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

Percentage Accurate: 96.1% → 97.7%

Time: 5.4s

Alternatives: 7

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: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+118}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -5e+118) (* z (* y (- x))) (- x (* (* y z) x))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5e+118) {
		tmp = z * (y * -x);
	} else {
		tmp = x - ((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 * z) <= (-5d+118)) then
        tmp = z * (y * -x)
    else
        tmp = x - ((y * z) * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5e+118) {
		tmp = z * (y * -x);
	} else {
		tmp = x - ((y * z) * x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= -5e+118:
		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) <= -5e+118)
		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) <= -5e+118)
		tmp = z * (y * -x);
	else
		tmp = x - ((y * z) * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -5e+118], 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) < -4.99999999999999972e118

   1. Initial program 84.1%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.9%

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

   4. Taylor expanded in y around inf 99.9%

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

      1. neg-mul-1 99.9%

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

      2. *-commutative 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

   6. Simplified 99.9%

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

   if -4.99999999999999972e118 < (*.f64 y z)

   1. Initial program 98.1%

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

      1. sub-neg 98.1%

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

      2. distribute-rgt-in 98.2%

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

      3. *-un-lft-identity 98.2%

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

      4. distribute-rgt-neg-in 98.2%

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

   4. Applied egg-rr 98.2%

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

      1. associate-*l* 92.5%

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

      2. add-sqr-sqrt 45.0%

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

      3. sqrt-unprod 63.1%

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

      4. sqr-neg 63.1%

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

      5. sqrt-unprod 23.5%

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

      6. add-sqr-sqrt 52.4%

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

      7. cancel-sign-sub-inv 52.4%

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

      8. associate-*l* 55.1%

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

      9. *-commutative 55.1%

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

      10. *-commutative 55.1%

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

      11. distribute-lft-neg-out 55.1%

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

      12. distribute-rgt-neg-out 55.1%

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

      13. associate-*l* 52.4%

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

      14. add-sqr-sqrt 23.5%

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

      15. sqrt-unprod 63.1%

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

      16. sqr-neg 63.1%

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

      17. sqrt-unprod 45.0%

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

      18. add-sqr-sqrt 92.5%

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

      19. associate-*l* 98.2%

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

      20. *-commutative 98.2%

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

   6. Applied egg-rr 98.2%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+118}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 69.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+39} \lor \neg \left(y \leq 2.65 \cdot 10^{-120}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.6e+39) (not (<= y 2.65e-120))) (* (* y z) (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.6e+39) || !(y <= 2.65e-120)) {
		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 <= (-1.6d+39)) .or. (.not. (y <= 2.65d-120))) 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 <= -1.6e+39) || !(y <= 2.65e-120)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.6e+39) or not (y <= 2.65e-120):
		tmp = (y * z) * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.6e+39) || !(y <= 2.65e-120))
		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 <= -1.6e+39) || ~((y <= 2.65e-120)))
		tmp = (y * z) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.6e+39], N[Not[LessEqual[y, 2.65e-120]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.59999999999999996e39 or 2.64999999999999999e-120 < y

   1. Initial program 93.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 65.9%

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

      1. mul-1-neg 65.9%

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

      2. distribute-rgt-neg-out 65.9%

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

   5. Simplified 65.9%

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

   if -1.59999999999999996e39 < y < 2.64999999999999999e-120

   1. Initial program 99.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.7%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+39} \lor \neg \left(y \leq 2.65 \cdot 10^{-120}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+39}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.5e+39)
   (* (* z x) (- y))
   (if (<= y 2.65e-120) x (* (* y z) (- x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.5e+39) {
		tmp = (z * x) * -y;
	} else if (y <= 2.65e-120) {
		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 <= (-1.5d+39)) then
        tmp = (z * x) * -y
    else if (y <= 2.65d-120) 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 <= -1.5e+39) {
		tmp = (z * x) * -y;
	} else if (y <= 2.65e-120) {
		tmp = x;
	} else {
		tmp = (y * z) * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.5e+39:
		tmp = (z * x) * -y
	elif y <= 2.65e-120:
		tmp = x
	else:
		tmp = (y * z) * -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.5e+39)
		tmp = Float64(Float64(z * x) * Float64(-y));
	elseif (y <= 2.65e-120)
		tmp = x;
	else
		tmp = Float64(Float64(y * z) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.5e+39)
		tmp = (z * x) * -y;
	elseif (y <= 2.65e-120)
		tmp = x;
	else
		tmp = (y * z) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.5e+39], N[(N[(z * x), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[y, 2.65e-120], x, N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.5e39

   1. Initial program 84.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 74.0%

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

      1. mul-1-neg 74.0%

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

      2. *-commutative 74.0%

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

      3. associate-*r* 87.1%

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

      4. distribute-rgt-neg-in 87.1%

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

   5. Simplified 87.1%

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

   if -1.5e39 < y < 2.64999999999999999e-120

   1. Initial program 99.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.7%

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

   if 2.64999999999999999e-120 < y

   1. Initial program 99.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. distribute-rgt-neg-out 59.0%

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

   5. Simplified 59.0%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+39}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+37}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.6e+37)
   (* z (* y (- x)))
   (if (<= y 2.65e-120) x (* (* y z) (- x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.6e+37) {
		tmp = z * (y * -x);
	} else if (y <= 2.65e-120) {
		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 <= (-7.6d+37)) then
        tmp = z * (y * -x)
    else if (y <= 2.65d-120) 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 <= -7.6e+37) {
		tmp = z * (y * -x);
	} else if (y <= 2.65e-120) {
		tmp = x;
	} else {
		tmp = (y * z) * -x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.6e+37:
		tmp = z * (y * -x)
	elif y <= 2.65e-120:
		tmp = x
	else:
		tmp = (y * z) * -x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.6e+37)
		tmp = Float64(z * Float64(y * Float64(-x)));
	elseif (y <= 2.65e-120)
		tmp = x;
	else
		tmp = Float64(Float64(y * z) * Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.6e+37)
		tmp = z * (y * -x);
	elseif (y <= 2.65e-120)
		tmp = x;
	else
		tmp = (y * z) * -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.6e+37], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.65e-120], x, N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.59999999999999979e37

   1. Initial program 84.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 90.3%

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

   4. Taylor expanded in y around inf 82.2%

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

      1. neg-mul-1 82.2%

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

      2. *-commutative 82.2%

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

      3. distribute-rgt-neg-in 82.2%

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

   6. Simplified 82.2%

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

   if -7.59999999999999979e37 < y < 2.64999999999999999e-120

   1. Initial program 99.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 74.7%

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

   if 2.64999999999999999e-120 < y

   1. Initial program 99.9%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. distribute-rgt-neg-out 59.0%

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

   5. Simplified 59.0%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+37}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+118}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -5e+118) (* z (* y (- x))) (* x (- 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5e+118) {
		tmp = z * (y * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	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 * z) <= (-5d+118)) then
        tmp = z * (y * -x)
    else
        tmp = x * (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5e+118) {
		tmp = z * (y * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= -5e+118:
		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) <= -5e+118)
		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) <= -5e+118)
		tmp = z * (y * -x);
	else
		tmp = x * (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -5e+118], 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) < -4.99999999999999972e118

   1. Initial program 84.1%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 99.9%

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

   4. Taylor expanded in y around inf 99.9%

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

      1. neg-mul-1 99.9%

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

      2. *-commutative 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

   6. Simplified 99.9%

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

   if -4.99999999999999972e118 < (*.f64 y z)

   1. Initial program 98.1%

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

Alternative 6: 51.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.8 \cdot 10^{+234}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 1.8e+234) x (/ (* z x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.8e+234) {
		tmp = x;
	} else {
		tmp = (z * x) / z;
	}
	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 <= 1.8d+234) then
        tmp = x
    else
        tmp = (z * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.8e+234) {
		tmp = x;
	} else {
		tmp = (z * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.8e+234:
		tmp = x
	else:
		tmp = (z * x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.8e+234)
		tmp = x;
	else
		tmp = Float64(Float64(z * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.8e+234)
		tmp = x;
	else
		tmp = (z * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.8e+234], x, N[(N[(z * x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.8e234

   1. Initial program 96.7%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 50.3%

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

   if 1.8e234 < z

   1. Initial program 82.0%

      \[x \cdot \left(1 - y \cdot z\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 93.6%

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

   4. Taylor expanded in y around 0 2.5%

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

      1. associate-*r/ 23.0%

         \[\leadsto \color{blue}{\frac{z \cdot x}{z}} \]

      2. *-commutative 23.0%

         \[\leadsto \frac{\color{blue}{x \cdot z}}{z} \]

   6. Applied egg-rr 23.0%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.8 \cdot 10^{+234}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.5% 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 95.8%

   \[x \cdot \left(1 - y \cdot z\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0 47.5%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))