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

Average Error: 0.04% → 0.04%

Time: 4.6s

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	0.04%
Target	0.03%
Herbie	0.04%

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

Derivation

1. Initial program 0.04

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

2. Final simplification 0.04

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

Alternatives

Alternative 1
Error	29%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-96} \lor \neg \left(y \leq 1.55 \cdot 10^{-49}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 2
Error	23.51%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-22} \lor \neg \left(y \leq 1.06 \cdot 10^{-16}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]

Alternative 3
Error	23.45%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -48 \lor \neg \left(y \leq 5.8 \cdot 10^{-15}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{z}\\ \end{array} \]

Alternative 4
Error	38.19%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-18}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Error	63.54%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023103 
(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)))