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

Average Error: 0.0 → 0.0

Time: 9.4s

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	20.4
Cost	848

\[\begin{array}{l} t_0 := \frac{x}{z - y}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+60}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{-34}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 0.00025:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+108}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 2
Error	26.1
Cost	784

\[\begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+57}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+108}:\\ \;\;\;\;-\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	15.2
Cost	648

\[\begin{array}{l} t_0 := \frac{x}{z - y}\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+24}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-32}:\\ \;\;\;\;-\frac{y}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	15.5
Cost	648

\[\begin{array}{l} t_0 := -\frac{x - y}{y}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+26}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-54}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	25.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+32}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	40.8
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023077 
(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)))