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

Average Accuracy: 99.6% → 99.6%

Time: 6.7s

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 99.6%

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

2. Final simplification 99.6%

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

Alternatives

Alternative 1
Accuracy	51.9%
Cost	1508

\[\begin{array}{l} t_0 := \frac{z}{\frac{y}{-4}}\\ t_1 := 4 \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+84}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-67}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-75}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+34}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+47}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 2
Accuracy	79.7%
Cost	978

\[\begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+84} \lor \neg \left(y \leq -8 \cdot 10^{+46} \lor \neg \left(y \leq -1.35 \cdot 10^{-68}\right) \land y \leq 2.05 \cdot 10^{+80}\right):\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{z - x}{y}\\ \end{array} \]

Alternative 3
Accuracy	51.3%
Cost	849

\[\begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+84}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+37} \lor \neg \left(y \leq -1.12 \cdot 10^{-67}\right) \land y \leq 2.5 \cdot 10^{+83}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 4
Accuracy	82.7%
Cost	844

\[\begin{array}{l} t_0 := -4 \cdot \frac{z - x}{y}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+22}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-32}:\\ \;\;\;\;4 + 4 \cdot \frac{x}{y}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+66}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;4 + -4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 5
Accuracy	99.5%
Cost	832

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

Alternative 6
Accuracy	73.9%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+126}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+83}:\\ \;\;\;\;-4 \cdot \frac{z - x}{y}\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 7
Accuracy	42.5%
Cost	64

\[4 \]

Reproduce

herbie shell --seed 2023135 
(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)))