Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1

Average Error: 0.0 → 0.0

Time: 25.0s

Precision: binary64

Cost: 704

Math

\[\frac{x - y}{z - y} \]

↓

\[\frac{y}{y - z} - \frac{x}{y - z} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (- x y) (- z y)))

↓

(FPCore (x y z) :precision binary64 (- (/ y (- y z)) (/ x (- y z))))

C

double code(double x, double y, double z) {
	return (x - y) / (z - y);
}

↓

double code(double x, double y, double z) {
	return (y / (y - z)) - (x / (y - z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x - y) / (z - y)
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (y / (y - z)) - (x / (y - z))
end function

Java

public static double code(double x, double y, double z) {
	return (x - y) / (z - y);
}

↓

public static double code(double x, double y, double z) {
	return (y / (y - z)) - (x / (y - z));
}

Python

def code(x, y, z):
	return (x - y) / (z - y)

↓

def code(x, y, z):
	return (y / (y - z)) - (x / (y - z))

Julia

function code(x, y, z)
	return Float64(Float64(x - y) / Float64(z - y))
end

↓

function code(x, y, z)
	return Float64(Float64(y / Float64(y - z)) - Float64(x / Float64(y - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x - y) / (z - y);
end

↓

function tmp = code(x, y, z)
	tmp = (y / (y - z)) - (x / (y - z));
end

Wolfram

code[x_, y_, z_] := N[(N[(x - y), $MachinePrecision] / N[(z - y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(N[(y / N[(y - z), $MachinePrecision]), $MachinePrecision] - N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Target

Original	0.0
Target	0.0
Herbie	0.0

\[\frac{x}{z - y} - \frac{y}{z - y} \]

Derivation

1. Initial program 0.0

   \[\frac{x - y}{z - y} \]

2. Applied egg-rr 0.0

   \[\leadsto \color{blue}{\frac{y}{y - z} - \frac{x}{y - z}} \]

3. Final simplification 0.0

   \[\leadsto \frac{y}{y - z} - \frac{x}{y - z} \]

Alternatives

Alternative 1
Error	21.4
Cost	1244

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{y}{-z}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{-19}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-67}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq -1.86 \cdot 10^{-103}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-145}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	27.7
Cost	1048

\[\begin{array}{l} t_0 := -\frac{x}{y}\\ \mathbf{if}\;y \leq -4.9 \cdot 10^{+128}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -16500:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-145}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 10^{-27}:\\ \;\;\;\;\frac{y}{-z}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+76}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	16.3
Cost	716

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -2.2 \cdot 10^{+84}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-143}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+39}:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	26.3
Cost	588

\[\begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+128}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -125000:\\ \;\;\;\;-\frac{x}{y}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	16.2
Cost	584

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -7 \cdot 10^{+83}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	15.3
Cost	584

\[\begin{array}{l} t_0 := \frac{x}{z - y}\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{-46}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	25.6
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-12}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8
Error	0.0
Cost	448

\[\frac{x - y}{z - y} \]

Alternative 9
Error	40.7
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023099 
(FPCore (x y z)
  :name "Graphics.Rasterific.Shading:$sgradientColorAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (- (/ x (- z y)) (/ y (- z y)))

  (/ (- x y) (- z y)))