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

Average Error: 0.1 → 0.0

Time: 1.2min

Precision: binary64

Cost: 832

Math

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

↓

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

FPCore

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

↓

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

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 * (y / z)) + (4.0 * ((x / z) - 0.5));
}

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) * (y / z)) + (4.0d0 * ((x / z) - 0.5d0))
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 * (y / z)) + (4.0 * ((x / z) - 0.5));
}

Python

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

↓

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

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(y / z)) + Float64(4.0 * Float64(Float64(x / z) - 0.5)))
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 * (y / z)) + (4.0 * ((x / z) - 0.5));
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[(y / z), $MachinePrecision]), $MachinePrecision] + N[(4.0 * N[(N[(x / z), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $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 y around inf 0.0

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

Alternatives

Alternative 1
Error	32.5
Cost	1508

\[\begin{array}{l} t_0 := \frac{x}{0.25 \cdot z}\\ t_1 := \frac{-4 \cdot y}{z}\\ \mathbf{if}\;y \leq -1.08 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-20}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-168}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-203}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-225}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-278}:\\ \;\;\;\;-2\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-249}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-13}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	16.3
Cost	976

\[\begin{array}{l} t_0 := \frac{4}{z} \cdot \left(x - y\right)\\ \mathbf{if}\;z \leq -1.18 \cdot 10^{+107}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-55}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-68}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+137}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 3
Error	12.7
Cost	976

\[\begin{array}{l} t_0 := \frac{4}{z} \cdot \left(x - y\right)\\ t_1 := \frac{-4 \cdot y}{z} - 2\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	30.4
Cost	848

\[\begin{array}{l} t_0 := \frac{x}{0.25 \cdot z}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+107}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-31}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-68}:\\ \;\;\;\;-2\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-5}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 5
Error	9.1
Cost	712

\[\begin{array}{l} t_0 := \frac{-4 \cdot y}{z} - 2\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{-40}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-66}:\\ \;\;\;\;\frac{x \cdot 4}{z} - 2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	0.0
Cost	576

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

Alternative 7
Error	36.8
Cost	64

\[-2 \]

Reproduce

herbie shell --seed 2023033 
(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))