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

Average Error: 0.0 → 0.0

Time: 5.5s

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	0.0
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. Final simplification 0.0

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

Alternatives

Alternative 1
Error	15.9
Cost	849

\[\begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+34}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -7000000000:\\ \;\;\;\;\frac{x - y}{z}\\ \mathbf{elif}\;y \leq -190 \lor \neg \left(y \leq 2.2 \cdot 10^{-38}\right):\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]

Alternative 2
Error	18.9
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{-36} \lor \neg \left(y \leq 1.22 \cdot 10^{-31}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 3
Error	15.5
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+29} \lor \neg \left(y \leq 6.8 \cdot 10^{-18}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]

Alternative 4
Error	15.8
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -76000 \lor \neg \left(y \leq 4.5 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{y}{y - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]

Alternative 5
Error	25.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+43}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	41.2
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023039 
(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)))