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

Average Accuracy: 94.4% → 99.7%

Time: 4.8s

Precision: binary64

Cost: 968

\[ \begin{array}{c}[y, z] = \mathsf{sort}([y, z])\\ \end{array} \]

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 10^{+187}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) (- INFINITY))
   (* y (* z (- x)))
   (if (<= (* y z) 1e+187) (* x (- 1.0 (* y z))) (* z (* y (- x))))))

C

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

↓

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -((double) INFINITY)) {
		tmp = y * (z * -x);
	} else if ((y * z) <= 1e+187) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = z * (y * -x);
	}
	return tmp;
}

Java

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

↓

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -Double.POSITIVE_INFINITY) {
		tmp = y * (z * -x);
	} else if ((y * z) <= 1e+187) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = z * (y * -x);
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	tmp = 0
	if (y * z) <= -math.inf:
		tmp = y * (z * -x)
	elif (y * z) <= 1e+187:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = z * (y * -x)
	return tmp

Julia

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

↓

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= Float64(-Inf))
		tmp = Float64(y * Float64(z * Float64(-x)));
	elseif (Float64(y * z) <= 1e+187)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(z * Float64(y * Float64(-x)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -Inf)
		tmp = y * (z * -x);
	elseif ((y * z) <= 1e+187)
		tmp = x * (1.0 - (y * z));
	else
		tmp = z * (y * -x);
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], (-Infinity)], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 1e+187], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -inf.0

   1. Initial program 0.0%

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

   2. Taylor expanded in y around inf 99.6%

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

   3. Simplified 99.6%

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

      [Start] 99.6	\[ -1 \cdot \left(y \cdot \left(z \cdot x\right)\right) \]
      mul-1-neg [=>] 99.6	\[ \color{blue}{-y \cdot \left(z \cdot x\right)} \]
      distribute-rgt-neg-in [=>] 99.6	\[ \color{blue}{y \cdot \left(-z \cdot x\right)} \]
      distribute-lft-neg-out [<=] 99.6	\[ y \cdot \color{blue}{\left(\left(-z\right) \cdot x\right)} \]
      *-commutative [=>] 99.6	\[ y \cdot \color{blue}{\left(x \cdot \left(-z\right)\right)} \]

   if -inf.0 < (*.f64 y z) < 9.99999999999999907e186

   1. Initial program 99.8%

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

   if 9.99999999999999907e186 < (*.f64 y z)

   1. Initial program 60.0%

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

   2. Taylor expanded in x around 0 60.0%

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

   3. Simplified 97.3%

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

      [Start] 60.0	\[ \left(1 - y \cdot z\right) \cdot x \]
      *-commutative [=>] 60.0	\[ \color{blue}{x \cdot \left(1 - y \cdot z\right)} \]
      distribute-rgt-out-- [<=] 60.0	\[ \color{blue}{1 \cdot x - \left(y \cdot z\right) \cdot x} \]
      associate-*r* [<=] 97.3	\[ 1 \cdot x - \color{blue}{y \cdot \left(z \cdot x\right)} \]
      *-lft-identity [=>] 97.3	\[ \color{blue}{x} - y \cdot \left(z \cdot x\right) \]

   4. Taylor expanded in y around inf 97.3%

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

   5. Simplified 98.3%

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

      [Start] 97.3	\[ -1 \cdot \left(y \cdot \left(z \cdot x\right)\right) \]
      associate-*r* [=>] 97.3	\[ \color{blue}{\left(-1 \cdot y\right) \cdot \left(z \cdot x\right)} \]
      neg-mul-1 [<=] 97.3	\[ \color{blue}{\left(-y\right)} \cdot \left(z \cdot x\right) \]
      *-commutative [=>] 97.3	\[ \left(-y\right) \cdot \color{blue}{\left(x \cdot z\right)} \]
      associate-*l* [<=] 98.3	\[ \color{blue}{\left(\left(-y\right) \cdot x\right) \cdot z} \]
      *-commutative [=>] 98.3	\[ \color{blue}{z \cdot \left(\left(-y\right) \cdot x\right)} \]
      distribute-lft-neg-out [=>] 98.3	\[ z \cdot \color{blue}{\left(-y \cdot x\right)} \]

3. Recombined 3 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 10^{+187}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	70.1%
Cost	914

\[\begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+176} \lor \neg \left(y \leq -2.25 \cdot 10^{+144} \lor \neg \left(y \leq -9.8 \cdot 10^{+118}\right) \land y \leq 3 \cdot 10^{-80}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Accuracy	72.7%
Cost	914

\[\begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+176} \lor \neg \left(y \leq -1.05 \cdot 10^{+142}\right) \land \left(y \leq -1.22 \cdot 10^{+121} \lor \neg \left(y \leq 4.3 \cdot 10^{-73}\right)\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3
Accuracy	72.5%
Cost	912

\[\begin{array}{l} t_0 := z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+176}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{+142}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -6.8 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-75}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 4
Accuracy	60.5%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023151 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))