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

Average Error: 0.1 → 0.0

Time: 1.1min

Precision: binary64

Cost: 960

Math

\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

↓

\[1 + \left(\left(1 + \frac{x}{y \cdot 0.25}\right) - \frac{z}{y \cdot 0.25}\right) \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))

↓

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (- (+ 1.0 (/ x (* y 0.25))) (/ z (* y 0.25)))))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

↓

double code(double x, double y, double z) {
	return 1.0 + ((1.0 + (x / (y * 0.25))) - (z / (y * 0.25)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 1.0d0 + ((4.0d0 * ((x + (y * 0.25d0)) - 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 = 1.0d0 + ((1.0d0 + (x / (y * 0.25d0))) - (z / (y * 0.25d0)))
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
}

↓

public static double code(double x, double y, double z) {
	return 1.0 + ((1.0 + (x / (y * 0.25))) - (z / (y * 0.25)));
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y)

↓

def code(x, y, z):
	return 1.0 + ((1.0 + (x / (y * 0.25))) - (z / (y * 0.25)))

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.25)) - z)) / y))
end

↓

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(1.0 + Float64(x / Float64(y * 0.25))) - Float64(z / Float64(y * 0.25))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.25)) - z)) / y);
end

↓

function tmp = code(x, y, z)
	tmp = 1.0 + ((1.0 + (x / (y * 0.25))) - (z / (y * 0.25)));
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.25), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(1.0 + N[(N[(1.0 + N[(x / N[(y * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z / N[(y * 0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.1

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]

2. Applied egg-rr 0.0

   \[\leadsto 1 + \color{blue}{\left(\left(1 + \frac{x}{y \cdot 0.25}\right) - \frac{z}{y \cdot 0.25}\right)} \]

Alternatives

Alternative 1
Error	30.6
Cost	1112

\[\begin{array}{l} t_0 := \frac{4 \cdot x}{y}\\ t_1 := -4 \cdot \frac{z}{y}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-246}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-273}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-161}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-133}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+169}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	16.1
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+139}:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+118}:\\ \;\;\;\;4 \cdot \frac{x - z}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 3
Error	11.8
Cost	712

\[\begin{array}{l} t_0 := 4 \cdot \frac{x - z}{y}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+29}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+91}:\\ \;\;\;\;2 + \frac{4 \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	8.6
Cost	712

\[\begin{array}{l} t_0 := 2 + \frac{4 \cdot x}{y}\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{-30}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+39}:\\ \;\;\;\;2 - 4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	30.2
Cost	584

\[\begin{array}{l} t_0 := -4 \cdot \frac{z}{y}\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+30}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+172}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	0.1
Cost	576

\[2 + \frac{\frac{x - z}{0.25}}{y} \]

Alternative 7
Error	36.5
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, C"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.25)) z)) y)))