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

Average Error: 0.2 → 0.0

Time: 5.4s

Precision: binary64

Cost: 576

Math

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

↓

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

FPCore

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

↓

(FPCore (x y z) :precision binary64 (+ 4.0 (* 4.0 (/ (- x 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 4.0 + (4.0 * ((x - 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 = 4.0d0 + (4.0d0 * ((x - 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 4.0 + (4.0 * ((x - 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 4.0 + (4.0 * ((x - 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(4.0 + Float64(4.0 * Float64(Float64(x - 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 = 4.0 + (4.0 * ((x - 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[(4.0 + N[(4.0 * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.2

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

2. Taylor expanded in y around 0 0.0

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

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	31.1
Cost	1240

\[\begin{array}{l} t_0 := 1 + \frac{z}{y} \cdot -4\\ t_1 := 1 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+156}:\\ \;\;\;\;4\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-187}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4500000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;4\\ \end{array} \]

Alternative 2
Error	13.9
Cost	976

\[\begin{array}{l} t_0 := 4 + -4 \cdot \frac{z}{y}\\ t_1 := 1 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+147}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+55}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	9.5
Cost	976

\[\begin{array}{l} t_0 := 4 + 4 \cdot \frac{x}{y}\\ t_1 := 4 + -4 \cdot \frac{z}{y}\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+74}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-34}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	29.5
Cost	712

\[\begin{array}{l} t_0 := 1 + 4 \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{-59}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+55}:\\ \;\;\;\;4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	58.1
Cost	64

\[1 \]

Alternative 6
Error	36.5
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)))