) + Offset
Log-Normal Peak B Modified With Offset 2D		y = a * exp(-0.5 * (ln(x/b)/c)^d) + Offset
Log-Normal Peak B Shifted With Offset 2D		y = a * exp(-0.5 * (ln((x-d/b))/c)²) + Offset
Log-Normal Peak B With Offset 2D		y = a * exp(-0.5 * (ln(x/b)/c)²) + Offset
Logistic Area With Offset 2D		y = a * exp(-1.0 * (x-b) / c) / (c * (1.0 + exp(-1.0 * (x-b) / c))²) + Offset
Logistic Peak With Offset 2D		y = 4a * exp(-1.0 * (x-b) / c) / (1.0 + exp(-1.0 * (x-b) / c))² + Offset
Lorentzian Modified Peak A With Offset 2D		y = 1.0 / (1.0 + (x-a)^b) + Offset
Lorentzian Modified Peak B With Offset 2D		y = 1.0 / (a + (x-b)^c) + Offset
Lorentzian Modified Peak C With Offset 2D		y = a / (b + (x-c)^d) + Offset
Lorentzian Modified Peak D With Offset 2D		y = 1.0 / (1.0 + ((x-a)/b)^c) + Offset
Lorentzian Modified Peak E With Offset 2D		y = 1.0 / (a + ((x-b)/c)^d) + Offset
Lorentzian Modified Peak F With Offset 2D		y = a / (b + ((x-c)/d)^f) + Offset
Lorentzian Modified Peak G With Offset 2D		y = a / (1.0 + ((x-b)/c)^d) + Offset
Lorentzian Peak A With Offset 2D		y = 1.0 / (1.0 + (x-a)²) + Offset
Lorentzian Peak B With Offset 2D		y = 1.0 / (a + (x-b)²) + Offset
Lorentzian Peak C With Offset 2D		y = a / (b + (x-c)²) + Offset
Lorentzian Peak D With Offset 2D		y = 1.0 / (1.0 + ((x-a)/b)²) + Offset
Lorentzian Peak E With Offset 2D		y = 1.0 / (a + ((x-b)/c)²) + Offset
Lorentzian Peak F With Offset 2D		y = a / (b + ((x-c)/d)²) + Offset
Lorentzian Peak G With Offset 2D		y = a / (1.0 + ((x-b)/c)²) + Offset
Pseudo-Voight Peak Modified With Offset 2D		y = a * (d * (1/(1+((x-b)/c)^f)) + (1-d) * exp(-0.5 * ((x-b)/c)^g)) + Offset
Pseudo-Voight Peak With Offset 2D		y = a * (d * (1/(1+((x-b)/c)²)) + (1-d) * exp(-0.5 * ((x-b)/c)²)) + Offset
Pulse Peak With Offset 2D		y = 4a * exp(-(x-b)/c) * (1.0 - exp(-(x-b)/c)) + Offset
UVED Fruit Growth Rate B With Offset 2D		y = c * ((t/5)^(a-1)(1-t/5)^(b-1))/(((a-1)/(a+b-2))^(a-1)((b-1)/(a+b-2))^(b-1)) + Offset [web citation]
UVED Fruit Growth Rate Scaled B With Offset 2D		y = d * ((ct)^(a-1)(1-(ct)^(b-1))/(((a-1)/(a+b-2))^(a-1)((b-1)/(a+b-2))^(b-1)) + Offset [web citation]
UVED Fruit Growth Rate Scaled With Offset 2D		y = ((ct)^(a-1)(1-(ct)^(b-1))/(((a-1)/(a+b-2))^(a-1)((b-1)/(a+b-2))^(b-1)) + Offset [web citation]
UVED Fruit Growth Rate Transform B With Offset 2D		y = f * ((ct+d)^(a-1)(1-(ct+d)^(b-1))/(((a-1)/(a+b-2))^(a-1)((b-1)/(a+b-2))^(b-1)) + Offset [web citation]
UVED Fruit Growth Rate Transform With Offset 2D		y = ((ct+d)^(a-1)(1-(ct+d)^(b-1))/(((a-1)/(a+b-2))^(a-1)((b-1)/(a+b-2))^(b-1)) + Offset [web citation]
UVED Fruit Growth Rate With Offset 2D		y = ((t/5)^(a-1)(1-t/5)^(b-1))/(((a-1)/(a+b-2))^(a-1)((b-1)/(a+b-2))^(b-1)) + Offset [web citation]
Weibull Peak Modified Shifted With Offset 2D		y = a * exp(-0.5 * (ln((x-f)/b)/c)^d) + Offset
Weibull Peak Modified With Offset 2D		y = a * exp(-0.5 * (ln(x/b)/c)^d) + Offset
Weibull Peak Shifted With Offset 2D		y = a * exp(-0.5 * (ln((x-d)/b)/c)²) + Offset
Weibull Peak With Offset 2D		y = a * exp(-0.5 * (ln(x/b)/c)²) + Offset

1st Order (Linear) 2D		y = a + bx
2nd Order (Quadratic) 2D		y = a + bx + cx²
3rd Order (Cubic) 2D		y = a + bx + cx² + dx³
4th Order (Quartic) 2D		y = a + bx + cx² + dx³ + fx⁴
5th Order (Quintic) 2D		y = a + bx + cx² + dx³ + fx⁴ + gx⁵
Marc Plante's Custom Quadratic 2D		y = (-b + (b² - 4 a (c - x))^0.5) / 2 / a
User-Customizable Polynomial 2D		y = user-customizable polynomial
User-Selectable Polynomial 2D		y = user-selectable polynomial



Marc Plante's Custom Quadratic With Offset 2D		y = (-b + (b² - 4 a (c - x))^0.5) / 2 / a + Offset

Geometric Modified 2D		y = a * x^(b/x)
Power A Modified 2D		y = a * b^x
Power A Modified Transform 2D		y = a * b^{cx + d}
Power B Modified 2D		y = a^ln(x)
Power B Modified Transform 2D		y = a^{ln(bx + c)}
Power C Modified 2D		y = (a + x)^b
Power C Modified Transform 2D		y = (a + bx)^c
Power Law With Exponential Cutoff 2D		p(k) = C * k^(-T) * exp(-k/K)
Root 2D		y = a^(1.0/x)
Simple Power 2D		y = x^a
Standard Geometric 2D		y = a * x^bx
Standard Power 2D		y = a * x^b
X Shifted Power 2D		y = a * (x-b)^c



Geometric Modified With Offset 2D		y = a * x^(b/x) + Offset
Power A Modified Transform With Offset 2D		y = a * b^{cx + d} + Offset
Power A Modified With Offset 2D		y = a * b^x + Offset
Power B Modified Transform With Offset 2D		y = a^{ln(bx + c)} + Offset
Power B Modified With Offset 2D		y = a^ln(x) + Offset
Power C Modified Transform With Offset 2D		y = (a + bx)^c + Offset
Power C Modified With Offset 2D		y = (a + x)^b + Offset
Power Law With Exponential Cutoff With Offset 2D		p(k) = C * k^(-T) * exp(-k/K) + Offset
Root With Offset 2D		y = a^(1.0/x) + Offset
Simple Power With Offset 2D		y = x^a + Offset
Standard Geometric With Offset 2D		y = a * x^bx + Offset
Standard Power With Offset 2D		y = a * x^b + Offset
X Shifted Power With Offset 2D		y = a * (x-b)^c + Offset

BET Sigmoidal A 2D		y = x / (a + bx - (a+b)x²)
BET Sigmoidal B 2D		y = abx / (1.0 + (b-2.0)x - (b-1.0)x²)
Boltzmann Sigmoid A 2D		y = (a - b) / (1.0 + exp((x-c)/d)) + b
Boltzmann Sigmoid B 2D		y = (a - b) / (1.0 + exp((x-c)/(dx))) + b
Chapman 2D		y = a * (1.0 - exp(-bx))^c
Don Levin Sigmoid 2D		y = a1 / (1.0 + exp(-(x-b1)/c1)) + a2 / (1.0 + exp(-(x-b2)/c2)) + a3 / (1.0 + exp(-(x-b3)/c3))
Five-Parameter Logistic 2D		y = d + (a-d) / (1.0 + (x/c)^b)^f
Four-Parameter Logistic 2D		y = d + (a-d) / (1.0 + (x/c)^b)
Generalised Logistic 2D		y = A + C / (1 + T * exp(-B * (x - M)))^1/T [web citation]
Gompertz A 2D		y = a * exp(-exp(b - cx))
Gompertz B 2D		y = a * exp(-exp((x-b)/c))
Gompertz C 2D		y = a * exp(b * exp(c * x))
Hill 2D		y = ax^b / (c^b + x^b)
Janoschek Growth 2D		w = a - (1.0 - exp(-b * t^c)) [web citation]
Janoschek Growth Modified 2D		w = a - (a - w0) * (1.0 - exp(-b * t^c)) [web citation]
Logistic A 2D		y = a / (1.0 + b*exp(-cx))
Logistic B 2D		y = a / (1.0 + (x/b)^c)
Lomolino 2D		y = a / (1.0 + b^ln(c/x))
Magnetic Saturation 2D		y = ax * (1.0 + b*exp(cx))
Morgan-Mercer-Flodin (MMF) 2D		y = (a * b + c * x^d) / (b + x^d)
Peters-Baskin Step-Stool: y (1) 2D		y = ln(c + exp(bdx)) / d [web citation]
Peters-Baskin Step-Stool: yI (2) 2D		yI = ln(exp(b2c1d1) + exp(b2d1x)) / d1 [web citation]
Peters-Baskin Step-Stool: yII (3) 2D		K = ln( exp(b2c1d1) + exp(b2d1x) ) yII = b1*x + K/d1 [web citation]
Peters-Baskin Step-Stool: yIII (6) 2D		K = ln( exp(b2c1d1) + exp(b2d1x) ) yII = b1x + K/d1 L = ln( exp(b2c1d1) + exp(b2c2d1) ) yIII = yII - ln( exp(d2(b1c1 + L/d1)) + exp(d2yII) ) / d2 [web citation]
Peters-Baskin Step-Stool: yIV (9) 2D		K = ln( exp(b2c1d1) + exp(b2d1x) ) yII = b1x + K/d1 L = ln( exp(b2c1d1) + exp(b2c2d1) ) yIII = yII - ln( exp(d2(b1c2 + L/d1)) + exp(d2yII) ) / d2 yII,0 = ln(exp(b2c1d1) + 1.0 ) / d1 yIII,0 = yII,0 - ln( exp(d2(b1c2 + L/d1)) + exp(d2*yII,0) ) / d2 yIV = yIII - yIII,0 [web citation]
Peters-Baskin Step-Stool: yV (10) 2D		K = ln( exp(b2c1d1) + exp(b2d1x) ) yII = b1x + K/d1 L = ln( exp(b2c1d1) + exp(b2c2d1) ) yIII = yII - ln( exp(d2(b1c2 + L/d1)) + exp(d2yII) ) / d2 yII,0 = ln(exp(b2c1d1) + 1.0 ) / d1 yIII,0 = yII,0 - ln( exp(d2(b1c2 + L/d1)) + exp(d2*yII,0) ) / d2 yIV = yIII - yIII,0 + q [web citation]
Peters-Baskin Step-Stool: yV (10) Scaled 2D		K = ln( exp(b2c1d1) + exp(b2d1x) ) yII = b1x + K/d1 L = ln( exp(b2c1d1) + exp(b2c2d1) ) yIII = yII - ln( exp(d2(b1c2 + L/d1)) + exp(d2yII) ) / d2 yII,0 = ln(exp(b2c1d1) + 1.0 ) / d1 yIII,0 = yII,0 - ln( exp(d2(b1c2 + L/d1)) + exp(d2yII,0) ) / d2 yIV = scale (yIII - yIII,0 )+ q [web citation]
Richards 2D		y = 1.0 / (a + b * e^(c*x))^d
Sigmoid A 2D		y = 1.0 / (1.0 + exp(-a(x-b)))
Sigmoid A Modified 2D		y = 1.0 / (1.0 + exp(-a(x-b)))^c
Sigmoid B 2D		y = a / (1.0 + exp(-(x-b)/c))
Sigmoid B Modified 2D		y = a / (1.0 + exp(-(x-b)/c))^d
Weibull 2D		y = a - b*exp(-cx^d)
Weibull CDF 2D		y = 1.0 - exp(-(x/b)^a)
Weibull CDF Scaled 2D		y = Scale * (1.0 - exp(-(x/b)^a))
Weibull PDF 2D		y = (a/b) * (x/b)^(a-1.0) * exp(-(x/b)^a)



BET Sigmoidal A With Offset 2D		y = x / (a + bx - (a+b)x²) + Offset
BET Sigmoidal B With Offset 2D		y = abx / (1.0 + (b-2.0)x - (b-1.0)x²) + Offset
Chapman With Offset 2D		y = a * (1.0 - exp(-bx))^c + Offset
Don Levin Sigmoid With Offset 2D		y = a1 / (1.0 + exp(-(x-b1)/c1)) + a2 / (1.0 + exp(-(x-b2)/c2)) + a3 / (1.0 + exp(-(x-b3)/c3)) + Offset
Gompertz A With Offset 2D		y = a * exp(-exp(b - cx)) + Offset
Gompertz B With Offset 2D		y = a * exp(-exp((x-b)/c)) + Offset
Gompertz C With Offset 2D		y = a * exp(b * exp(c * x)) + Offset
Hill With Offset 2D		y = ax^b / (c^b + x^b) + Offset
Logistic A With Offset 2D		y = a / (1.0 + b*exp(-cx)) + Offset
Logistic B With Offset 2D		y = a / (1.0 + (x/b)^c) + Offset
Lomolino With Offset 2D		y = a / (1.0 + b^ln(c/x)) + Offset
Magnetic Saturation With Offset 2D		y = ax * (1.0 + b*exp(cx)) + Offset
Morgan-Mercer-Flodin (MMF) With Offset 2D		y = (a * b + c * x^d) / (b + x^d) + Offset
Peters-Baskin Step-Stool: y (1) With Offset 2D		y = ln(c + exp(bdx)) / d + Offset [web citation]
Peters-Baskin Step-Stool: yI (2) With Offset 2D		yI = ln(exp(b2c1d1) + exp(b2d1x)) / d1 + Offset [web citation]
Peters-Baskin Step-Stool: yII (3) With Offset 2D		K = ln( exp(b2c1d1) + exp(b2d1x) ) yII = b1*x + K/d1 + Offset [web citation]
Peters-Baskin Step-Stool: yIII (6) With Offset 2D		K = ln( exp(b2c1d1) + exp(b2d1x) ) yII = b1x + K/d1 L = ln( exp(b2c1d1) + exp(b2c2d1) ) yIII = yII - ln( exp(d2(b1c1 + L/d1)) + exp(d2yII) ) / d2 + Offset [web citation]
Peters-Baskin Step-Stool: yIV (9) With Offset 2D		K = ln( exp(b2c1d1) + exp(b2d1x) ) yII = b1x + K/d1 L = ln( exp(b2c1d1) + exp(b2c2d1) ) yIII = yII - ln( exp(d2(b1c2 + L/d1)) + exp(d2yII) ) / d2 yII,0 = ln(exp(b2c1d1) + 1.0 ) / d1 yIII,0 = yII,0 - ln( exp(d2(b1c2 + L/d1)) + exp(d2*yII,0) ) / d2 yIV = yIII - yIII,0 + Offset [web citation]
Richards With Offset 2D		y = 1.0 / (a + b * e^(c*x))^d + Offset
Sigmoid A Modified With Offset 2D		y = 1.0 / (1.0 + exp(-a(x-b)))^c + Offset
Sigmoid A With Offset 2D		y = 1.0 / (1.0 + exp(-a(x-b))) + Offset
Sigmoid B Modified With Offset 2D		y = a / (1.0 + exp(-(x-b)/c))^d + Offset
Sigmoid B With Offset 2D		y = a / (1.0 + exp(-(x-b)/c)) + Offset
Weibull CDF Scaled With Offset 2D		y = Scale * (1.0 - exp(-(x/b)^a)) + Offset
Weibull CDF With Offset 2D		y = 1.0 - exp(-(x/b)^a) + Offset
Weibull PDF With Offset 2D		y = (a/b) * (x/b)^(a-1.0) * exp(-(x/b)^a) + Offset

Spline 2D		y = B-Spline Interpolation Curve

Spline 3D		z = B-Spline Interpolation Surface

User Defined Function 2D		y = user defined function

User Defined Function 3D		z = user defined function

Simple Equation 01 2D		y = a
Simple Equation 02 2D		y = a/pow(x,-2.0)
Simple Equation 03 2D		y = a*pow(ln(x),b)
Simple Equation 04 2D		y = a*pow(x,3.0)
Simple Equation 05 2D		y = a*pow(x,4.0)
Simple Equation 06 2D		y = x/(a+b*pow(x,2.0))
Simple Equation 07 2D		y = a * pow(b,x) * pow(x,c)
Simple Equation 08 2D		y = apow(b,1.0/x)pow(x,c)
Simple Equation 09 2D		y = a*exp(pow(x-b,2.0)/c)
Simple Equation 10 2D		y = a*exp(pow(ln(x)-b,2.0)/c)
Simple Equation 13 2D		y = apow(x/b,c)exp(x/b)
Simple Equation 14 2D		y = apow(x,b+cx)
Simple Equation 15 2D		y = a*pow(x,b+c/x)
Simple Equation 16 2D		y = apow(x,b+cln(x))
Simple Equation 17 2D		y = apow(x,bx+c*pow(x,2.0))
Simple Equation 18 2D		y = aexp(bx+c*pow(x,0.5))
Simple Equation 19 2D		y = aexp(b/x+cx)
Simple Equation 20 2D		y = (a+x)/(b+c*x)
Simple Equation 21 2D		y = (a+x)/(b+c*pow(x,2.0))
Simple Equation 22 2D		y = a(exp(bx)-exp(c*x))
Simple Equation 23 2D		y = aexp(bexp(c*x))
Simple Equation 24 2D		y = a/(1.0 + b * exp(c*x))
Simple Equation 25 2D		y = a/(b+pow(x,c))
Simple Equation 26 2D		y = a/pow(1.0 + b * pow(x,c),2.0)
Simple Equation 27 2D		y = pow(a+b*x,c)
Simple Equation 28 2D		y = exp(a+b/x+c*ln(x))
Simple Equation 29 2D		y = aexp(bpow(x,c))
Simple Equation 30 2D		y = apow(x,bpow(x,c))
Simple Equation 31 2D		y = a*ln(x+b)
Simple Equation 32 2D		y = a/x+b*pow(x,c)
Simple Equation 33 2D		y = a/x+b*exp(c/x)
Simple Equation 34 2D		y = a/x+bexp(cx)
Simple Equation 35 2D		y = aexp(bx)/x
Simple Equation 36 2D		y = a*exp(b/x)/x
Simple Equation 37 2D		y = apow(x,b)ln(x)
Simple Equation 38 2D		y = a*pow(x,b)/ln(x)
Simple Equation 39 2D		y = apow(x,b)ln(x+c)
Simple Equation 40 2D		y = a*pow(ln(x+b),c)
Simple Equation 41 2D		y = apow(x,b/x)+cx
Simple Equation 42 2D		y = apow(x,b/x)+cln(x)
Simple Reciprocal 2D		y = a / x



Simple Equation 02 With Offset 2D		y = a/pow(x,-2.0) + Offset
Simple Equation 03 With Offset 2D		y = a*pow(ln(x),b) + Offset
Simple Equation 04 With Offset 2D		y = a*pow(x,3.0) + Offset
Simple Equation 05 With Offset 2D		y = a*pow(x,4.0) + Offset
Simple Equation 06 With Offset 2D		y = x/(a+b*pow(x,2.0)) + Offset
Simple Equation 07 With Offset 2D		y = a * pow(b,x) * pow(x,c) + Offset
Simple Equation 08 With Offset 2D		y = apow(b,1.0/x)pow(x,c) + Offset
Simple Equation 09 With Offset 2D		y = a*exp(pow(x-b,2.0)/c) + Offset
Simple Equation 10 With Offset 2D		y = a*exp(pow(ln(x)-b,2.0)/c) + Offset
Simple Equation 13 With Offset 2D		y = apow(x/b,c)exp(x/b) + Offset
Simple Equation 14 With Offset 2D		y = apow(x,b+cx) + Offset
Simple Equation 15 With Offset 2D		y = a*pow(x,b+c/x) + Offset
Simple Equation 16 With Offset 2D		y = apow(x,b+cln(x)) + Offset
Simple Equation 17 With Offset 2D		y = apow(x,bx+c*pow(x,2.0)) + Offset
Simple Equation 18 With Offset 2D		y = aexp(bx+c*pow(x,0.5)) + Offset
Simple Equation 19 With Offset 2D		y = aexp(b/x+cx) + Offset
Simple Equation 20 With Offset 2D		y = (a+x)/(b+c*x) + Offset
Simple Equation 21 With Offset 2D		y = (a+x)/(b+c*pow(x,2.0)) + Offset
Simple Equation 22 With Offset 2D		y = a(exp(bx)-exp(c*x)) + Offset
Simple Equation 23 With Offset 2D		y = aexp(bexp(c*x)) + Offset
Simple Equation 24 With Offset 2D		y = a/(1.0 + b * exp(c*x)) + Offset
Simple Equation 25 With Offset 2D		y = a/(b+pow(x,c)) + Offset
Simple Equation 26 With Offset 2D		y = a/pow(1.0 + b * pow(x,c),2.0) + Offset
Simple Equation 27 With Offset 2D		y = pow(a+b*x,c) + Offset
Simple Equation 28 With Offset 2D		y = exp(a+b/x+c*ln(x)) + Offset
Simple Equation 29 With Offset 2D		y = aexp(bpow(x,c)) + Offset
Simple Equation 30 With Offset 2D		y = apow(x,bpow(x,c)) + Offset
Simple Equation 31 With Offset 2D		y = a*ln(x+b) + Offset
Simple Equation 32 With Offset 2D		y = a/x+b*pow(x,c) + Offset
Simple Equation 33 With Offset 2D		y = a/x+b*exp(c/x) + Offset
Simple Equation 34 With Offset 2D		y = a/x+bexp(cx) + Offset
Simple Equation 35 With Offset 2D		y = aexp(bx)/x + Offset
Simple Equation 36 With Offset 2D		y = a*exp(b/x)/x + Offset
Simple Equation 37 With Offset 2D		y = apow(x,b)ln(x) + Offset
Simple Equation 38 With Offset 2D		y = a*pow(x,b)/ln(x) + Offset
Simple Equation 39 With Offset 2D		y = apow(x,b)ln(x+c) + Offset
Simple Equation 40 With Offset 2D		y = a*pow(ln(x+b),c) + Offset
Simple Equation 41 With Offset 2D		y = apow(x,b/x)+cx + Offset
Simple Equation 42 With Offset 2D		y = apow(x,b/x)+cln(x) + Offset
Simple Reciprocal With Offset 2D		y = a / x + Offset

Cardinal Sine (sinc) Squared [radians] 2D		y = amplitude * sin(pi * (x - center) / width)² / (pi * (x - center) / width)
Cardinal Sine (sinc) [radians] 2D		y = amplitude * sin(pi * (x - center) / width) / (pi * (x - center) / width)
Great Circle [Degrees] 2D		latitude = arctan(Acos((B + longitude) / 57.2957795131)) 57.2957795131
Great Circle [radians] 2D		latitude = arctan(A*cos(B + longitude))
Hyperbolic Cosine [radians] 2D		y = amplitude * cosh(pi * (x - center) / width)
Sine Squared [radians] 2D		y = amplitude * sin(pi * (x - center) / width)²
Sine [radians] 2D		y = amplitude * sin(pi * (x - center) / width)
Tangent [radians] 2D		y = amplitude * tan(pi * (x - center) / width)



Cardinal Sine (sinc) Squared [radians] With Offset 2D		y = amplitude * sin(pi * (x - center) / width)² / (pi * (x - center) / width) + Offset
Cardinal Sine (sinc) [radians] With Offset 2D		y = amplitude * sin(pi * (x - center) / width) / (pi * (x - center) / width) + Offset
Hyperbolic Cosine [radians] With Offset 2D		y = amplitude * cosh(pi * (x - center) / width) + Offset
Sine Squared [radians] With Offset 2D		y = amplitude * sin(pi * (x - center) / width)² + Offset
Sine [radians] With Offset 2D		y = amplitude * sin(pi * (x - center) / width) + Offset
Tangent [radians] With Offset 2D		y = amplitude * tan(pi * (x - center) / width) + Offset

Bleasdale 2D		y = 1.0 / (a + bx)^(-1.0/c)
Extended Holliday 2D		y = a / (a + bx + cx²)
Harris 2D		y = 1.0 / (a + bx^c)
Holliday 2D		y = 1.0 / (a + bx + cx²)
Inverse Bleasdale 2D		y = x / (a + bx)^(-1.0/c)
InverseHarris 2D		y = x / (a + bx^c)
Nelder 2D		y = (a + x) / (b + c(a + x) + d(a + x)²



Bleasdale With Offset 2D		y = 1.0 / (a + bx)^(-1.0/c) + Offset
Extended Holliday With Offset 2D		y = a / (a + bx + cx²) + Offset
Harris With Offset 2D		y = 1.0 / (a + bx^c) + Offset
Holliday With Offset 2D		y = 1.0 / (a + bx + cx²) + Offset
Inverse Bleasdale With Offset 2D		y = x / (a + bx)^(-1.0/c) + Offset
InverseHarris With Offset 2D		y = x / (a + bx^c) + Offset
Nelder With Offset 2D		y = (a + x) / (b + c(a + x) + d(a + x)² + Offset

Chen-Clayton 3D		r.h.(T_k,M) = exp(-(C1/T^C2) * exp(-C3T^C4M)) [web citation]
Chen-Clayton Scaled 3D		z = Scale * exp(-(C1/T^C2) * exp(-C3T^C4M)) [web citation]
High-Low Affinity Double Isotope Displacement (y = [Hot]) 3D		z = aby / (1+b(x+y)) + cdy / (1+d(x+y))
High-Low Affinity Isotope Displacement (y = [Hot]) 3D		z = aby / (1+b(x+y))
Logistic Growth 3D		z = a / (1 + exp(-(b + cx + dy + fxy))) + g
Michaelis-Menten Double Isotope Displacement (y = [Hot]) 3D		z = ay / (b + x + y) + cy / (d + x + y)
Michaelis-Menten Isotope Displacement (y = [Hot]) 3D		z = ay / (b + x + y)
Modified Chung-Pfost 3D		r.h.(T,M) = exp(-(C1/(T+C2)) * exp(-C3*M)) [web citation]
Modified Halsey 3D		r.h.(T,M) = exp(-exp(C1 + C2T) M^-C3) [web citation]
Modified Halsey Scaled 3D		z = Scale * exp(-exp(C1 + C2T) M^-C3) [web citation]
Modified Henderson 3D		r.h.(T,M) = 1 - exp(-C1 * (T + C2) * M^C3) [web citation]
Strohman-Yoerger 3D		r.h.(P_s,M) = exp(C1exp(-C2M)ln(P_s) - C3exp(-C4*M)) [web citation]



Chen-Clayton Scaled With Offset 3D		z = Scale * exp(-(C1/T^C2) * exp(-C3T^C4M)) + Offset [web citation]
Chen-Clayton With Offset 3D		r.h.(T_k,M) = exp(-(C1/T^C2) * exp(-C3T^C4M)) + Offset [web citation]
High-Low Affinity Double Isotope Displacement (y = [Hot]) With Offset 3D		z = aby / (1+b(x+y)) + cdy / (1+d(x+y)) + Offset
High-Low Affinity Isotope Displacement (y = [Hot]) With Offset 3D		z = aby / (1+b(x+y)) + Offset
Michaelis-Menten Double Isotope Displacement (y = [Hot]) With Offset 3D		z = ay / (b + x + y) + cy / (d + x + y) + Offset
Michaelis-Menten Isotope Displacement (y = [Hot]) With Offset 3D		z = ay / (b + x + y) + Offset
Modified Chung-Pfost With Offset 3D		r.h.(T,M) = exp(-(C1/(T+C2)) * exp(-C3*M)) + Offset [web citation]
Modified Halsey Scaled With Offset 3D		z = Scale * exp(-exp(C1 + C2T) M^-C3) + Offset [web citation]
Modified Halsey With Offset 3D		r.h.(T,M) = exp(-exp(C1 + C2T) M^-C3) + Offset [web citation]
Modified Henderson With Offset 3D		r.h.(T,M) = 1 - exp(-C1 * (T + C2) * M^C3) + Offset [web citation]
Strohman-Yoerger With Offset 3D		r.h.(P_s,M) = exp(C1exp(-C2M)ln(P_s) - C3exp(-C4*M)) + Offset [web citation]

Competitive Inhibition A 3D		z = ax / (b(1 + y/c) + x)
Competitive Inhibition B 3D		z = ay / (b(1 + x/c) + y)
Competitive Inhibition C 3D		z = axy / (b(1 + x/c) + y)
Inhibition By Competing Substrate A 3D		z = (ax/b) / (1 + x/b + y/c)
Inhibition By Competing Substrate B 3D		z = (ay/b) / (1 + y/b + x/c)
Inhibition By Competing Substrate C 3D		z = (axy/b) / (1 + y/b + x/c)
Michaelis Menten Product Inhibition 3D		z = (ax/b - cy/d) / (1 + x/b + y/d)
Mixed Inhibition A 3D		z = ax / (b(1 + y/c) + x(1 + y/d))
Mixed Inhibition B 3D		z = ay / (b(1 + x/c) + y(1 + x/d))
Noncompetitive Inhibition A 3D		z = ax / ((b + x)(1 + y/c))
Noncompetitive Inhibition B 3D		z = ay / ((b + y)(1 + x/c))
Ping Pong Bi Bi A 3D		z = ax / (bx + cy + xy)
Ping Pong Bi Bi B 3D		z = ay / (by + cx + xy)
Ping Pong Bi Bi C 3D		z = axy / (by + cx + xy)
Uncompetitive Inhibition A 3D		z = ax / (b + x(1 + y/c))
Uncompetitive Inhibition B 3D		z = ay / (b + y(1 + x/c))



Competitive Inhibition A With Offset 3D		z = ax / (b(1 + y/c) + x) + Offset
Competitive Inhibition B With Offset 3D		z = ay / (b(1 + x/c) + y) + Offset
Competitive Inhibition C With Offset 3D		z = axy / (b(1 + x/c) + y) + Offset
Inhibition By Competing Substrate A With Offset 3D		z = (ax/b) / (1 + x/b + y/c) + Offset
Inhibition By Competing Substrate B With Offset 3D		z = (ay/b) / (1 + y/b + x/c) + Offset
Inhibition By Competing Substrate C With Offset 3D		z = (axy/b) / (1 + y/b + x/c) + Offset
Michaelis Menten Product Inhibition With Offset 3D		z = (ax/b - cy/d) / (1 + x/b + y/d) + Offset
Mixed Inhibition A With Offset 3D		z = ax / (b(1 + y/c) + x(1 + y/d)) + Offset
Mixed Inhibition B With Offset 3D		z = ay / (b(1 + x/c) + y(1 + x/d)) + Offset
Noncompetitive Inhibition A With Offset 3D		z = ax / ((b + x)(1 + y/c)) + Offset
Noncompetitive Inhibition B With Offset 3D		z = ay / ((b + y)(1 + x/c)) + Offset
Ping Pong Bi Bi A With Offset 3D		z = ax / (bx + cy + xy) + Offset
Ping Pong Bi Bi B With Offset 3D		z = ay / (by + cx + xy) + Offset
Ping Pong Bi Bi C With Offset 3D		z = axy / (by + cx + xy) + Offset
Uncompetitive Inhibition A With Offset 3D		z = ax / (b + x(1 + y/c)) + Offset
Uncompetitive Inhibition B With Offset 3D		z = ay / (b + y(1 + x/c)) + Offset

Full Cubic Exponential 3D		z = a + bexp(x) + cexp(y) + dexp(x)² + fexp(y)² + gexp(x)³ + hexp(y)³ + iexp(x)exp(y) + jexp(x)²exp(y) + kexp(x)exp(y)²
Full Quadratic Exponential 3D		z = a + bexp(x) + cexp(y) + dexp(x)² + fexp(y)² + gexp(x)exp(y)
Linear Exponential 3D		z = a + bexp(x) + cexp(y)
Simplified Cubic Exponential 3D		z = a + bexp(x) + cexp(y) + dexp(x)² + eexp(y)² + fexp(x)³ + gexp(y)³
Simplified Quadratic Exponential 3D		z = a + bexp(x) + cexp(y) + dexp(x)² + fexp(y)²
Transform Full Cubic Exponential 3D		z = a + bexp(mx+n) + cexp(oy+p) + dexp(mx+n)² + fexp(oy+p)² + gexp(mx+n)³ + hexp(oy+p)³ + iexp(mx+n)exp(oy+p) + jexp(mx+n)²exp(oy+p) + kexp(mx+n)exp(oy+p)²
Transform Full Quadratic Exponential 3D		z = a + bexp(hx+i) + cexp(jy+k) + dexp(hx+i)² + eexp(jy+k)² + fexp(hx+i)exp(jy+k)
Transform Linear Exponential 3D		z = a + bexp(dx+f) + cexp(gy+h)
Transform Simplified Cubic Exponential 3D		z = a + bexp(ix+j) + cexp(ky+m) + dexp(ix+j)² + fexp(ky+m)² + gexp(ix+j)³ + hexp(ky+m)³
Transform Simplified Quadratic Exponential 3D		z = a + bexp(gx+h) + cexp(iy+j) + dexp(gx+h)² + fexp(iy+j)²

Full Cubic Logarithmic 3D		z = a + bln(x) + cln(y) + dln(x)² + fln(y)² + gln(x)³ + hln(y)³ + iln(x)ln(y) + jln(x)²ln(y) + kln(x)ln(y)²
Full Quadratic Logarithmic 3D		z = a + bln(x) + cln(y) + dln(x)² + fln(y)² + gln(x)ln(y)
Linear Logarithmic 3D		z = a + bln(x) + cln(y)
Simplified Cubic Logarithmic 3D		z = a + bln(x) + cln(y) + dln(x)² + fln(y)² + gln(x)³ + hln(y)³
Simplified Quadratic Logarithmic 3D		z = a + bln(x) + cln(y) + dln(x)² + fln(y)²
Transform Full Cubic Logarithmic 3D		z = a + bln(mx+n) + cln(oy+p) + dln(mx+n)² + fln(oy+p)² + gln(mx+n)³ + hln(oy+p)³ + iln(mx+n)ln(oy+p) + jln(mx+n)²ln(oy+p) + kln(mx+n)ln(oy+p)²
Transform Full Quadratic Logarithmic 3D		z = a + bln(hx+i) + cln(jy+k) + dln(hx+i)² + fln(jy+k)² + gln(hx+i)ln(jy+k)
Transform Linear Logarithmic 3D		z = a + bln(dx+f) + cln(gy+h)
Transform Simplified Cubic Logarithmic 3D		z = a + bln(ix+j) + cln(ky+m) + dln(ix+j)² + fln(ky+m)² + gln(ix+j)³ + hln(ky+m)³
Transform Simplified Quadratic Logarithmic 3D		z = a + bln(gx+h) + cln(iy+j) + dln(gx+h)² + fln(iy+j)²

Gary Cler's Custom Equation Transform 3D		z = a * (dx + f)^b * (gy + h)^c
Gaussian Curvature Of Paraboloid 3D		z = 4a² / (1 + 4a² * (x² + y²))²
Gaussian Curvature Of Paraboloid Scaled 3D		z = Scale * 4a² / (1 + 4a² * (x² + y²))²
Gaussian Curvature Of Richmond's Minimal Surface 3D		z = -1.0 * a * (x² + y²)³ / (b + (x² + y²)²)⁴
Gaussian Curvature Of Whitney's Umbrella A 3D		z = -1.0 * a * y² / (x² + a * (y² + y⁴))²
Gaussian Curvature Of Whitney's Umbrella B 3D		z = -1.0 * a * x² / (y² + a * (x² + x⁴))²
Liping Zheng's core loss coefficients 3D		z = ax²y + bx²y² + cx^1.5y^1.5
Mean Curvature Of Paraboloid 3D		z = 2 * (a + 2a³ * (x² + y²)) / (1 + 4a² * (x² + y²))^1.5
Mean Curvature Of Paraboloid Scaled 3D		z = Scale * (a + 2a³ * (x² + y²)) / (1 + 4a² * (x² + y²))^1.5
Mean Curvature Of Whitney's Umbrella A 3D		z = -1.0 * x * (a + b * y²) / (x² + a * (y² + y⁴))^1.5
Mean Curvature Of Whitney's Umbrella B 3D		z = -1.0 * y * (a + b * x²) / (y² + a * (x² + x⁴))^1.5
Menn's Surface A 3D		z = ax⁴ + bx²y - cy²
Menn's Surface B 3D		z = ay⁴ + by²x - cx²
Monkey Saddle A 3D		z = ax³ - bxy²
Monkey Saddle B 3D		z = ay³ - byx²
Monkey Saddle Transform A 3D		z = a(cx + d)³ - b(cx + d)(fy + g)²
Monkey Saddle Transform B 3D		z = a(cy + d)³ - b(cy + d)(fx + g)²
Paraboloid 3D		z = a * (x² + y²)
Paraboloid Transform 3D		z = a * ((bx + c)² + (dy + f)²)
Paschen's Law for Breakdown Field Strength 3D		Ebreakdown = pressure * (a / (ln(pressure * distance) + b))
Paschen's Law for Breakdown Voltage 3D		Vbreakdown = a(pressure * distance) / (ln(pressure * distance) + b)
Rex Kelfkens' Custom Equation 3D		z = exp(A+Bln(x)+Cln(y))
Rex Kelfkens' Custom Equation Transform 3D		z = exp(A+Bln(x xscale + xoffset)+Cln(y yscale + yoffset))



Gary Cler's Custom Equation Transform With Offset 3D		z = a * (dx + f)^b * (gy + h)^c + Offset
Gaussian Curvature Of Paraboloid Scaled With Offset 3D		z = Scale * 4a² / (1 + 4a² * (x² + y²))² + Offset
Gaussian Curvature Of Paraboloid With Offset 3D		z = 4a² / (1 + 4a² * (x² + y²))² + Offset
Gaussian Curvature Of Richmond's Minimal Surface With Offset 3D		z = -1.0 * a * (x² + y²)³ / (b + (x² + y²)²)⁴ + Offset
Gaussian Curvature Of Whitney's Umbrella A With Offset 3D		z = -1.0 * a * y² / (x² + a * (y² + y⁴))² + Offset
Gaussian Curvature Of Whitney's Umbrella B With Offset 3D		z = -1.0 * a * x² / (y² + a * (x² + x⁴))² + Offset
Liping Zheng's core loss coefficients With Offset 3D		z = ax²y + bx²y² + cx^1.5y^1.5 + Offset
Mean Curvature Of Paraboloid Scaled With Offset 3D		z = Scale * (a + 2a³ * (x² + y²)) / (1 + 4a² * (x² + y²))^1.5 + Offset
Mean Curvature Of Paraboloid With Offset 3D		z = 2 * (a + 2a³ * (x² + y²)) / (1 + 4a² * (x² + y²))^1.5 + Offset
Mean Curvature Of Whitney's Umbrella A With Offset 3D		z = -1.0 * x * (a + b * y²) / (x² + a * (y² + y⁴))^1.5 + Offset
Mean Curvature Of Whitney's Umbrella B With Offset 3D		z = -1.0 * y * (a + b * x²) / (y² + a * (x² + x⁴))^1.5 + Offset
Menn's Surface A With Offset 3D		z = ax⁴ + bx²y - cy² + Offset
Menn's Surface B With Offset 3D		z = ay⁴ + by²x - cx² + Offset
Monkey Saddle A With Offset 3D		z = ax³ - bxy² + Offset
Monkey Saddle B With Offset 3D		z = ay³ - byx² + Offset
Monkey Saddle Transform A With Offset 3D		z = a(cx + d)³ - b(cx + d)(fy + g)² + Offset
Monkey Saddle Transform B With Offset 3D		z = a(cy + d)³ - b(cy + d)(fx + g)² + Offset
Paraboloid Transform With Offset 3D		z = a * ((bx + c)² + (dy + f)²) + Offset
Paraboloid With Offset 3D		z = a * (x² + y²) + Offset
Paschen's Law for Breakdown Field Strength With Offset 3D		Ebreakdown = pressure * (a / (ln(pressure * distance) + b)) + Offset
Paschen's Law for Breakdown Voltage With Offset 3D		Vbreakdown = a(pressure * distance) / (ln(pressure * distance) + b) + Offset
Rex Kelfkens' Custom Equation Transform With Offset 3D		z = exp(A+Bln(x xscale + xoffset)+Cln(y yscale + yoffset)) + Offset
Rex Kelfkens' Custom Equation With Offset 3D		z = exp(A+Bln(x)+Cln(y)) + Offset

NIST Nelson 3D		log(y) = b1 - b2 * X1 * exp(-b3*X2) [web citation]
NIST Nelson Autolog 3D		z = exp(b1 - b2 * x * exp(-b3*y)) [web citation]



NIST Nelson Autolog With Offset 3D		z = exp(b1 - b2 * x * exp(-b3*y)) + Offset [web citation]

Sag For Asphere 0 3D		s² = x² + y² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) [web citation]
Sag For Asphere 0 Borisovsky 3D		s² = (x - a)² + (y - b)² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + offset
Sag For Asphere 0 Scaled 3D		s² = x² + y² z = Scale * (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) [web citation]
Sag For Asphere 1 3D		s² = x² + y² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4*s⁴ [web citation]
Sag For Asphere 2 3D		s² = x² + y² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4s⁴ + A6s⁶ [web citation]
Sag For Asphere 3 3D		s² = x² + y² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4s⁴ + A6s⁶ + A8*s⁸ [web citation]
Transform Sag For Asphere 0 3D		s² = (ax+b)² + (cy+d)² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) [web citation]
Transform Sag For Asphere 1 3D		s² = (ax+b)² + (cy+d)² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4*s⁴ [web citation]
Transform Sag For Asphere 2 3D		s² = (ax+b)² + (cy+d)² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4s⁴ + A6s⁶ [web citation]
Transform Sag For Asphere 3 3D		s² = (ax+b)² + (cy+d)² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4s⁴ + A6s⁶ + A8*s⁸ [web citation]



Sag For Asphere 0 Borisovsky With Offset 3D		s² = (x - a)² + (y - b)² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + offset + Offset
Sag For Asphere 0 Scaled With Offset 3D		s² = x² + y² z = Scale * (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + Offset [web citation]
Sag For Asphere 0 With Offset 3D		s² = x² + y² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + Offset [web citation]
Sag For Asphere 1 With Offset 3D		s² = x² + y² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4*s⁴ + Offset [web citation]
Sag For Asphere 2 With Offset 3D		s² = x² + y² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4s⁴ + A6s⁶ + Offset [web citation]
Sag For Asphere 3 With Offset 3D		s² = x² + y² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4s⁴ + A6s⁶ + A8*s⁸ + Offset [web citation]
Transform Sag For Asphere 0 With Offset 3D		s² = (ax+b)² + (cy+d)² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + Offset [web citation]
Transform Sag For Asphere 1 With Offset 3D		s² = (ax+b)² + (cy+d)² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4*s⁴ + Offset [web citation]
Transform Sag For Asphere 2 With Offset 3D		s² = (ax+b)² + (cy+d)² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4s⁴ + A6s⁶ + Offset [web citation]
Transform Sag For Asphere 3 With Offset 3D		s² = (ax+b)² + (cy+d)² z = (s²/r) / (1+(1-(k+1)(s/r)²)^1/2) + A4s⁴ + A6s⁶ + A8*s⁸ + Offset [web citation]

Extreme Value A 3D		z = a * exp(-exp(-(x-b)/c)-(x-b)/c+1) + d * exp(-exp(-(y-f)/g)-(y-f)/g+1)
Extreme Value B 3D		z = a * exp(-exp(-(x-b)/c)-(x-b)/c+1) * exp(-exp(-(y-d)/f)-(y-d)/f+1)
Gaussian A 3D		z = a * exp(-0.5 * (((x-b)/c)² + ((y-d)/f)²))
Gaussian B 3D		z = a * exp(-0.5 * (((x-b)/c)²)) + d * exp(-0.5 * (((y-f)/g)²))
Log-Normal A 3D		z = a * exp(-0.5 * (((ln(x)-b)/c)² + ((ln(y)-d)/f)²))
Log-Normal B 3D		z = a * exp(-0.5 * (((ln(x)-b)/c)²)) + d * exp(-0.5 * (((ln(y)-f)/g)²))
Logistic A 3D		z = 4a * exp(-((x-b)/c))/((1+exp(-((x-b)/c)))²) + 4d * exp(-((y-f)/g))/((1+exp(-((y-f)/g)))²)
Logistic B 3D		z = 16a * exp(-((x-b)/c)-((y-d)/f)) / ((1+exp(-((x-b)/c)))² * (1+exp(-((y-d)/f)))²)
Lorentzian A 3D		z = a / ((1+((x-b)/c)²)*(1+((y-d)/f)²))
Lorentzian B 3D		z = a / (1+((x-b)/c)²) + d * (1+((y-f)/g)²)



Extreme Value A With Offset 3D		z = a * exp(-exp(-(x-b)/c)-(x-b)/c+1) + d * exp(-exp(-(y-f)/g)-(y-f)/g+1) + Offset
Extreme Value B With Offset 3D		z = a * exp(-exp(-(x-b)/c)-(x-b)/c+1) * exp(-exp(-(y-d)/f)-(y-d)/f+1) + Offset
Gaussian A With Offset 3D		z = a * exp(-0.5 * (((x-b)/c)² + ((y-d)/f)²)) + Offset
Gaussian B With Offset 3D		z = a * exp(-0.5 * (((x-b)/c)²)) + d * exp(-0.5 * (((y-f)/g)²)) + Offset
Log-Normal A With Offset 3D		z = a * exp(-0.5 * (((ln(x)-b)/c)² + ((ln(y)-d)/f)²)) + Offset
Log-Normal B With Offset 3D		z = a * exp(-0.5 * (((ln(x)-b)/c)²)) + d * exp(-0.5 * (((ln(y)-f)/g)²)) + Offset
Logistic A With Offset 3D		z = 4a * exp(-((x-b)/c))/((1+exp(-((x-b)/c)))²) + 4d * exp(-((y-f)/g))/((1+exp(-((y-f)/g)))²) + Offset
Logistic B With Offset 3D		z = 16a * exp(-((x-b)/c)-((y-d)/f)) / ((1+exp(-((x-b)/c)))² * (1+exp(-((y-d)/f)))²) + Offset
Lorentzian A With Offset 3D		z = a / ((1+((x-b)/c)²)*(1+((y-d)/f)²)) + Offset
Lorentzian B With Offset 3D		z = a / (1+((x-b)/c)²) + d * (1+((y-f)/g)²) + Offset

Full Cubic 3D		z = a + bx + cy + dx² + fy² + gx³ + hy³ + ixy + jx²y + kxy²
Full Quadratic 3D		z = a + bx + cy + dx² + fy² + gxy
Linear 3D		z = a + bx + cy
Simplified Cubic 3D		z = a + bx + cy + dx² + fy² + gx³ + hy³
Simplified Quadratic 3D		z = a + bx + cy + dx² + fy²
User-Selectable Polynomial 3D		z = user-selectable polynomial

Power A 3D		z = a * (x^b + y^c)
Power B 3D		z = a + x^b + y^c
Power C 3D		z = a + x^b * y^c
Power D 3D		z = ax^b + cy^d
Power E 3D		z = a * x^b * y^c
Transform Power A 3D		z = a * ((dx + f)^b + (gy + h)^c)
Transform Power B 3D		z = a + (dx + f)^b + (gy + h)^c
Transform Power C 3D		z = a + (dx + f)^b * (gy + h)^c
Transform Power D 3D		z = a(fx + g)^b + c(hy + i)^d
Transform Power E 3D		z = a * (dx + f)^b * (gy + h)^c



Power A With Offset 3D		z = a * (x^b + y^c) + Offset
Power D With Offset 3D		z = ax^b + cy^d + Offset
Power E With Offset 3D		z = a * x^b * y^c + Offset
Transform Power A With Offset 3D		z = a * ((dx + f)^b + (gy + h)^c) + Offset
Transform Power D With Offset 3D		z = a(fx + g)^b + c(hy + i)^d + Offset
Transform Power E With Offset 3D		z = a * (dx + f)^b * (gy + h)^c + Offset

Rational A 3D		z = (a + bx + cy)/(1 + dx + fy)
Rational B 3D		z = (a + bln(x) + cln(y))/(1 + dx + fy)
Rational C 3D		z = (a + bexp(x) + cln(y))/(1 + dx + fy)
Rational D 3D		z = (a + bln(x) + cexp(y))/(1 + dx + fy)
Rational E 3D		z = (a + bexp(x) + cexp(y))/(1 + dx + fy)
Rational F 3D		z = (a + bx + cy)/(1 + dln(x) + fln(y))
Rational G 3D		z = (a + bx + cy)/(1 + dexp(x) + fln(y))
Rational H 3D		z = (a + bx + cy)/(1 + dln(x) + fexp(y))
Rational I 3D		z = (a + bx + cy)/(1 + dexp(x) + fexp(y))
Rational J 3D		z = (a + bln(x) + cln(y))/(1 + dln(x) + fln(y))
Rational K 3D		z = (a + bexp(x) + cln(y))/(1 + dexp(x) + fln(y))
Rational L 3D		z = (a + bln(x) + cexp(y))/(1 + dln(x) + fexp(y))
Rational M 3D		z = (a + bexp(x) + cexp(y))/(1 + dexp(x) + fexp(y))
Rational N 3D		z = (a + bx + cy + dxy)/(1 + fx + gy + hxy)
Rational O 3D		z = (a + bln(x) + cln(y) + d*ln(x)ln(y))/(1 + fx + gy + hxy)
Rational P 3D		z = (a + bexp(x) + cln(y) + d*exp(x)ln(y))/(1 + fx + gy + hxy)
Rational Q 3D		z = (a + bln(x) + cexp(y) + d*ln(x)exp(y))/(1 + fx + gy + hxy)
Rational R 3D		z = (a + bexp(x) + cexp(y) + d*exp(x)exp(y))/(1 + fx + gy + hxy)
Rational S 3D		z = (a + bx + cy + dxy)/(1 + fln(x) + gln(y) + hln(x)ln(y))
Rational T 3D		z = (a + bx + cy + dxy)/(1 + fexp(x) + gln(y) + hexp(x)ln(y))
Rational U 3D		z = (a + bx + cy + dxy)/(1 + fln(x) + gexp(y) + hln(x)exp(y))
Rational V 3D		z = (a + bx + cy + dxy)/(1 + fexp(x) + gexp(y) + hexp(x)exp(y))
Rational W 3D		z = (a + bln(x) + cln(y) + dln(x)ln(y))/(1 + fln(x) + gln(y) + hln(x)ln(y))
Rational X 3D		z = (a + bexp(x) + cln(y) + dexp(x)ln(y))/(1 + fexp(x) + gln(y) + hexp(x)ln(y))
Rational Y 3D		z = (a + bln(x) + cexp(y) + dln(x)exp(y))/(1 + fln(x) + gexp(y) + hln(x)exp(y))
Rational Z 3D		z = (a + bexp(x) + cexp(y) + dexp(x)exp(y))/(1 + fexp(x) + gexp(y) + hexp(x)exp(y))



Rational A With Offset 3D		z = (a + bx + cy)/(1 + dx + fy) + Offset
Rational B With Offset 3D		z = (a + bln(x) + cln(y))/(1 + dx + fy) + Offset
Rational C With Offset 3D		z = (a + bexp(x) + cln(y))/(1 + dx + fy) + Offset
Rational D With Offset 3D		z = (a + bln(x) + cexp(y))/(1 + dx + fy) + Offset
Rational E With Offset 3D		z = (a + bexp(x) + cexp(y))/(1 + dx + fy) + Offset
Rational F With Offset 3D		z = (a + bx + cy)/(1 + dln(x) + fln(y)) + Offset
Rational G With Offset 3D		z = (a + bx + cy)/(1 + dexp(x) + fln(y)) + Offset
Rational H With Offset 3D		z = (a + bx + cy)/(1 + dln(x) + fexp(y)) + Offset
Rational I With Offset 3D		z = (a + bx + cy)/(1 + dexp(x) + fexp(y)) + Offset
Rational J With Offset 3D		z = (a + bln(x) + cln(y))/(1 + dln(x) + fln(y)) + Offset
Rational K With Offset 3D		z = (a + bexp(x) + cln(y))/(1 + dexp(x) + fln(y)) + Offset
Rational L With Offset 3D		z = (a + bln(x) + cexp(y))/(1 + dln(x) + fexp(y)) + Offset
Rational M With Offset 3D		z = (a + bexp(x) + cexp(y))/(1 + dexp(x) + fexp(y)) + Offset
Rational N With Offset 3D		z = (a + bx + cy + dxy)/(1 + fx + gy + hxy) + Offset
Rational O With Offset 3D		z = (a + bln(x) + cln(y) + d*ln(x)ln(y))/(1 + fx + gy + hxy) + Offset
Rational P With Offset 3D		z = (a + bexp(x) + cln(y) + d*exp(x)ln(y))/(1 + fx + gy + hxy) + Offset
Rational Q With Offset 3D		z = (a + bln(x) + cexp(y) + d*ln(x)exp(y))/(1 + fx + gy + hxy) + Offset
Rational R With Offset 3D		z = (a + bexp(x) + cexp(y) + d*exp(x)exp(y))/(1 + fx + gy + hxy) + Offset
Rational S With Offset 3D		z = (a + bx + cy + dxy)/(1 + fln(x) + gln(y) + hln(x)ln(y)) + Offset
Rational T With Offset 3D		z = (a + bx + cy + dxy)/(1 + fexp(x) + gln(y) + hexp(x)ln(y)) + Offset
Rational U With Offset 3D		z = (a + bx + cy + dxy)/(1 + fln(x) + gexp(y) + hln(x)exp(y)) + Offset
Rational V With Offset 3D		z = (a + bx + cy + dxy)/(1 + fexp(x) + gexp(y) + hexp(x)exp(y)) + Offset
Rational W With Offset 3D		z = (a + bln(x) + cln(y) + dln(x)ln(y))/(1 + fln(x) + gln(y) + hln(x)ln(y)) + Offset
Rational X With Offset 3D		z = (a + bexp(x) + cln(y) + dexp(x)ln(y))/(1 + fexp(x) + gln(y) + hexp(x)ln(y)) + Offset
Rational Y With Offset 3D		z = (a + bln(x) + cexp(y) + dln(x)exp(y))/(1 + fln(x) + gexp(y) + hln(x)exp(y)) + Offset
Rational Z With Offset 3D		z = (a + bexp(x) + cexp(y) + dexp(x)exp(y))/(1 + fexp(x) + gexp(y) + hexp(x)exp(y)) + Offset

Roman Surface (minus) 3D		z = (k(y²-x²) - (x²-y²)sqrt(k²-x²-y²)) / (2(x²+y²))
Roman Surface (minus) Offset XY 3D		z = (k((y+b)²-(x+a)²) - ((x+a)²-(y+b)²)sqrt(k²-(x+a)²-(y+b)²)) / (2((x+a)²+(y+b)²))
Roman Surface (minus) Scaled And Offset XY 3D		z = (k((cy+d)²-(ax+b)²) - ((ax+b)²-(cy+d)²)sqrt(k²-(ax+b)²-(cy+d)²)) / (2((ax+b)²+(cy+d)²))
Roman Surface (plus) 3D		z = (k(y²-x²) + (x²-y²)sqrt(k²-x²-y²)) / (2(x²+y²))
Roman Surface (plus) Offset XY 3D		z = (k((y+b)²-(x+a)²) + ((x+a)²-(y+b)²)sqrt(k²-(x+a)²-(y+b)²)) / (2((x+a)²+(y+b)²))
Roman Surface (plus) Scaled 3D		z = Scale * (k(y²-x²) + (x²-y²)sqrt(k²-x²-y²)) / (2(x²+y²))
Roman Surface (plus) Scaled And Offset XY 3D		z = (k((cy+d)²-(ax+b)²) + ((ax+b)²-(cy+d)²)sqrt(k²-(ax+b)²-(cy+d)²)) / (2((ax+b)²+(cy+d)²))



Roman Surface (minus) Offset XY With Offset 3D		z = (k((y+b)²-(x+a)²) - ((x+a)²-(y+b)²)sqrt(k²-(x+a)²-(y+b)²)) / (2((x+a)²+(y+b)²)) + Offset
Roman Surface (minus) Scaled And Offset XY With Offset 3D		z = (k((cy+d)²-(ax+b)²) - ((ax+b)²-(cy+d)²)sqrt(k²-(ax+b)²-(cy+d)²)) / (2((ax+b)²+(cy+d)²)) + Offset
Roman Surface (minus) With Offset 3D		z = (k(y²-x²) - (x²-y²)sqrt(k²-x²-y²)) / (2(x²+y²)) + Offset
Roman Surface (plus) Offset XY With Offset 3D		z = (k((y+b)²-(x+a)²) + ((x+a)²-(y+b)²)sqrt(k²-(x+a)²-(y+b)²)) / (2((x+a)²+(y+b)²)) + Offset
Roman Surface (plus) Scaled And Offset XY With Offset 3D		z = (k((cy+d)²-(ax+b)²) + ((ax+b)²-(cy+d)²)sqrt(k²-(ax+b)²-(cy+d)²)) / (2((ax+b)²+(cy+d)²)) + Offset
Roman Surface (plus) Scaled With Offset 3D		z = Scale * (k(y²-x²) + (x²-y²)sqrt(k²-x²-y²)) / (2(x²+y²)) + Offset
Roman Surface (plus) With Offset 3D		z = (k(y²-x²) + (x²-y²)sqrt(k²-x²-y²)) / (2(x²+y²)) + Offset

Andrea Prunotto Sigmoid A 3D		z = a0 + (a1 / (1.0 + exp(a2 * (x + a3 + a4 * y + a5 * x * y))))
Andrea Prunotto Sigmoid B 3D		z = a0 + (a1 / (1.0 + exp(a2 * (x * a3 + a4 * y + a5 * x * y))))
Fraser Smith Sigmoid 3D		z = 1.0 / ((1.0 + exp(a - bx)) * (1.0 + exp(c - dy)))
Fraser Smith Sigmoid Scaled 3D		z = Scale / ((1.0 + exp(a - bx)) * (1.0 + exp(c - dy)))
Sigmoid 3D		z = a / ((1.0 + exp(b - cx)) * (1.0 + exp(d - fy)))



Fraser Smith Sigmoid Scaled With Offset 3D		z = Scale / ((1.0 + exp(a - bx)) * (1.0 + exp(c - dy))) + Offset
Fraser Smith Sigmoid With Offset 3D		z = 1.0 / ((1.0 + exp(a - bx)) * (1.0 + exp(c - dy))) + Offset
Sigmoid With Offset 3D		z = a / ((1.0 + exp(b - cx)) * (1.0 + exp(d - fy))) + Offset

Simple Equation 01 3D		z = apow(x,b)pow(y,c)
Simple Equation 02 3D		z = x/(a+b*y)
Simple Equation 03 3D		z = y/(a+b*x)
Simple Equation 04 3D		z = apow(x,by)
Simple Equation 05 3D		z = apow(y,bx)
Simple Equation 06 3D		z = a*pow(x,b/y)
Simple Equation 07 3D		z = a*pow(y,b/x)
Simple Equation 08 3D		z = ax+bpow(y,2.0)
Simple Equation 09 3D		z = ay+bpow(x,2.0)
Simple Equation 10 3D		z = x/(a+b*pow(y,2.0))
Simple Equation 11 3D		z = y/(a+b*pow(x,2.0))
Simple Equation 12 3D		z = apow(b,x)pow(y,c)
Simple Equation 13 3D		z = apow(b,y)pow(x,c)
Simple Equation 14 3D		z = apow(xy,b)
Simple Equation 15 3D		z = a*pow(x/y,b)
Simple Equation 16 3D		z = a(pow(b,1.0/x))pow(y,c)
Simple Equation 17 3D		z = apow(b,1.0/y)pow(x,c)
Simple Equation 18 3D		z = apow(x/b,c)exp(y/b)
Simple Equation 19 3D		z = apow(y/b,c)exp(x/b)
Simple Equation 20 3D		z = apow(x,b+cy)
Simple Equation 21 3D		z = apow(y,b+cx)
Simple Equation 22 3D		z = a*pow(x,b+c/y)
Simple Equation 23 3D		z = a*pow(y,b+c/x)
Simple Equation 24 3D		z = apow(x,b+cln(y))
Simple Equation 25 3D		z = apow(y,b+cln(x))
Simple Equation 26 3D		z = a*pow(y,b+c/ln(x))
Simple Equation 27 3D		z = a*pow(x,b+c/ln(y))
Simple Equation 28 3D		z = aexp(bx+c*pow(y,2.0))
Simple Equation 29 3D		z = aexp(by+c*pow(x,2.0))
Simple Equation 30 3D		z = aexp(b/x+cy)
Simple Equation 31 3D		z = aexp(b/y+cx)
Simple Equation 32 3D		z = (a+x)/(b+c*y)
Simple Equation 33 3D		z = (a+y)/(b+c*x)
Simple Equation 34 3D		z = (a+x)/(b+c*pow(y,2.0))
Simple Equation 35 3D		z = (a+y)/(b+c*pow(x,2.0))
Simple Equation 36 3D		z = a(exp(bx)-exp(c*y))
Simple Equation 37 3D		z = apow(x,bpow(y,c))
Simple Equation 38 3D		z = apow(y,bpow(x,c))
Simple Equation 39 3D		z = x/(a+by+cpow(y,0.5))
Simple Equation 40 3D		z = y/(a+bx+cpow(x,0.5))
Simple Equation 41 3D		z = exp(a+b/x+c*ln(y))
Simple Equation 42 3D		z = exp(a+b/y+c*ln(x))
Simple Equation 43 3D		z = apow(x,b)ln(y+c)
Simple Equation 44 3D		z = apow(y,b)ln(x+c)



Simple Equation 01 With Offset 3D		z = apow(x,b)pow(y,c) + Offset
Simple Equation 02 With Offset 3D		z = x/(a+b*y) + Offset
Simple Equation 03 With Offset 3D		z = y/(a+b*x) + Offset
Simple Equation 04 With Offset 3D		z = apow(x,by) + Offset
Simple Equation 05 With Offset 3D		z = apow(y,bx) + Offset
Simple Equation 06 With Offset 3D		z = a*pow(x,b/y) + Offset
Simple Equation 07 With Offset 3D		z = a*pow(y,b/x) + Offset
Simple Equation 08 With Offset 3D		z = ax+bpow(y,2.0) + Offset
Simple Equation 09 With Offset 3D		z = ay+bpow(x,2.0) + Offset
Simple Equation 10 With Offset 3D		z = x/(a+b*pow(y,2.0)) + Offset
Simple Equation 11 With Offset 3D		z = y/(a+b*pow(x,2.0)) + Offset
Simple Equation 12 With Offset 3D		z = apow(b,x)pow(y,c) + Offset
Simple Equation 13 With Offset 3D		z = apow(b,y)pow(x,c) + Offset
Simple Equation 14 With Offset 3D		z = apow(xy,b) + Offset
Simple Equation 15 With Offset 3D		z = a*pow(x/y,b) + Offset
Simple Equation 16 With Offset 3D		z = a(pow(b,1.0/x))pow(y,c) + Offset
Simple Equation 17 With Offset 3D		z = apow(b,1.0/y)pow(x,c) + Offset
Simple Equation 18 With Offset 3D		z = apow(x/b,c)exp(y/b) + Offset
Simple Equation 19 With Offset 3D		z = apow(y/b,c)exp(x/b) + Offset
Simple Equation 20 With Offset 3D		z = apow(x,b+cy) + Offset
Simple Equation 21 With Offset 3D		z = apow(y,b+cx) + Offset
Simple Equation 22 With Offset 3D		z = a*pow(x,b+c/y) + Offset
Simple Equation 23 With Offset 3D		z = a*pow(y,b+c/x) + Offset
Simple Equation 24 With Offset 3D		z = apow(x,b+cln(y)) + Offset
Simple Equation 25 With Offset 3D		z = apow(y,b+cln(x)) + Offset
Simple Equation 26 With Offset 3D		z = a*pow(y,b+c/ln(x)) + Offset
Simple Equation 27 With Offset 3D		z = a*pow(x,b+c/ln(y)) + Offset
Simple Equation 28 With Offset 3D		z = aexp(bx+c*pow(y,2.0)) + Offset
Simple Equation 29 With Offset 3D		z = aexp(by+c*pow(x,2.0)) + Offset
Simple Equation 30 With Offset 3D		z = aexp(b/x+cy) + Offset
Simple Equation 31 With Offset 3D		z = aexp(b/y+cx) + Offset
Simple Equation 32 With Offset 3D		z = (a+x)/(b+c*y) + Offset
Simple Equation 33 With Offset 3D		z = (a+y)/(b+c*x) + Offset
Simple Equation 34 With Offset 3D		z = (a+x)/(b+c*pow(y,2.0)) + Offset
Simple Equation 35 With Offset 3D		z = (a+y)/(b+c*pow(x,2.0)) + Offset
Simple Equation 36 With Offset 3D		z = a(exp(bx)-exp(c*y)) + Offset
Simple Equation 37 With Offset 3D		z = apow(x,bpow(y,c)) + Offset
Simple Equation 38 With Offset 3D		z = apow(y,bpow(x,c)) + Offset
Simple Equation 39 With Offset 3D		z = x/(a+by+cpow(y,0.5)) + Offset
Simple Equation 40 With Offset 3D		z = y/(a+bx+cpow(x,0.5)) + Offset
Simple Equation 41 With Offset 3D		z = exp(a+b/x+c*ln(y)) + Offset
Simple Equation 42 With Offset 3D		z = exp(a+b/y+c*ln(x)) + Offset
Simple Equation 43 With Offset 3D		z = apow(x,b)ln(y+c) + Offset
Simple Equation 44 With Offset 3D		z = apow(y,b)ln(x+c) + Offset

Taylor Series A 3D		z = a + bx + cy + dx² + fy² + gxy
Taylor Series B 3D		z = a + bln(x) + cy + dln(x)² + fy² + gln(x)y
Taylor Series C 3D		z = a + bx + cln(y) + dx² + fln(y)² + gxln(y)
Taylor Series D 3D		z = a + bln(x) + cln(y) + dln(x)² + fln(y)² + gln(x)ln(y)
Taylor Series E 3D		z = a + b/x + cy + d/x² + fy² + gy/x
Taylor Series F 3D		z = a + b/ln(x) + cy + d/ln(x)² + fy² + gy/ln(x)
Taylor Series G 3D		z = a + b/x + cln(y) + d/x² + fln(y)² + g*ln(y)/x
Taylor Series H 3D		z = a + b/ln(x) + cln(y) + d/ln(x)² + fln(y)² + g*ln(y)/ln(x)
Taylor Series I 3D		z = a + bx + c/y + dx² + f/y² + gx/y
Taylor Series J 3D		z = a + bln(x) + c/y + dln(x)² + f/y² + g*ln(x)/y
Taylor Series K 3D		z = a + bx + c/ln(y) + dx² + f/ln(y)² + gx/ln(y)
Taylor Series L 3D		z = a + bln(x) + c/ln(y) + dln(x)² + f/ln(y)² + g*ln(x)/ln(y)
Taylor Series M 3D		z = a + b/x + c/y + d/x² + f/y² + g/(xy)
Taylor Series N 3D		z = a + b/ln(x) + c/y + d/ln(x)² + f/y² + g/(ln(x)*y)
Taylor Series O 3D		z = a + b/x + c/ln(y) + d/x² + f/ln(y)² + g/(x*ln(y))
Taylor Series P 3D		z = a + b/ln(x) + c/ln(y) + d/ln(x)² + f/ln(y)² + g/(ln(x)*ln(y))

Cosh X Plus Cosh Y [radians] 3D		z = amplitude_x * cosh(pi * (x - center_x) / width_x) + amplitude_y * cosh(pi * (y - center_y) / width_y)
Cosh X Plus Sine Y [radians] 3D		z = amplitude_x * cosh(pi * (x - center_x) / width_x) + amplitude_y * sin(pi * (y - center_y) / width_y)
Cosh X Plus Tangent Y [radians] 3D		z = amplitude_x * cosh(pi * (x - center_x) / width_x) + amplitude_y * tan(pi * (y - center_y) / width_y)
Cosh X Times Cosh Y[radians] 3D		z = amplitude * cosh(pi * (x - center_x) / width_x) * cosh(pi * (y - center_y) / width_y)
Cosh X Times Sine Y [radians] 3D		z = amplitude * cosh(pi * (x - center_x) / width_x) * sin(pi * (y - center_y) / width_y)
Cosh X Times Tangent Y [radians] 3D		z = amplitude * cosh(pi * (x - center_x) / width_x) * tan(pi * (y - center_y) / width_y)
Cosh XY [radians] 3D		z = amplitude * cosh(pi * (xy - center) / width)
Reza's Custom Equation One [radians] 3D		z = (cos(ax - by) + sin(cx - dy))ⁿ - (cos(fx - gy) + sin(hx- iy))ⁿ
Reza's Custom Equation Two [radians] 3D		z = abs(cos((A(x+B)) + C(y+D))) + abs(cos((A(x+B)) - C(y+D))) - (sin(Ex+F))² - (sin(Ey+G))²
Sine X Plus Cosh Y [radians] 3D		z = amplitude_x * sin(pi * (x - center_x) / width_x) + amplitude_y * cosh(pi * (y - center_y) / width_y)
Sine X Plus Sine Y [radians] 3D		z = amplitude_x * sin(pi * (x - center_x) / width_x) + amplitude_y * sin(pi * (y - center_y) / width_y)
Sine X Plus Tangent Y [radians] 3D		z = amplitude_x * sin(pi * (x - center_x) / width_x) + amplitude_y * tan(pi * (y - center_y) / width_y)
Sine X Times Cosh Y [radians] 3D		z = amplitude * sine(pi * (x - center_x) / width_x) * cosh(pi * (y - center_y) / width_y)
Sine X Times Sine Y [radians] 3D		z = amplitude * sin(pi * (x - center_x) / width_x) * sin(pi * (y - center_y) / width_y)
Sine X Times Tangent Y [radians] 3D		z = amplitude * sin(pi * (x - center_x) / width_x) * tan(pi * (y - center_y) / width_y)
Sine XY [radians] 3D		z = amplitude * sin(pi * (xy - center) / width)
Tangent X Plus Cosh Y [radians] 3D		z = amplitude_x * tan(pi * (x - center_x) / width_x) + amplitude_y * cosh(pi * (y - center_y) / width_y)
Tangent X Plus Sine Y [radians] 3D		z = amplitude_x * tan(pi * (x - center_x) / width_x) + amplitude_y * sin(pi * (y - center_y) / width_y)
Tangent X Plus Tangent Y [radians] 3D		z = amplitude_x * tan(pi * (x - center_x) / width_x) + amplitude_y * tan(pi * (y - center_y) / width_y)
Tangent X Times Cosh Y [radians] 3D		z = amplitude * tan(pi * (x - center_x) / width_x) * cosh(pi * (y - center_y) / width_y)
Tangent X Times Sine Y [radians] 3D		z = amplitude * tan(pi * (x - center_x) / width_x) * sin(pi * (y - center_y) / width_y)
Tangent X Times Tangent Y [radians] 3D		z = amplitude * tan(pi * (x - center_x) / width_x) * tan(pi * (y - center_y) / width_y)
Tangent XY [radians] 3D		z = amplitude * tan(pi * (xy - center) / width)



Cosh X Plus Cosh Y [radians] With Offset 3D		z = amplitude_x * cosh(pi * (x - center_x) / width_x) + amplitude_y * cosh(pi * (y - center_y) / width_y) + Offset
Cosh X Plus Sine Y [radians] With Offset 3D		z = amplitude_x * cosh(pi * (x - center_x) / width_x) + amplitude_y * sin(pi * (y - center_y) / width_y) + Offset
Cosh X Plus Tangent Y [radians] With Offset 3D		z = amplitude_x * cosh(pi * (x - center_x) / width_x) + amplitude_y * tan(pi * (y - center_y) / width_y) + Offset
Cosh X Times Cosh Y[radians] With Offset 3D		z = amplitude * cosh(pi * (x - center_x) / width_x) * cosh(pi * (y - center_y) / width_y) + Offset
Cosh X Times Sine Y [radians] With Offset 3D		z = amplitude * cosh(pi * (x - center_x) / width_x) * sin(pi * (y - center_y) / width_y) + Offset
Cosh X Times Tangent Y [radians] With Offset 3D		z = amplitude * cosh(pi * (x - center_x) / width_x) * tan(pi * (y - center_y) / width_y) + Offset
Cosh XY [radians] With Offset 3D		z = amplitude * cosh(pi * (xy - center) / width) + Offset
Reza's Custom Equation One [radians] With Offset 3D		z = (cos(ax - by) + sin(cx - dy))ⁿ - (cos(fx - gy) + sin(hx- iy))ⁿ + Offset
Reza's Custom Equation Two [radians] With Offset 3D		z = abs(cos((A(x+B)) + C(y+D))) + abs(cos((A(x+B)) - C(y+D))) - (sin(Ex+F))² - (sin(Ey+G))² + Offset
Sine X Plus Cosh Y [radians] With Offset 3D		z = amplitude_x * sin(pi * (x - center_x) / width_x) + amplitude_y * cosh(pi * (y - center_y) / width_y) + Offset
Sine X Plus Sine Y [radians] With Offset 3D		z = amplitude_x * sin(pi * (x - center_x) / width_x) + amplitude_y * sin(pi * (y - center_y) / width_y) + Offset
Sine X Plus Tangent Y [radians] With Offset 3D		z = amplitude_x * sin(pi * (x - center_x) / width_x) + amplitude_y * tan(pi * (y - center_y) / width_y) + Offset
Sine X Times Cosh Y [radians] With Offset 3D		z = amplitude * sine(pi * (x - center_x) / width_x) * cosh(pi * (y - center_y) / width_y) + Offset
Sine X Times Sine Y [radians] With Offset 3D		z = amplitude * sin(pi * (x - center_x) / width_x) * sin(pi * (y - center_y) / width_y) + Offset
Sine X Times Tangent Y [radians] With Offset 3D		z = amplitude * sin(pi * (x - center_x) / width_x) * tan(pi * (y - center_y) / width_y) + Offset
Sine XY [radians] With Offset 3D		z = amplitude * sin(pi * (xy - center) / width) + Offset
Tangent X Plus Cosh Y [radians] With Offset 3D		z = amplitude_x * tan(pi * (x - center_x) / width_x) + amplitude_y * cosh(pi * (y - center_y) / width_y) + Offset
Tangent X Plus Sine Y [radians] With Offset 3D		z = amplitude_x * tan(pi * (x - center_x) / width_x) + amplitude_y * sin(pi * (y - center_y) / width_y) + Offset
Tangent X Plus Tangent Y [radians] With Offset 3D		z = amplitude_x * tan(pi * (x - center_x) / width_x) + amplitude_y * tan(pi * (y - center_y) / width_y) + Offset
Tangent X Times Cosh Y [radians] With Offset 3D		z = amplitude * tan(pi * (x - center_x) / width_x) * cosh(pi * (y - center_y) / width_y) + Offset
Tangent X Times Sine Y [radians] With Offset 3D		z = amplitude * tan(pi * (x - center_x) / width_x) * sin(pi * (y - center_y) / width_y) + Offset
Tangent X Times Tangent Y [radians] With Offset 3D		z = amplitude * tan(pi * (x - center_x) / width_x) * tan(pi * (y - center_y) / width_y) + Offset
Tangent XY [radians] With Offset 3D		z = amplitude * tan(pi * (xy - center) / width) + Offset

List Of All 2D Equations	-	Standard Versions Only
List Of All 2D Equations	-	Including Extended Versions