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

Average Accuracy: 100.0% → 100.0%

Time: 6.6s

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	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	72.2%
Cost	1505

\[\begin{array}{l} t_0 := \frac{x - y}{z}\\ t_1 := 1 + \frac{z - x}{y}\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+35}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-173}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-49}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-11} \lor \neg \left(z \leq 6.5 \cdot 10^{+112}\right) \land z \leq 7 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Accuracy	67.4%
Cost	980

\[\begin{array}{l} t_0 := 1 + \frac{z}{y}\\ t_1 := \frac{x}{z - y}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+163}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+39}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+114}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Accuracy	58.9%
Cost	588

\[\begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+163}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-49}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4
Accuracy	58.9%
Cost	588

\[\begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+163}:\\ \;\;\;\;1 + \frac{z}{y}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-46}:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5
Accuracy	76.8%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -9 \lor \neg \left(x \leq 8.5 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]

Alternative 6
Accuracy	61.1%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -30:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Accuracy	36.3%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023141 
(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)))