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

Percentage Accurate: 95.9% → 97.9%

Time: 4.8s

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: 95.9% 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: 97.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 y z))) < -inf.0

   1. Initial program 79.9%

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

   2. Taylor expanded in y around 0 79.9%

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

      1. mul-1-neg 79.9%

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

      2. unsub-neg 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in y around inf 79.9%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. neg-mul-1 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

   7. Simplified 100.0%

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

   if -inf.0 < (*.f64 x (-.f64 1 (*.f64 y z)))

   1. Initial program 99.0%

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

   2. Taylor expanded in y around 0 99.1%

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

      1. mul-1-neg 99.1%

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

      2. unsub-neg 99.1%

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

   4. Simplified 99.1%

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

4. Final simplification 99.2%

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

Alternative 2: 69.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-125}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+27}:\\ \;\;\;\;\left(-y\right) \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x (- y)))))
   (if (<= z -2.8e-125)
     t_0
     (if (<= z 2.5e-5)
       x
       (if (<= z 4e+27)
         (* (- y) (* x z))
         (if (<= z 1.95e+46)
           x
           (if (<= z 1.8e+125)
             (* x (* y (- z)))
             (if (<= z 2.8e+127) x t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * -y);
	double tmp;
	if (z <= -2.8e-125) {
		tmp = t_0;
	} else if (z <= 2.5e-5) {
		tmp = x;
	} else if (z <= 4e+27) {
		tmp = -y * (x * z);
	} else if (z <= 1.95e+46) {
		tmp = x;
	} else if (z <= 1.8e+125) {
		tmp = x * (y * -z);
	} else if (z <= 2.8e+127) {
		tmp = 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
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (x * -y)
    if (z <= (-2.8d-125)) then
        tmp = t_0
    else if (z <= 2.5d-5) then
        tmp = x
    else if (z <= 4d+27) then
        tmp = -y * (x * z)
    else if (z <= 1.95d+46) then
        tmp = x
    else if (z <= 1.8d+125) then
        tmp = x * (y * -z)
    else if (z <= 2.8d+127) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (x * -y);
	double tmp;
	if (z <= -2.8e-125) {
		tmp = t_0;
	} else if (z <= 2.5e-5) {
		tmp = x;
	} else if (z <= 4e+27) {
		tmp = -y * (x * z);
	} else if (z <= 1.95e+46) {
		tmp = x;
	} else if (z <= 1.8e+125) {
		tmp = x * (y * -z);
	} else if (z <= 2.8e+127) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * -y)
	tmp = 0
	if z <= -2.8e-125:
		tmp = t_0
	elif z <= 2.5e-5:
		tmp = x
	elif z <= 4e+27:
		tmp = -y * (x * z)
	elif z <= 1.95e+46:
		tmp = x
	elif z <= 1.8e+125:
		tmp = x * (y * -z)
	elif z <= 2.8e+127:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * Float64(-y)))
	tmp = 0.0
	if (z <= -2.8e-125)
		tmp = t_0;
	elseif (z <= 2.5e-5)
		tmp = x;
	elseif (z <= 4e+27)
		tmp = Float64(Float64(-y) * Float64(x * z));
	elseif (z <= 1.95e+46)
		tmp = x;
	elseif (z <= 1.8e+125)
		tmp = Float64(x * Float64(y * Float64(-z)));
	elseif (z <= 2.8e+127)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * -y);
	tmp = 0.0;
	if (z <= -2.8e-125)
		tmp = t_0;
	elseif (z <= 2.5e-5)
		tmp = x;
	elseif (z <= 4e+27)
		tmp = -y * (x * z);
	elseif (z <= 1.95e+46)
		tmp = x;
	elseif (z <= 1.8e+125)
		tmp = x * (y * -z);
	elseif (z <= 2.8e+127)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e-125], t$95$0, If[LessEqual[z, 2.5e-5], x, If[LessEqual[z, 4e+27], N[((-y) * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.95e+46], x, If[LessEqual[z, 1.8e+125], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.8e+127], x, t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.8e-125 or 2.8000000000000002e127 < z

   1. Initial program 93.3%

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

   2. Taylor expanded in y around 0 93.4%

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

      1. mul-1-neg 93.4%

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

      2. unsub-neg 93.4%

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

   4. Simplified 93.4%

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

   5. Taylor expanded in y around inf 59.3%

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

      1. associate-*r* 63.6%

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

      2. *-commutative 63.6%

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

      3. neg-mul-1 63.6%

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

      4. distribute-rgt-neg-in 63.6%

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

      5. distribute-rgt-neg-in 63.6%

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

   7. Simplified 63.6%

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

   if -2.8e-125 < z < 2.50000000000000012e-5 or 4.0000000000000001e27 < z < 1.94999999999999997e46 or 1.8000000000000002e125 < z < 2.8000000000000002e127

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 79.8%

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

   if 2.50000000000000012e-5 < z < 4.0000000000000001e27

   1. Initial program 99.5%

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

      1. flip-- 70.4%

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

      2. associate-*r/ 71.0%

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

      3. metadata-eval 71.0%

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

      4. pow2 71.0%

         \[\leadsto \frac{x \cdot \left(1 - \color{blue}{{\left(y \cdot z\right)}^{2}}\right)}{1 + y \cdot z} \]

   3. Applied egg-rr 71.0%

      \[\leadsto \color{blue}{\frac{x \cdot \left(1 - {\left(y \cdot z\right)}^{2}\right)}{1 + y \cdot z}} \]
   4. Step-by-step derivation

      1. associate-/l* 71.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{1 + y \cdot z}{1 - {\left(y \cdot z\right)}^{2}}}} \]

      2. +-commutative 71.0%

         \[\leadsto \frac{x}{\frac{\color{blue}{y \cdot z + 1}}{1 - {\left(y \cdot z\right)}^{2}}} \]

   5. Simplified 71.0%

      \[\leadsto \color{blue}{\frac{x}{\frac{y \cdot z + 1}{1 - {\left(y \cdot z\right)}^{2}}}} \]

   6. Taylor expanded in y around inf 76.7%

      \[\leadsto \frac{x}{\color{blue}{\frac{-1}{y \cdot z}}} \]
   7. Step-by-step derivation

      1. associate-/r/ 76.7%

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

      2. associate-*r* 48.2%

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

      3. div-inv 48.2%

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

      4. metadata-eval 48.2%

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

      5. associate-*r* 48.2%

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

      6. neg-mul-1 48.2%

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

      7. *-commutative 48.2%

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

      8. associate-*r* 77.2%

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

      9. neg-mul-1 77.2%

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

      10. associate-*r* 77.2%

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

   8. Applied egg-rr 77.2%

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

   9. Taylor expanded in z around 0 76.7%

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

       1. mul-1-neg 76.7%

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

       2. *-commutative 76.7%

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

       3. associate-*r* 77.2%

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

       4. distribute-rgt-neg-in 77.2%

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

   11. Simplified 77.2%

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

   if 1.94999999999999997e46 < z < 1.8000000000000002e125

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 56.0%

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

      1. mul-1-neg 56.0%

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

      2. distribute-rgt-neg-in 56.0%

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

      3. distribute-rgt-neg-out 56.0%

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

   4. Simplified 56.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(-z\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+27}:\\ \;\;\;\;\left(-y\right) \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 3: 97.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* y z)))))
   (if (<= t_0 (- INFINITY)) (* z (* x (- y))) t_0)))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = z * (x * -y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (x * -y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - (y * z))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = z * (x * -y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(y * z)))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(z * Float64(x * Float64(-y)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - (y * z));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = z * (x * -y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 y z))) < -inf.0

   1. Initial program 79.9%

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

   2. Taylor expanded in y around 0 79.9%

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

      1. mul-1-neg 79.9%

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

      2. unsub-neg 79.9%

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

   4. Simplified 79.9%

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

   5. Taylor expanded in y around inf 79.9%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. neg-mul-1 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

   7. Simplified 100.0%

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

   if -inf.0 < (*.f64 x (-.f64 1 (*.f64 y z)))

   1. Initial program 99.0%

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

4. Final simplification 99.2%

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

Alternative 4: 69.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-125}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x (- y)))))
   (if (<= z -2.8e-125)
     t_0
     (if (<= z 9e+45)
       x
       (if (<= z 3e+125) (* x (* y (- z))) (if (<= z 2.1e+127) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * -y);
	double tmp;
	if (z <= -2.8e-125) {
		tmp = t_0;
	} else if (z <= 9e+45) {
		tmp = x;
	} else if (z <= 3e+125) {
		tmp = x * (y * -z);
	} else if (z <= 2.1e+127) {
		tmp = 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
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (x * -y)
    if (z <= (-2.8d-125)) then
        tmp = t_0
    else if (z <= 9d+45) then
        tmp = x
    else if (z <= 3d+125) then
        tmp = x * (y * -z)
    else if (z <= 2.1d+127) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (x * -y);
	double tmp;
	if (z <= -2.8e-125) {
		tmp = t_0;
	} else if (z <= 9e+45) {
		tmp = x;
	} else if (z <= 3e+125) {
		tmp = x * (y * -z);
	} else if (z <= 2.1e+127) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * -y)
	tmp = 0
	if z <= -2.8e-125:
		tmp = t_0
	elif z <= 9e+45:
		tmp = x
	elif z <= 3e+125:
		tmp = x * (y * -z)
	elif z <= 2.1e+127:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * Float64(-y)))
	tmp = 0.0
	if (z <= -2.8e-125)
		tmp = t_0;
	elseif (z <= 9e+45)
		tmp = x;
	elseif (z <= 3e+125)
		tmp = Float64(x * Float64(y * Float64(-z)));
	elseif (z <= 2.1e+127)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * -y);
	tmp = 0.0;
	if (z <= -2.8e-125)
		tmp = t_0;
	elseif (z <= 9e+45)
		tmp = x;
	elseif (z <= 3e+125)
		tmp = x * (y * -z);
	elseif (z <= 2.1e+127)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e-125], t$95$0, If[LessEqual[z, 9e+45], x, If[LessEqual[z, 3e+125], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e+127], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e-125 or 2.09999999999999992e127 < z

   1. Initial program 93.3%

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

   2. Taylor expanded in y around 0 93.4%

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

      1. mul-1-neg 93.4%

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

      2. unsub-neg 93.4%

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

   4. Simplified 93.4%

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

   5. Taylor expanded in y around inf 59.3%

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

      1. associate-*r* 63.6%

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

      2. *-commutative 63.6%

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

      3. neg-mul-1 63.6%

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

      4. distribute-rgt-neg-in 63.6%

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

      5. distribute-rgt-neg-in 63.6%

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

   7. Simplified 63.6%

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

   if -2.8e-125 < z < 8.9999999999999997e45 or 3.00000000000000015e125 < z < 2.09999999999999992e127

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 77.8%

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

   if 8.9999999999999997e45 < z < 3.00000000000000015e125

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 56.0%

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

      1. mul-1-neg 56.0%

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

      2. distribute-rgt-neg-in 56.0%

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

      3. distribute-rgt-neg-out 56.0%

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

   4. Simplified 56.0%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-125}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+45}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot \left(-y\right)\right)\\ \end{array} \]

Alternative 5: 65.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-188} \lor \neg \left(z \leq 2.5 \cdot 10^{+46}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.4e-188) (not (<= z 2.5e+46))) (* x (* y (- z))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4e-188) || !(z <= 2.5e+46)) {
		tmp = x * (y * -z);
	} 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 ((z <= (-5.4d-188)) .or. (.not. (z <= 2.5d+46))) then
        tmp = x * (y * -z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.4e-188) || !(z <= 2.5e+46)) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.4e-188) or not (z <= 2.5e+46):
		tmp = x * (y * -z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.4e-188) || !(z <= 2.5e+46))
		tmp = Float64(x * Float64(y * Float64(-z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.4e-188) || ~((z <= 2.5e+46)))
		tmp = x * (y * -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.4e-188], N[Not[LessEqual[z, 2.5e+46]], $MachinePrecision]], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.4000000000000002e-188 or 2.5000000000000001e46 < z

   1. Initial program 94.7%

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

   2. Taylor expanded in y around inf 55.5%

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

      1. mul-1-neg 55.5%

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

      2. distribute-rgt-neg-in 55.5%

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

      3. distribute-rgt-neg-out 55.5%

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

   4. Simplified 55.5%

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

   if -5.4000000000000002e-188 < z < 2.5000000000000001e46

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 78.5%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-188} \lor \neg \left(z \leq 2.5 \cdot 10^{+46}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 50.8% 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 96.6%

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

2. Taylor expanded in y around 0 54.4%

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

3. Final simplification 54.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))