Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J

Average Error: 3.5 → 0.2

Time: 12.5s

Precision: binary64

Cost: 840

Math

\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

↓

\[\begin{array}{l} t_0 := x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+47}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(\left(y - 1\right) \cdot x\right) + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* (- 1.0 y) z)))))
   (if (<= x -2e+47) t_0 (if (<= x 2.5e+49) (+ (* z (* (- y 1.0) x)) x) t_0))))

C

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

↓

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double tmp;
	if (x <= -2e+47) {
		tmp = t_0;
	} else if (x <= 2.5e+49) {
		tmp = (z * ((y - 1.0) * x)) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

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

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (1.0d0 - ((1.0d0 - y) * z))
    if (x <= (-2d+47)) then
        tmp = t_0
    else if (x <= 2.5d+49) then
        tmp = (z * ((y - 1.0d0) * x)) + x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double tmp;
	if (x <= -2e+47) {
		tmp = t_0;
	} else if (x <= 2.5e+49) {
		tmp = (z * ((y - 1.0) * x)) + x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	t_0 = x * (1.0 - ((1.0 - y) * z))
	tmp = 0
	if x <= -2e+47:
		tmp = t_0
	elif x <= 2.5e+49:
		tmp = (z * ((y - 1.0) * x)) + x
	else:
		tmp = t_0
	return tmp

Julia

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

↓

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
	tmp = 0.0
	if (x <= -2e+47)
		tmp = t_0;
	elseif (x <= 2.5e+49)
		tmp = Float64(Float64(z * Float64(Float64(y - 1.0) * x)) + x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - ((1.0 - y) * z));
	tmp = 0.0;
	if (x <= -2e+47)
		tmp = t_0;
	elseif (x <= 2.5e+49)
		tmp = (z * ((y - 1.0) * x)) + x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e+47], t$95$0, If[LessEqual[x, 2.5e+49], N[(N[(z * N[(N[(y - 1.0), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Target

Original	3.5
Target	0.2
Herbie	0.2

\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if x < -2.0000000000000001e47 or 2.5000000000000002e49 < x

   1. Initial program 0.1

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   if -2.0000000000000001e47 < x < 2.5000000000000002e49

   1. Initial program 5.1

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 0.2

      \[\leadsto \color{blue}{z \cdot \left(\left(y - 1\right) \cdot x\right) + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+47}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+49}:\\ \;\;\;\;z \cdot \left(\left(y - 1\right) \cdot x\right) + x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	2.3
Cost	964

\[\begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t_0 \leq 10^{+280}:\\ \;\;\;\;x \cdot \left(1 - t_0\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \end{array} \]

Alternative 2
Error	21.8
Cost	784

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 10^{-159}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.00012:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	4.1
Cost	712

\[\begin{array}{l} t_0 := \left(y \cdot z + 1\right) \cdot x\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;z \cdot \left(-x\right) + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	4.1
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;\left(y \cdot z + 1\right) \cdot x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;z \cdot \left(-x\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 5
Error	2.2
Cost	712

\[\begin{array}{l} t_0 := y \cdot \left(z \cdot x\right) + x\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;z \cdot \left(-x\right) + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	11.8
Cost	648

\[\begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \left(-x\right) + x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 7
Error	11.8
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+97}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 8
Error	19.7
Cost	520

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.00012:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Error	33.6
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023074 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (if (< (* x (- 1.0 (* (- 1.0 y) z))) -1.618195973607049e+50) (+ x (* (- 1.0 y) (* (- z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (- z) x)))))

  (* x (- 1.0 (* (- 1.0 y) z))))