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

Average Error: 5.12% → 0.24%

Time: 7.5s

Precision: binary64

Cost: 1353

Math

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

↓

\[\begin{array}{l} t_0 := \left(1 - y\right) \cdot z\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+217} \lor \neg \left(t_0 \leq 2 \cdot 10^{+301}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - t_0\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (- 1.0 y) z)))
   (if (or (<= t_0 -2e+217) (not (<= t_0 2e+301)))
     (* z (* x (+ y -1.0)))
     (* x (- 1.0 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 = (1.0 - y) * z;
	double tmp;
	if ((t_0 <= -2e+217) || !(t_0 <= 2e+301)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x * (1.0 - 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 = (1.0d0 - y) * z
    if ((t_0 <= (-2d+217)) .or. (.not. (t_0 <= 2d+301))) then
        tmp = z * (x * (y + (-1.0d0)))
    else
        tmp = x * (1.0d0 - 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 = (1.0 - y) * z;
	double tmp;
	if ((t_0 <= -2e+217) || !(t_0 <= 2e+301)) {
		tmp = z * (x * (y + -1.0));
	} else {
		tmp = x * (1.0 - 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 = (1.0 - y) * z
	tmp = 0
	if (t_0 <= -2e+217) or not (t_0 <= 2e+301):
		tmp = z * (x * (y + -1.0))
	else:
		tmp = x * (1.0 - 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(Float64(1.0 - y) * z)
	tmp = 0.0
	if ((t_0 <= -2e+217) || !(t_0 <= 2e+301))
		tmp = Float64(z * Float64(x * Float64(y + -1.0)));
	else
		tmp = Float64(x * Float64(1.0 - 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 = (1.0 - y) * z;
	tmp = 0.0;
	if ((t_0 <= -2e+217) || ~((t_0 <= 2e+301)))
		tmp = z * (x * (y + -1.0));
	else
		tmp = x * (1.0 - 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[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -2e+217], N[Not[LessEqual[t$95$0, 2e+301]], $MachinePrecision]], N[(z * N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]]]

Target

Original	5.12%
Target	0.33%
Herbie	0.24%

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 1 y) z) < -1.99999999999999992e217 or 2.00000000000000011e301 < (*.f64 (-.f64 1 y) z)

   1. Initial program 48.22

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

   2. Taylor expanded in z around inf 1.25

      \[\leadsto \color{blue}{z \cdot \left(\left(y - 1\right) \cdot x\right)} \]

   if -1.99999999999999992e217 < (*.f64 (-.f64 1 y) z) < 2.00000000000000011e301

   1. Initial program 0.12

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.24

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -2 \cdot 10^{+217} \lor \neg \left(\left(1 - y\right) \cdot z \leq 2 \cdot 10^{+301}\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	31.7%
Cost	848

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+47}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Error	31.7%
Cost	848

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{+47}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-16}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;z \leq 10^{-6}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+117}:\\ \;\;\;\;y \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 3
Error	19.44%
Cost	848

\[\begin{array}{l} t_0 := y \cdot \left(z \cdot x\right)\\ \mathbf{if}\;y \leq -540000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{+109}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+152}:\\ \;\;\;\;z \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+223}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Error	14.92%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-15} \lor \neg \left(z \leq 7.6\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 5
Error	1.62%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -1.05 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(x \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]

Alternative 6
Error	30.71%
Cost	652

\[\begin{array}{l} t_0 := z \cdot \left(-x\right)\\ \mathbf{if}\;z \leq -3.7 \cdot 10^{+48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	30.39%
Cost	521

\[\begin{array}{l} \mathbf{if}\;z \leq -10800000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;z \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	51.5%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023102 
(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))))