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

Percentage Accurate: 96.1% → 99.0%

Time: 4.6s

Alternatives: 6

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y \cdot z\right) \end{array} \]

FPCore

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

C

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

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 - (y * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - y \cdot z\right) \end{array} \]

FPCore

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

C

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

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 - (y * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+70}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) (- INFINITY)) (not (<= (* y z) 2e+70)))
   (* z (* y (- x)))
   (- x (* (* y z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -((double) INFINITY)) || !((y * z) <= 2e+70)) {
		tmp = z * (y * -x);
	} else {
		tmp = x - ((y * z) * x);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -Double.POSITIVE_INFINITY) || !((y * z) <= 2e+70)) {
		tmp = z * (y * -x);
	} else {
		tmp = x - ((y * z) * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((y * z) <= -math.inf) or not ((y * z) <= 2e+70):
		tmp = z * (y * -x)
	else:
		tmp = x - ((y * z) * x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= Float64(-Inf)) || !(Float64(y * z) <= 2e+70))
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = Float64(x - Float64(Float64(y * z) * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((y * z) <= -Inf) || ~(((y * z) <= 2e+70)))
		tmp = z * (y * -x);
	else
		tmp = x - ((y * z) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], (-Infinity)], N[Not[LessEqual[N[(y * z), $MachinePrecision], 2e+70]], $MachinePrecision]], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -inf.0 or 2.00000000000000015e70 < (*.f64 y z)

   1. Initial program 78.2%

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

   2. Taylor expanded in x around 0 78.2%

      \[\leadsto \color{blue}{\left(1 - y \cdot z\right) \cdot x} \]
   3. Step-by-step derivation

      1. *-commutative 78.2%

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

      2. distribute-rgt-out-- 78.2%

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

      3. associate-*r* 98.4%

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

      4. *-lft-identity 98.4%

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

   4. Simplified 98.4%

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

   5. Taylor expanded in y around inf 98.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 98.4%

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

      2. associate-*r* 78.2%

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

      3. distribute-rgt-neg-in 78.2%

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

      4. *-commutative 78.2%

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

      5. associate-*r* 99.8%

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

   7. Simplified 99.8%

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

   if -inf.0 < (*.f64 y z) < 2.00000000000000015e70

   1. Initial program 99.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Step-by-step derivation

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

   3. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{x + \left(y \cdot \left(-z\right)\right) \cdot x} \]
   4. Step-by-step derivation

      1. distribute-rgt-neg-out 99.9%

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

      2. cancel-sign-sub-inv 99.9%

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

      3. *-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+70}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \]

Alternative 2: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+70}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) (- INFINITY)) (not (<= (* y z) 2e+70)))
   (* z (* y (- x)))
   (* x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -((double) INFINITY)) || !((y * z) <= 2e+70)) {
		tmp = z * (y * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -Double.POSITIVE_INFINITY) || !((y * z) <= 2e+70)) {
		tmp = z * (y * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((y * z) <= -math.inf) or not ((y * z) <= 2e+70):
		tmp = z * (y * -x)
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= Float64(-Inf)) || !(Float64(y * z) <= 2e+70))
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((y * z) <= -Inf) || ~(((y * z) <= 2e+70)))
		tmp = z * (y * -x);
	else
		tmp = x * (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(y * z), $MachinePrecision], (-Infinity)], N[Not[LessEqual[N[(y * z), $MachinePrecision], 2e+70]], $MachinePrecision]], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -inf.0 or 2.00000000000000015e70 < (*.f64 y z)

   1. Initial program 78.2%

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

   2. Taylor expanded in x around 0 78.2%

      \[\leadsto \color{blue}{\left(1 - y \cdot z\right) \cdot x} \]
   3. Step-by-step derivation

      1. *-commutative 78.2%

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

      2. distribute-rgt-out-- 78.2%

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

      3. associate-*r* 98.4%

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

      4. *-lft-identity 98.4%

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

   4. Simplified 98.4%

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

   5. Taylor expanded in y around inf 98.4%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 98.4%

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

      2. associate-*r* 78.2%

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

      3. distribute-rgt-neg-in 78.2%

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

      4. *-commutative 78.2%

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

      5. associate-*r* 99.8%

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

   7. Simplified 99.8%

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

   if -inf.0 < (*.f64 y z) < 2.00000000000000015e70

   1. Initial program 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+70}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 3: 68.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.000112 \lor \neg \left(y \leq 1.5 \cdot 10^{-146}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.000112) (not (<= y 1.5e-146))) (* (* y z) (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.000112) || !(y <= 1.5e-146)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	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
    real(8) :: tmp
    if ((y <= (-0.000112d0)) .or. (.not. (y <= 1.5d-146))) then
        tmp = (y * z) * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.000112) || !(y <= 1.5e-146)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.000112) or not (y <= 1.5e-146):
		tmp = (y * z) * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.000112) || !(y <= 1.5e-146))
		tmp = Float64(Float64(y * z) * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.000112) || ~((y <= 1.5e-146)))
		tmp = (y * z) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.000112], N[Not[LessEqual[y, 1.5e-146]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.11999999999999998e-4 or 1.50000000000000009e-146 < y

   1. Initial program 90.3%

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

   2. Taylor expanded in y around inf 64.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot x\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 64.6%

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

      2. associate-*r* 60.0%

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

      3. distribute-lft-neg-in 60.0%

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

      4. distribute-rgt-neg-out 60.0%

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

      5. *-commutative 60.0%

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

   4. Simplified 60.0%

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

   if -1.11999999999999998e-4 < y < 1.50000000000000009e-146

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 73.2%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.000112 \lor \neg \left(y \leq 1.5 \cdot 10^{-146}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.000105 \lor \neg \left(y \leq 1.95 \cdot 10^{-185}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.000105) (not (<= y 1.95e-185))) (* y (* z (- x))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.000105) || !(y <= 1.95e-185)) {
		tmp = y * (z * -x);
	} else {
		tmp = x;
	}
	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
    real(8) :: tmp
    if ((y <= (-0.000105d0)) .or. (.not. (y <= 1.95d-185))) then
        tmp = y * (z * -x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.000105) || !(y <= 1.95e-185)) {
		tmp = y * (z * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.000105) or not (y <= 1.95e-185):
		tmp = y * (z * -x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.000105) || !(y <= 1.95e-185))
		tmp = Float64(y * Float64(z * Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.000105) || ~((y <= 1.95e-185)))
		tmp = y * (z * -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.000105], N[Not[LessEqual[y, 1.95e-185]], $MachinePrecision]], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e-4 or 1.95e-185 < y

   1. Initial program 90.7%

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

   2. Taylor expanded in y around inf 62.1%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot x\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 62.1%

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

      2. distribute-rgt-neg-in 62.1%

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

      3. distribute-lft-neg-out 62.1%

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

      4. *-commutative 62.1%

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

   4. Simplified 62.1%

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

   if -1.05e-4 < y < 1.95e-185

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 73.2%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.000105 \lor \neg \left(y \leq 1.95 \cdot 10^{-185}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 68.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.000112:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-185}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.000112)
   (* z (* y (- x)))
   (if (<= y 1.95e-185) x (* y (* z (- x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.000112) {
		tmp = z * (y * -x);
	} else if (y <= 1.95e-185) {
		tmp = x;
	} else {
		tmp = y * (z * -x);
	}
	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
    real(8) :: tmp
    if (y <= (-0.000112d0)) then
        tmp = z * (y * -x)
    else if (y <= 1.95d-185) then
        tmp = x
    else
        tmp = y * (z * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.000112) {
		tmp = z * (y * -x);
	} else if (y <= 1.95e-185) {
		tmp = x;
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.000112:
		tmp = z * (y * -x)
	elif y <= 1.95e-185:
		tmp = x
	else:
		tmp = y * (z * -x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.000112)
		tmp = Float64(z * Float64(y * Float64(-x)));
	elseif (y <= 1.95e-185)
		tmp = x;
	else
		tmp = Float64(y * Float64(z * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.000112)
		tmp = z * (y * -x);
	elseif (y <= 1.95e-185)
		tmp = x;
	else
		tmp = y * (z * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.000112], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e-185], x, N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.11999999999999998e-4

   1. Initial program 88.6%

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

   2. Taylor expanded in x around 0 88.6%

      \[\leadsto \color{blue}{\left(1 - y \cdot z\right) \cdot x} \]
   3. Step-by-step derivation

      1. *-commutative 88.6%

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

      2. distribute-rgt-out-- 88.6%

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

      3. associate-*r* 96.5%

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

      4. *-lft-identity 96.5%

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

   4. Simplified 96.5%

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

   5. Taylor expanded in y around inf 77.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot x\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 77.9%

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

      2. associate-*r* 70.1%

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

      3. distribute-rgt-neg-in 70.1%

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

      4. *-commutative 70.1%

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

      5. associate-*r* 81.4%

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

   7. Simplified 81.4%

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

   if -1.11999999999999998e-4 < y < 1.95e-185

   1. Initial program 99.8%

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

   2. Taylor expanded in y around 0 73.2%

      \[\leadsto \color{blue}{x} \]

   if 1.95e-185 < y

   1. Initial program 92.2%

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

   2. Taylor expanded in y around inf 51.3%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(z \cdot x\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 51.3%

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

      2. distribute-rgt-neg-in 51.3%

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

      3. distribute-lft-neg-out 51.3%

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

      4. *-commutative 51.3%

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

   4. Simplified 51.3%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.000112:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-185}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 6: 51.3% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

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

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
end function

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 94.0%

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

2. Taylor expanded in y around 0 48.0%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 48.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023196 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))