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

Average Error: 0.0 → 0.0

Time: 6.8s

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	16.6
Cost	1377

\[\begin{array}{l} t_0 := \frac{x}{z - y}\\ t_1 := \frac{x - y}{z}\\ t_2 := \frac{y}{y - z}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.92 \cdot 10^{-61}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-70} \lor \neg \left(z \leq 1.68 \cdot 10^{-37}\right) \land z \leq 2.1 \cdot 10^{+51}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	25.7
Cost	720

\[\begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+120}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{+26}:\\ \;\;\;\;\frac{-y}{z}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-33}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-21}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	18.7
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-86} \lor \neg \left(y \leq 1.55 \cdot 10^{-28}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 4
Error	15.3
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-33} \lor \neg \left(y \leq 3 \cdot 10^{-28}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]

Alternative 5
Error	15.3
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+31} \lor \neg \left(x \leq 10^{+29}\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]

Alternative 6
Error	24.9
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-33}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-23}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	40.5
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023010 
(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)))