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

Average Error: 3.3 → 0.1

Time: 10.8s

Precision: binary64

Cost: 840

Math

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

↓

\[\begin{array}{l} t_0 := x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{-29}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+25}:\\ \;\;\;\;z \cdot \left(\left(y - 1\right) \cdot x\right) + x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

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 -4e-29) t_0 (if (<= x 5e+25) (+ (* 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 <= -4e-29) {
		tmp = t_0;
	} else if (x <= 5e+25) {
		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 <= (-4d-29)) then
        tmp = t_0
    else if (x <= 5d+25) 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 <= -4e-29) {
		tmp = t_0;
	} else if (x <= 5e+25) {
		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 <= -4e-29:
		tmp = t_0
	elif x <= 5e+25:
		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 <= -4e-29)
		tmp = t_0;
	elseif (x <= 5e+25)
		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 <= -4e-29)
		tmp = t_0;
	elseif (x <= 5e+25)
		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, -4e-29], t$95$0, If[LessEqual[x, 5e+25], N[(N[(z * N[(N[(y - 1.0), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision], t$95$0]]]

Target

Original	3.3
Target	0.3
Herbie	0.1

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

Derivation

1. Split input into 2 regimes

2. if x < -3.99999999999999977e-29 or 5.00000000000000024e25 < x

   1. Initial program 0.1

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

   if -3.99999999999999977e-29 < x < 5.00000000000000024e25

   1. Initial program 5.5

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

   2. Taylor expanded in z around 0 0.1

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

4. Final simplification 0.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+25}:\\ \;\;\;\;z \cdot \left(\left(y - 1\right) \cdot x\right) + x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	1.7
Cost	964

\[\begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t_0 \leq 10^{+255}:\\ \;\;\;\;x \cdot \left(1 - t_0\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - 1\right) \cdot x\right)\\ \end{array} \]

Alternative 2
Error	19.8
Cost	716

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 110000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	19.7
Cost	716

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-41}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2700000000000:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	9.6
Cost	712

\[\begin{array}{l} t_0 := z \cdot \left(\left(y - 1\right) \cdot x\right)\\ \mathbf{if}\;z \leq -20:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-41}:\\ \;\;\;\;x - x \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 5
Error	1.3
Cost	712

\[\begin{array}{l} t_0 := z \cdot \left(\left(y - 1\right) \cdot x\right)\\ \mathbf{if}\;z \leq -310000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-14}:\\ \;\;\;\;x + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 6
Error	13.6
Cost	584

\[\begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+208}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+105}:\\ \;\;\;\;\left(1 - z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \end{array} \]

Alternative 7
Error	19.5
Cost	520

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

Alternative 8
Error	33.7
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023064 
(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))))