Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B

Average Error: 0.1 → 0.0

Time: 9.6s

Precision: binary64

Cost: 576

Math

\[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

↓

\[4 \cdot \frac{x - y}{z} - 2 \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* 4.0 (- (- x y) (* z 0.5))) z))

↓

(FPCore (x y z) :precision binary64 (- (* 4.0 (/ (- x y) z)) 2.0))

C

double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

↓

double code(double x, double y, double z) {
	return (4.0 * ((x - y) / z)) - 2.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (4.0d0 * ((x - y) - (z * 0.5d0))) / z
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 = (4.0d0 * ((x - y) / z)) - 2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return (4.0 * ((x - y) - (z * 0.5))) / z;
}

↓

public static double code(double x, double y, double z) {
	return (4.0 * ((x - y) / z)) - 2.0;
}

Python

def code(x, y, z):
	return (4.0 * ((x - y) - (z * 0.5))) / z

↓

def code(x, y, z):
	return (4.0 * ((x - y) / z)) - 2.0

Julia

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - y) - Float64(z * 0.5))) / z)
end

↓

function code(x, y, z)
	return Float64(Float64(4.0 * Float64(Float64(x - y) / z)) - 2.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - y) - (z * 0.5))) / z;
end

↓

function tmp = code(x, y, z)
	tmp = (4.0 * ((x - y) / z)) - 2.0;
end

Wolfram

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] - N[(z * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

↓

code[x_, y_, z_] := N[(N[(4.0 * N[(N[(x - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]

Target

Original	0.1
Target	0.0
Herbie	0.0

\[4 \cdot \frac{x}{z} - \left(2 + 4 \cdot \frac{y}{z}\right) \]

Derivation

1. Initial program 0.1

   \[\frac{4 \cdot \left(\left(x - y\right) - z \cdot 0.5\right)}{z} \]

2. Taylor expanded in z around 0 0.0

   \[\leadsto \color{blue}{4 \cdot \frac{x - y}{z} - 2} \]

Alternatives

Alternative 1
Error	32.7
Cost	1112

\[\begin{array}{l} t_0 := \frac{-4 \cdot y}{z}\\ t_1 := \frac{x \cdot 4}{z}\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-197}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-252}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 10^{-160}:\\ \;\;\;\;-2\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+26}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+77}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	16.2
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{+115}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+102}:\\ \;\;\;\;\frac{4}{z} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 3
Error	11.2
Cost	712

\[\begin{array}{l} t_0 := \frac{4}{z} \cdot \left(x - y\right)\\ \mathbf{if}\;x \leq -1.45 \cdot 10^{+59}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+78}:\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	8.9
Cost	712

\[\begin{array}{l} t_0 := 4 \cdot \frac{x}{z} - 2\\ \mathbf{if}\;x \leq -1.42 \cdot 10^{+37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+60}:\\ \;\;\;\;-4 \cdot \frac{y}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	29.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+77}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+25}:\\ \;\;\;\;\frac{-4 \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 6
Error	36.4
Cost	64

\[-2 \]

Reproduce

herbie shell --seed 2023010 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, B"
  :precision binary64

  :herbie-target
  (- (* 4.0 (/ x z)) (+ 2.0 (* 4.0 (/ y z))))

  (/ (* 4.0 (- (- x y) (* z 0.5))) z))