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

Average Error: 0.04% → 0.04%

Time: 4.7s

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	0.04%
Target	0.03%
Herbie	0.04%

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

Derivation

1. Initial program 0.04

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

2. Final simplification 0.04

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

Alternatives

Alternative 1
Error	24.85%
Cost	1245

\[\begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{x - y}{z}\\ \mathbf{if}\;y \leq -2.26 \cdot 10^{+86}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-28}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-114}:\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+134} \lor \neg \left(y \leq 9.5 \cdot 10^{+200}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]

Alternative 2
Error	40.68%
Cost	852

\[\begin{array}{l} t_0 := \frac{-x}{y}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+129}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -950:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-54}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3
Error	31.47%
Cost	850

\[\begin{array}{l} \mathbf{if}\;y \leq -3.45 \cdot 10^{-93} \lor \neg \left(y \leq 4 \cdot 10^{-176}\right) \land \left(y \leq 6.2 \cdot 10^{-116} \lor \neg \left(y \leq 6.6 \cdot 10^{-28}\right)\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z}\\ \end{array} \]

Alternative 4
Error	24.91%
Cost	850

\[\begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+54} \lor \neg \left(x \leq -0.0042 \lor \neg \left(x \leq -1.3 \cdot 10^{-83}\right) \land x \leq 3.4 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{x}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - z}\\ \end{array} \]

Alternative 5
Error	24.39%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-31} \lor \neg \left(y \leq 3.3 \cdot 10^{-15}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z - y}\\ \end{array} \]

Alternative 6
Error	40.27%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -3.45 \cdot 10^{-93}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	64.05%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023088 
(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)))