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

Average Error: 0.37% → 0.37%

Time: 6.6s

Precision: binary64

Cost: 832

Math

\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]

↓

\[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

↓

(FPCore (x y z)
 :precision binary64
 (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))

C

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

↓

double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - 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 = 1.0d0 + ((4.0d0 * ((x + (y * 0.75d0)) - 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 + ((4.0d0 * ((x + (y * 0.75d0)) - z)) / y)
end function

Java

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

↓

public static double code(double x, double y, double z) {
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
}

Python

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

↓

def code(x, y, z):
	return 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y)

Julia

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

↓

function code(x, y, z)
	return Float64(1.0 + Float64(Float64(4.0 * Float64(Float64(x + Float64(y * 0.75)) - z)) / y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

↓

function tmp = code(x, y, z)
	tmp = 1.0 + ((4.0 * ((x + (y * 0.75)) - z)) / y);
end

Wolfram

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := N[(1.0 + N[(N[(4.0 * N[(N[(x + N[(y * 0.75), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.37

   \[1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]

2. Final simplification 0.37

   \[\leadsto 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.75\right) - z\right)}{y} \]

Alternatives

Alternative 1
Error	48.68%
Cost	1376

\[\begin{array}{l} t_0 := 4 \cdot \frac{x}{y}\\ t_1 := z \cdot \frac{-4}{y}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+159}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+82}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-49}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-68}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2600000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+97}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 2
Error	48.63%
Cost	1376

\[\begin{array}{l} t_0 := 4 \cdot \frac{x}{y}\\ t_1 := \frac{z}{\frac{y}{-4}}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+159}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{+82}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-51}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-66}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+98}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 3
Error	14.69%
Cost	977

\[\begin{array}{l} t_0 := 4 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{+75}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+23}:\\ \;\;\;\;\frac{-4}{y} \cdot \left(z - x\right)\\ \mathbf{elif}\;x \leq -5.9 \cdot 10^{-34} \lor \neg \left(x \leq 6 \cdot 10^{-52}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 4
Error	18.03%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{+91} \lor \neg \left(x \leq 1.65 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{-4}{y} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 5
Error	26.87%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+160}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{+209}:\\ \;\;\;\;\frac{-4}{y} \cdot \left(z - x\right)\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 6
Error	46.2%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+92} \lor \neg \left(x \leq 4.6 \cdot 10^{+55}\right):\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 7
Error	0.25%
Cost	576

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

Alternative 8
Error	56.99%
Cost	64

\[4 \]

Reproduce

herbie shell --seed 2023090 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.ColorRamp:rampColorHotToCold from repa-algorithms-3.4.0.1, A"
  :precision binary64
  (+ 1.0 (/ (* 4.0 (- (+ x (* y 0.75)) z)) y)))