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

Average Accuracy: 100.0% → 100.0%

Time: 9.7s

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	74.1%
Cost	850

\[\begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{+68} \lor \neg \left(z \leq 2.5 \cdot 10^{-105} \lor \neg \left(z \leq 3.8 \cdot 10^{-53}\right) \land z \leq 3.1 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{y}\\ \end{array} \]

Alternative 2
Accuracy	59.7%
Cost	720

\[\begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+107}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{+67}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{+39}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-40}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Accuracy	75.2%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+22} \lor \neg \left(x \leq 2.6 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]

Alternative 4
Accuracy	67.5%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -2.25 \cdot 10^{+166}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Accuracy	60.6%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+40}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-36}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Accuracy	35.7%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023135 
(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)))