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

Percentage Accurate: 95.9% → 98.1%

Time: 6.7s

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: 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: 98.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -((double) INFINITY)) {
		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) {
		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:
		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))
		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)
		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], (-Infinity)], 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

   1. Initial program 58.3%

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

   3. Taylor expanded in z around inf 99.8%

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

   4. Taylor expanded in y around inf 99.8%

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

      1. neg-mul-1 99.8%

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

      2. distribute-lft-neg-in 99.8%

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

   6. Simplified 99.8%

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

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

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. distribute-rgt-in 98.3%

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

      3. *-un-lft-identity 98.3%

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

      4. distribute-rgt-neg-in 98.3%

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

   4. Applied egg-rr 98.3%

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

      1. associate-*l* 94.5%

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

      2. add-sqr-sqrt 44.3%

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

      3. sqrt-unprod 66.0%

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

      4. sqr-neg 66.0%

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

      5. sqrt-unprod 26.3%

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

      6. add-sqr-sqrt 50.7%

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

      7. cancel-sign-sub-inv 50.7%

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

      8. associate-*l* 52.3%

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

      9. distribute-rgt-neg-out 52.3%

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

      10. distribute-lft-neg-in 52.3%

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

      11. associate-*r* 50.7%

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

      12. add-sqr-sqrt 26.3%

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

      13. sqrt-unprod 66.0%

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

      14. sqr-neg 66.0%

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

      15. sqrt-unprod 44.3%

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

      16. add-sqr-sqrt 94.5%

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

      17. *-commutative 94.5%

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

      18. *-commutative 94.5%

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

      19. associate-*l* 98.3%

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

      20. *-commutative 98.3%

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

   6. Applied egg-rr 98.3%

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

4. Final simplification 98.4%

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

Alternative 2: 70.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-141} \lor \neg \left(z \leq 1.45 \cdot 10^{+84}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5e-141) (not (<= z 1.45e+84))) (* z (* y (- x))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5e-141) || !(z <= 1.45e+84)) {
		tmp = z * (y * -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 ((z <= (-5d-141)) .or. (.not. (z <= 1.45d+84))) then
        tmp = z * (y * -x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5e-141) || !(z <= 1.45e+84)) {
		tmp = z * (y * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5e-141) or not (z <= 1.45e+84):
		tmp = z * (y * -x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5e-141) || !(z <= 1.45e+84))
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5e-141) || ~((z <= 1.45e+84)))
		tmp = z * (y * -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5e-141], N[Not[LessEqual[z, 1.45e+84]], $MachinePrecision]], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999999e-141 or 1.44999999999999994e84 < z

   1. Initial program 92.3%

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

   3. Taylor expanded in z around inf 94.3%

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

   4. Taylor expanded in y around inf 68.2%

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

      1. neg-mul-1 68.2%

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

      2. distribute-lft-neg-in 68.2%

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

   6. Simplified 68.2%

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

   if -4.9999999999999999e-141 < z < 1.44999999999999994e84

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 73.3%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-141} \lor \neg \left(z \leq 1.45 \cdot 10^{+84}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+75} \lor \neg \left(y \leq 6.8 \cdot 10^{-118}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.8e+75) (not (<= y 6.8e-118))) (* (* y z) (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.8e+75) || !(y <= 6.8e-118)) {
		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 <= (-9.8d+75)) .or. (.not. (y <= 6.8d-118))) 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 <= -9.8e+75) || !(y <= 6.8e-118)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9.8e+75) or not (y <= 6.8e-118):
		tmp = (y * z) * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.8e+75) || !(y <= 6.8e-118))
		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 <= -9.8e+75) || ~((y <= 6.8e-118)))
		tmp = (y * z) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9.8e+75], N[Not[LessEqual[y, 6.8e-118]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -9.8000000000000002e75 or 6.79999999999999981e-118 < y

   1. Initial program 91.6%

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

   3. Taylor expanded in y around inf 66.0%

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

      1. mul-1-neg 66.0%

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

      2. distribute-rgt-neg-out 66.0%

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

   5. Simplified 66.0%

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

   if -9.8000000000000002e75 < y < 6.79999999999999981e-118

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 72.3%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{+75} \lor \neg \left(y \leq 6.8 \cdot 10^{-118}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.3e+97)
   (* z (* y (- x)))
   (if (<= y 2.05e-119) x (* y (* z (- x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.3e+97) {
		tmp = z * (y * -x);
	} else if (y <= 2.05e-119) {
		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 <= (-5.3d+97)) then
        tmp = z * (y * -x)
    else if (y <= 2.05d-119) 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 <= -5.3e+97) {
		tmp = z * (y * -x);
	} else if (y <= 2.05e-119) {
		tmp = x;
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.3e+97:
		tmp = z * (y * -x)
	elif y <= 2.05e-119:
		tmp = x
	else:
		tmp = y * (z * -x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.3e+97)
		tmp = Float64(z * Float64(y * Float64(-x)));
	elseif (y <= 2.05e-119)
		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 <= -5.3e+97)
		tmp = z * (y * -x);
	elseif (y <= 2.05e-119)
		tmp = x;
	else
		tmp = y * (z * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.3e+97], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.05e-119], x, N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.3000000000000003e97

   1. Initial program 85.5%

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

   3. Taylor expanded in z around inf 85.0%

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

   4. Taylor expanded in y around inf 82.9%

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

      1. neg-mul-1 82.9%

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

      2. distribute-lft-neg-in 82.9%

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

   6. Simplified 82.9%

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

   if -5.3000000000000003e97 < y < 2.0500000000000001e-119

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 71.0%

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

   if 2.0500000000000001e-119 < y

   1. Initial program 94.1%

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

   3. Taylor expanded in y around inf 61.0%

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

      1. mul-1-neg 61.0%

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

      2. *-commutative 61.0%

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

      3. associate-*r* 63.3%

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

      4. distribute-rgt-neg-in 63.3%

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

   5. Simplified 63.3%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-119}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -((double) INFINITY)) {
		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) {
		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:
		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))
		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)
		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], (-Infinity)], 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

   1. Initial program 58.3%

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

   3. Taylor expanded in z around inf 99.8%

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

   4. Taylor expanded in y around inf 99.8%

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

      1. neg-mul-1 99.8%

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

      2. distribute-lft-neg-in 99.8%

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

   6. Simplified 99.8%

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

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

   1. Initial program 98.3%

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

4. Final simplification 98.4%

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

Alternative 6: 50.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.5 \cdot 10^{+163}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x 2.5e+163) x (/ (* z x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.5e+163) {
		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 (x <= 2.5d+163) 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 (x <= 2.5e+163) {
		tmp = x;
	} else {
		tmp = (z * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= 2.5e+163:
		tmp = x
	else:
		tmp = (z * x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= 2.5e+163)
		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 (x <= 2.5e+163)
		tmp = x;
	else
		tmp = (z * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, 2.5e+163], x, N[(N[(z * x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.5e163

   1. Initial program 95.1%

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

   3. Taylor expanded in y around 0 52.0%

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

   if 2.5e163 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 80.0%

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

   4. Taylor expanded in y around 0 31.7%

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

      1. *-commutative 31.7%

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

      2. associate-*l/ 41.2%

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

   6. Applied egg-rr 41.2%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.5 \cdot 10^{+163}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.1% 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 50.4%

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

Reproduce

herbie shell --seed 2024184 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))