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

Average Accuracy: 100.0% → 100.0%

Time: 8.2s

Precision: binary64

Cost: 448

Math

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

↓

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

FPCore

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

↓

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

C

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

↓

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

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 = (x - y) / (z - y)
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 (x - y) / (z - y);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Target

Original	100.0%
Target	100.0%
Herbie	100.0%

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	74.2%
Cost	1114

\[\begin{array}{l} t_0 := \frac{x - y}{z}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+179}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+139}:\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+55} \lor \neg \left(z \leq -85000000 \lor \neg \left(z \leq -5.8 \cdot 10^{-52}\right) \land z \leq 0.00042\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 2
Accuracy	68.7%
Cost	848

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{-115}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1650000000:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq 3400000000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Accuracy	75.0%
Cost	848

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{x}{z - y}\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{+15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1950000:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Accuracy	60.7%
Cost	652

\[\begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+15}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-31}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+29}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Accuracy	75.3%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-52} \lor \neg \left(y \leq 4 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]

Alternative 6
Accuracy	60.9%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+16}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3700000000:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Accuracy	35.2%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023151 
(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)))