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

Percentage Accurate: 96.2% → 98.0%

Time: 7.9s

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: 96.2% 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: 98.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 1.4 \cdot 10^{+242}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(z, -y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 1.4e+242) (* x (fma z (- y) 1.0)) (* y (* z (- x)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 1.4e+242) {
		tmp = x * fma(z, -y, 1.0);
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 1.4e+242)
		tmp = Float64(x * fma(z, Float64(-y), 1.0));
	else
		tmp = Float64(y * Float64(z * Float64(-x)));
	end
	return tmp
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 1.4e+242], N[(x * N[(z * (-y) + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 1.4e242

   1. Initial program 98.2%

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

      1. cancel-sign-sub-inv 98.2%

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

      2. +-commutative 98.2%

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

      3. *-commutative 98.2%

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

      4. fma-def 98.2%

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

   3. Simplified 98.2%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(z, -y, 1\right)} \]
   4. Add Preprocessing

   if 1.4e242 < (*.f64 y z)

   1. Initial program 75.0%

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

   3. Taylor expanded in y around inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. distribute-rgt-neg-in 75.0%

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

      3. distribute-rgt-neg-in 75.0%

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

   5. Simplified 75.0%

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

      1. distribute-rgt-neg-out 75.0%

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

      2. distribute-rgt-neg-in 75.0%

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

      3. neg-sub0 75.0%

         \[\leadsto \color{blue}{0 - x \cdot \left(y \cdot z\right)} \]

      4. flip-- 9.1%

         \[\leadsto \color{blue}{\frac{0 \cdot 0 - \left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}{0 + x \cdot \left(y \cdot z\right)}} \]

      5. metadata-eval 9.1%

         \[\leadsto \frac{\color{blue}{0} - \left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}{0 + x \cdot \left(y \cdot z\right)} \]

      6. pow2 9.1%

         \[\leadsto \frac{0 - \color{blue}{{\left(x \cdot \left(y \cdot z\right)\right)}^{2}}}{0 + x \cdot \left(y \cdot z\right)} \]

      7. add-sqr-sqrt 9.0%

         \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\sqrt{x \cdot \left(y \cdot z\right)} \cdot \sqrt{x \cdot \left(y \cdot z\right)}}} \]

      8. sqrt-unprod 9.1%

         \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\sqrt{\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}}} \]

      9. sqr-neg 9.1%

         \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \sqrt{\color{blue}{\left(-x \cdot \left(y \cdot z\right)\right) \cdot \left(-x \cdot \left(y \cdot z\right)\right)}}} \]

      10. sqrt-unprod 0.0%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\sqrt{-x \cdot \left(y \cdot z\right)} \cdot \sqrt{-x \cdot \left(y \cdot z\right)}}} \]

      11. add-sqr-sqrt 0.1%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\left(-x \cdot \left(y \cdot z\right)\right)}} \]

      12. sub-neg 0.1%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{0 - x \cdot \left(y \cdot z\right)}} \]

      13. neg-sub0 0.1%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{-x \cdot \left(y \cdot z\right)}} \]

      14. add-sqr-sqrt 0.0%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{\sqrt{-x \cdot \left(y \cdot z\right)} \cdot \sqrt{-x \cdot \left(y \cdot z\right)}}} \]

      15. sqrt-unprod 9.1%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{\sqrt{\left(-x \cdot \left(y \cdot z\right)\right) \cdot \left(-x \cdot \left(y \cdot z\right)\right)}}} \]

      16. sqr-neg 9.1%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\sqrt{\color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}}} \]

      17. sqrt-unprod 9.0%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{\sqrt{x \cdot \left(y \cdot z\right)} \cdot \sqrt{x \cdot \left(y \cdot z\right)}}} \]

      18. add-sqr-sqrt 9.1%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{x \cdot \left(y \cdot z\right)}} \]

   7. Applied egg-rr 9.1%

      \[\leadsto \color{blue}{\frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{x \cdot \left(y \cdot z\right)}} \]
   8. Step-by-step derivation

      1. sub0-neg 9.1%

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

      2. associate-*r* 9.2%

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

      3. associate-*r* 15.7%

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

   9. Simplified 15.7%

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

       1. distribute-frac-neg 15.7%

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

       2. pow1 15.7%

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

       3. pow-div 99.9%

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

       4. metadata-eval 99.9%

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

       5. pow1 99.9%

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

       6. associate-*r* 75.0%

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

       7. distribute-lft-neg-in 75.0%

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

       8. *-commutative 75.0%

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

       9. associate-*r* 99.8%

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

   11. Applied egg-rr 99.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 1.4 \cdot 10^{+242}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(z, -y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-72} \lor \neg \left(z \leq 2.05 \cdot 10^{+61}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.7e-72) (not (<= z 2.05e+61))) (* (* y z) (- x)) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.7e-72) || !(z <= 2.05e+61)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 <= (-2.7d-72)) .or. (.not. (z <= 2.05d+61))) then
        tmp = (y * z) * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.7e-72) || !(z <= 2.05e+61)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -2.7e-72) or not (z <= 2.05e+61):
		tmp = (y * z) * -x
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.7e-72) || !(z <= 2.05e+61))
		tmp = Float64(Float64(y * z) * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.7e-72) || ~((z <= 2.05e+61)))
		tmp = (y * z) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -2.7e-72], N[Not[LessEqual[z, 2.05e+61]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.7e-72 or 2.04999999999999986e61 < z

   1. Initial program 92.8%

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

   3. Taylor expanded in y around inf 61.7%

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

      1. mul-1-neg 61.7%

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

      2. distribute-rgt-neg-in 61.7%

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

      3. distribute-rgt-neg-in 61.7%

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

   5. Simplified 61.7%

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

   if -2.7e-72 < z < 2.04999999999999986e61

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.0%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-72} \lor \neg \left(z \leq 2.05 \cdot 10^{+61}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-72} \lor \neg \left(z \leq 1.82 \cdot 10^{+59}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.15e-72) (not (<= z 1.82e+59))) (* z (* y (- x))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.15e-72) || !(z <= 1.82e+59)) {
		tmp = z * (y * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 <= (-2.15d-72)) .or. (.not. (z <= 1.82d+59))) then
        tmp = z * (y * -x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.15e-72) || !(z <= 1.82e+59)) {
		tmp = z * (y * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -2.15e-72) or not (z <= 1.82e+59):
		tmp = z * (y * -x)
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.15e-72) || !(z <= 1.82e+59))
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.15e-72) || ~((z <= 1.82e+59)))
		tmp = z * (y * -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -2.15e-72], N[Not[LessEqual[z, 1.82e+59]], $MachinePrecision]], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.1499999999999999e-72 or 1.82000000000000008e59 < z

   1. Initial program 92.8%

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

   3. Taylor expanded in y around inf 61.7%

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

      1. mul-1-neg 61.7%

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

      2. distribute-rgt-neg-in 61.7%

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

      3. distribute-rgt-neg-in 61.7%

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

   5. Simplified 61.7%

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

      1. distribute-rgt-neg-out 61.7%

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

      2. distribute-rgt-neg-in 61.7%

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

      3. neg-sub0 61.7%

         \[\leadsto \color{blue}{0 - x \cdot \left(y \cdot z\right)} \]

      4. flip-- 18.3%

         \[\leadsto \color{blue}{\frac{0 \cdot 0 - \left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}{0 + x \cdot \left(y \cdot z\right)}} \]

      5. metadata-eval 18.3%

         \[\leadsto \frac{\color{blue}{0} - \left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}{0 + x \cdot \left(y \cdot z\right)} \]

      6. pow2 18.3%

         \[\leadsto \frac{0 - \color{blue}{{\left(x \cdot \left(y \cdot z\right)\right)}^{2}}}{0 + x \cdot \left(y \cdot z\right)} \]

      7. add-sqr-sqrt 5.9%

         \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\sqrt{x \cdot \left(y \cdot z\right)} \cdot \sqrt{x \cdot \left(y \cdot z\right)}}} \]

      8. sqrt-unprod 5.5%

         \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\sqrt{\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}}} \]

      9. sqr-neg 5.5%

         \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \sqrt{\color{blue}{\left(-x \cdot \left(y \cdot z\right)\right) \cdot \left(-x \cdot \left(y \cdot z\right)\right)}}} \]

      10. sqrt-unprod 0.8%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\sqrt{-x \cdot \left(y \cdot z\right)} \cdot \sqrt{-x \cdot \left(y \cdot z\right)}}} \]

      11. add-sqr-sqrt 1.6%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\left(-x \cdot \left(y \cdot z\right)\right)}} \]

      12. sub-neg 1.6%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{0 - x \cdot \left(y \cdot z\right)}} \]

      13. neg-sub0 1.6%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{-x \cdot \left(y \cdot z\right)}} \]

      14. add-sqr-sqrt 0.8%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{\sqrt{-x \cdot \left(y \cdot z\right)} \cdot \sqrt{-x \cdot \left(y \cdot z\right)}}} \]

      15. sqrt-unprod 5.5%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{\sqrt{\left(-x \cdot \left(y \cdot z\right)\right) \cdot \left(-x \cdot \left(y \cdot z\right)\right)}}} \]

      16. sqr-neg 5.5%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\sqrt{\color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}}} \]

      17. sqrt-unprod 5.9%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{\sqrt{x \cdot \left(y \cdot z\right)} \cdot \sqrt{x \cdot \left(y \cdot z\right)}}} \]

      18. add-sqr-sqrt 18.3%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{x \cdot \left(y \cdot z\right)}} \]

   7. Applied egg-rr 18.3%

      \[\leadsto \color{blue}{\frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{x \cdot \left(y \cdot z\right)}} \]
   8. Step-by-step derivation

      1. sub0-neg 18.3%

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

      2. associate-*r* 16.1%

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

      3. associate-*r* 18.4%

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

   9. Simplified 18.4%

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

       1. distribute-frac-neg 18.4%

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

       2. pow1 18.4%

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

       3. pow-div 63.8%

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

       4. metadata-eval 63.8%

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

       5. pow1 63.8%

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

       6. associate-*r* 61.7%

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

       7. distribute-lft-neg-in 61.7%

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

       8. associate-*r* 63.8%

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

   11. Applied egg-rr 63.8%

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

   if -2.1499999999999999e-72 < z < 1.82000000000000008e59

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.0%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-72} \lor \neg \left(z \leq 1.82 \cdot 10^{+59}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-73}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= z -3.1e-73)
   (* z (* y (- x)))
   (if (<= z 3.6e+58) x (* y (* z (- x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.1e-73) {
		tmp = z * (y * -x);
	} else if (z <= 3.6e+58) {
		tmp = x;
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 <= (-3.1d-73)) then
        tmp = z * (y * -x)
    else if (z <= 3.6d+58) then
        tmp = x
    else
        tmp = y * (z * -x)
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.1e-73) {
		tmp = z * (y * -x);
	} else if (z <= 3.6e+58) {
		tmp = x;
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if z <= -3.1e-73:
		tmp = z * (y * -x)
	elif z <= 3.6e+58:
		tmp = x
	else:
		tmp = y * (z * -x)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (z <= -3.1e-73)
		tmp = Float64(z * Float64(y * Float64(-x)));
	elseif (z <= 3.6e+58)
		tmp = x;
	else
		tmp = Float64(y * Float64(z * Float64(-x)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.1e-73)
		tmp = z * (y * -x);
	elseif (z <= 3.6e+58)
		tmp = x;
	else
		tmp = y * (z * -x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[z, -3.1e-73], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.6e+58], x, N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.09999999999999969e-73

   1. Initial program 95.2%

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

   3. Taylor expanded in y around inf 55.7%

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

      1. mul-1-neg 55.7%

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

      2. distribute-rgt-neg-in 55.7%

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

      3. distribute-rgt-neg-in 55.7%

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

   5. Simplified 55.7%

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

      1. distribute-rgt-neg-out 55.7%

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

      2. distribute-rgt-neg-in 55.7%

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

      3. neg-sub0 55.7%

         \[\leadsto \color{blue}{0 - x \cdot \left(y \cdot z\right)} \]

      4. flip-- 15.1%

         \[\leadsto \color{blue}{\frac{0 \cdot 0 - \left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}{0 + x \cdot \left(y \cdot z\right)}} \]

      5. metadata-eval 15.1%

         \[\leadsto \frac{\color{blue}{0} - \left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}{0 + x \cdot \left(y \cdot z\right)} \]

      6. pow2 15.1%

         \[\leadsto \frac{0 - \color{blue}{{\left(x \cdot \left(y \cdot z\right)\right)}^{2}}}{0 + x \cdot \left(y \cdot z\right)} \]

      7. add-sqr-sqrt 4.1%

         \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\sqrt{x \cdot \left(y \cdot z\right)} \cdot \sqrt{x \cdot \left(y \cdot z\right)}}} \]

      8. sqrt-unprod 3.5%

         \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\sqrt{\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}}} \]

      9. sqr-neg 3.5%

         \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \sqrt{\color{blue}{\left(-x \cdot \left(y \cdot z\right)\right) \cdot \left(-x \cdot \left(y \cdot z\right)\right)}}} \]

      10. sqrt-unprod 0.8%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\sqrt{-x \cdot \left(y \cdot z\right)} \cdot \sqrt{-x \cdot \left(y \cdot z\right)}}} \]

      11. add-sqr-sqrt 1.6%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\left(-x \cdot \left(y \cdot z\right)\right)}} \]

      12. sub-neg 1.6%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{0 - x \cdot \left(y \cdot z\right)}} \]

      13. neg-sub0 1.6%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{-x \cdot \left(y \cdot z\right)}} \]

      14. add-sqr-sqrt 0.8%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{\sqrt{-x \cdot \left(y \cdot z\right)} \cdot \sqrt{-x \cdot \left(y \cdot z\right)}}} \]

      15. sqrt-unprod 3.5%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{\sqrt{\left(-x \cdot \left(y \cdot z\right)\right) \cdot \left(-x \cdot \left(y \cdot z\right)\right)}}} \]

      16. sqr-neg 3.5%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\sqrt{\color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}}} \]

      17. sqrt-unprod 4.1%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{\sqrt{x \cdot \left(y \cdot z\right)} \cdot \sqrt{x \cdot \left(y \cdot z\right)}}} \]

      18. add-sqr-sqrt 15.1%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{x \cdot \left(y \cdot z\right)}} \]

   7. Applied egg-rr 15.1%

      \[\leadsto \color{blue}{\frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{x \cdot \left(y \cdot z\right)}} \]
   8. Step-by-step derivation

      1. sub0-neg 15.1%

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

      2. associate-*r* 15.1%

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

      3. associate-*r* 16.2%

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

   9. Simplified 16.2%

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

       1. distribute-frac-neg 16.2%

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

       2. pow1 16.2%

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

       3. pow-div 58.1%

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

       4. metadata-eval 58.1%

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

       5. pow1 58.1%

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

       6. associate-*r* 55.7%

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

       7. distribute-lft-neg-in 55.7%

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

       8. associate-*r* 58.1%

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

   11. Applied egg-rr 58.1%

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

   if -3.09999999999999969e-73 < z < 3.59999999999999996e58

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.0%

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

   if 3.59999999999999996e58 < z

   1. Initial program 89.4%

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

   3. Taylor expanded in y around inf 70.5%

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

      1. mul-1-neg 70.5%

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

      2. distribute-rgt-neg-in 70.5%

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

      3. distribute-rgt-neg-in 70.5%

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

   5. Simplified 70.5%

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

      1. distribute-rgt-neg-out 70.5%

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

      2. distribute-rgt-neg-in 70.5%

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

      3. neg-sub0 70.5%

         \[\leadsto \color{blue}{0 - x \cdot \left(y \cdot z\right)} \]

      4. flip-- 23.0%

         \[\leadsto \color{blue}{\frac{0 \cdot 0 - \left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}{0 + x \cdot \left(y \cdot z\right)}} \]

      5. metadata-eval 23.0%

         \[\leadsto \frac{\color{blue}{0} - \left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}{0 + x \cdot \left(y \cdot z\right)} \]

      6. pow2 23.0%

         \[\leadsto \frac{0 - \color{blue}{{\left(x \cdot \left(y \cdot z\right)\right)}^{2}}}{0 + x \cdot \left(y \cdot z\right)} \]

      7. add-sqr-sqrt 8.5%

         \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\sqrt{x \cdot \left(y \cdot z\right)} \cdot \sqrt{x \cdot \left(y \cdot z\right)}}} \]

      8. sqrt-unprod 8.4%

         \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\sqrt{\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}}} \]

      9. sqr-neg 8.4%

         \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \sqrt{\color{blue}{\left(-x \cdot \left(y \cdot z\right)\right) \cdot \left(-x \cdot \left(y \cdot z\right)\right)}}} \]

      10. sqrt-unprod 0.9%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\sqrt{-x \cdot \left(y \cdot z\right)} \cdot \sqrt{-x \cdot \left(y \cdot z\right)}}} \]

      11. add-sqr-sqrt 1.5%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\left(-x \cdot \left(y \cdot z\right)\right)}} \]

      12. sub-neg 1.5%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{0 - x \cdot \left(y \cdot z\right)}} \]

      13. neg-sub0 1.5%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{-x \cdot \left(y \cdot z\right)}} \]

      14. add-sqr-sqrt 0.9%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{\sqrt{-x \cdot \left(y \cdot z\right)} \cdot \sqrt{-x \cdot \left(y \cdot z\right)}}} \]

      15. sqrt-unprod 8.4%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{\sqrt{\left(-x \cdot \left(y \cdot z\right)\right) \cdot \left(-x \cdot \left(y \cdot z\right)\right)}}} \]

      16. sqr-neg 8.4%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\sqrt{\color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}}} \]

      17. sqrt-unprod 8.5%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{\sqrt{x \cdot \left(y \cdot z\right)} \cdot \sqrt{x \cdot \left(y \cdot z\right)}}} \]

      18. add-sqr-sqrt 23.0%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{x \cdot \left(y \cdot z\right)}} \]

   7. Applied egg-rr 23.0%

      \[\leadsto \color{blue}{\frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{x \cdot \left(y \cdot z\right)}} \]
   8. Step-by-step derivation

      1. sub0-neg 23.0%

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

      2. associate-*r* 17.6%

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

      3. associate-*r* 21.5%

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

   9. Simplified 21.5%

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

       1. distribute-frac-neg 21.5%

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

       2. pow1 21.5%

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

       3. pow-div 72.0%

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

       4. metadata-eval 72.0%

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

       5. pow1 72.0%

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

       6. associate-*r* 70.5%

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

       7. distribute-lft-neg-in 70.5%

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

       8. *-commutative 70.5%

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

       9. associate-*r* 75.9%

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

   11. Applied egg-rr 75.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-73}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 1.4 \cdot 10^{+242}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 1.4e+242) (* x (- 1.0 (* y z))) (* y (* z (- x)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 1.4e+242) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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) <= 1.4d+242) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = y * (z * -x)
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 1.4e+242) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 1.4e+242:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = y * (z * -x)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 1.4e+242)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(y * Float64(z * Float64(-x)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 1.4e+242)
		tmp = x * (1.0 - (y * z));
	else
		tmp = y * (z * -x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 1.4e+242], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 1.4e242

   1. Initial program 98.2%

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

   if 1.4e242 < (*.f64 y z)

   1. Initial program 75.0%

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

   3. Taylor expanded in y around inf 75.0%

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

      1. mul-1-neg 75.0%

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

      2. distribute-rgt-neg-in 75.0%

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

      3. distribute-rgt-neg-in 75.0%

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

   5. Simplified 75.0%

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

      1. distribute-rgt-neg-out 75.0%

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

      2. distribute-rgt-neg-in 75.0%

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

      3. neg-sub0 75.0%

         \[\leadsto \color{blue}{0 - x \cdot \left(y \cdot z\right)} \]

      4. flip-- 9.1%

         \[\leadsto \color{blue}{\frac{0 \cdot 0 - \left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}{0 + x \cdot \left(y \cdot z\right)}} \]

      5. metadata-eval 9.1%

         \[\leadsto \frac{\color{blue}{0} - \left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}{0 + x \cdot \left(y \cdot z\right)} \]

      6. pow2 9.1%

         \[\leadsto \frac{0 - \color{blue}{{\left(x \cdot \left(y \cdot z\right)\right)}^{2}}}{0 + x \cdot \left(y \cdot z\right)} \]

      7. add-sqr-sqrt 9.0%

         \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\sqrt{x \cdot \left(y \cdot z\right)} \cdot \sqrt{x \cdot \left(y \cdot z\right)}}} \]

      8. sqrt-unprod 9.1%

         \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\sqrt{\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}}} \]

      9. sqr-neg 9.1%

         \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \sqrt{\color{blue}{\left(-x \cdot \left(y \cdot z\right)\right) \cdot \left(-x \cdot \left(y \cdot z\right)\right)}}} \]

      10. sqrt-unprod 0.0%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\sqrt{-x \cdot \left(y \cdot z\right)} \cdot \sqrt{-x \cdot \left(y \cdot z\right)}}} \]

      11. add-sqr-sqrt 0.1%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{0 + \color{blue}{\left(-x \cdot \left(y \cdot z\right)\right)}} \]

      12. sub-neg 0.1%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{0 - x \cdot \left(y \cdot z\right)}} \]

      13. neg-sub0 0.1%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{-x \cdot \left(y \cdot z\right)}} \]

      14. add-sqr-sqrt 0.0%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{\sqrt{-x \cdot \left(y \cdot z\right)} \cdot \sqrt{-x \cdot \left(y \cdot z\right)}}} \]

      15. sqrt-unprod 9.1%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{\sqrt{\left(-x \cdot \left(y \cdot z\right)\right) \cdot \left(-x \cdot \left(y \cdot z\right)\right)}}} \]

      16. sqr-neg 9.1%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\sqrt{\color{blue}{\left(x \cdot \left(y \cdot z\right)\right) \cdot \left(x \cdot \left(y \cdot z\right)\right)}}} \]

      17. sqrt-unprod 9.0%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{\sqrt{x \cdot \left(y \cdot z\right)} \cdot \sqrt{x \cdot \left(y \cdot z\right)}}} \]

      18. add-sqr-sqrt 9.1%

          \[\leadsto \frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{\color{blue}{x \cdot \left(y \cdot z\right)}} \]

   7. Applied egg-rr 9.1%

      \[\leadsto \color{blue}{\frac{0 - {\left(x \cdot \left(y \cdot z\right)\right)}^{2}}{x \cdot \left(y \cdot z\right)}} \]
   8. Step-by-step derivation

      1. sub0-neg 9.1%

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

      2. associate-*r* 9.2%

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

      3. associate-*r* 15.7%

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

   9. Simplified 15.7%

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

       1. distribute-frac-neg 15.7%

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

       2. pow1 15.7%

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

       3. pow-div 99.9%

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

       4. metadata-eval 99.9%

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

       5. pow1 99.9%

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

       6. associate-*r* 75.0%

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

       7. distribute-lft-neg-in 75.0%

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

       8. *-commutative 75.0%

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

       9. associate-*r* 99.8%

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

   11. Applied egg-rr 99.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 1.4 \cdot 10^{+242}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.5% accurate, 7.0× speedup

Math

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

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 x)

C

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

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return x

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return x
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := x

Derivation

1. Initial program 96.2%

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

3. Taylor expanded in y around 0 53.0%

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

4. Final simplification 53.0%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024024 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))