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

Average Accuracy: 99.8% → 100.0%

Time: 9.7s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

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

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 (4.0 * ((x - z) / y)) + 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 = 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 = (4.0d0 * ((x - z) / y)) + 2.0d0
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 (4.0 * ((x - z) / y)) + 2.0;
}

Python

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

↓

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

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(Float64(4.0 * Float64(Float64(x - z) / y)) + 2.0)
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 = (4.0 * ((x - z) / y)) + 2.0;
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[(N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision]

Derivation

1. Initial program 99.8%

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

2. Simplified 99.7%

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

   [Start] 99.8	\[ 1 + \frac{4 \cdot \left(\left(x + y \cdot 0.25\right) - z\right)}{y} \]
   associate-/l* [=>] 99.7	\[ 1 + \color{blue}{\frac{4}{\frac{y}{\left(x + y \cdot 0.25\right) - z}}} \]
   associate--l+ [=>] 99.7	\[ 1 + \frac{4}{\frac{y}{\color{blue}{x + \left(y \cdot 0.25 - z\right)}}} \]

3. Taylor expanded in y around 0 100.0%

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

4. Simplified 100.0%

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

   [Start] 100.0	\[ 2 + 4 \cdot \frac{x - z}{y} \]
   +-commutative [=>] 100.0	\[ \color{blue}{4 \cdot \frac{x - z}{y} + 2} \]

5. Final simplification 100.0%

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

Alternatives

Alternative 1
Accuracy	51.0%
Cost	1900

\[\begin{array}{l} t_0 := 4 \cdot \frac{x}{y} + 1\\ t_1 := 1 + -4 \cdot \frac{z}{y}\\ \mathbf{if}\;z \leq -4.35 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-56}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-99}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-152}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-246}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-211}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-161}:\\ \;\;\;\;2\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-74}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+58}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+172}:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	52.3%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-137} \lor \neg \left(x \leq 35000000000\right):\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 3
Accuracy	78.5%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+136} \lor \neg \left(x \leq 8.4 \cdot 10^{+43}\right):\\ \;\;\;\;4 \cdot \frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \end{array} \]

Alternative 4
Accuracy	86.0%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.76 \cdot 10^{+47} \lor \neg \left(z \leq 1.85 \cdot 10^{-75}\right):\\ \;\;\;\;2 + -4 \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;2 + 4 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5
Accuracy	53.1%
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -0.059:\\ \;\;\;\;2\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+43}:\\ \;\;\;\;4 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;2\\ \end{array} \]

Alternative 6
Accuracy	9.8%
Cost	64

\[1 \]

Alternative 7
Accuracy	42.6%
Cost	64

\[2 \]

Reproduce

herbie shell --seed 2023151 
(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)))