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

Percentage Accurate: 95.8% → 99.7%

Time: 7.3s

Alternatives: 9

Speedup: 0.3×

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: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - (y * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+231} \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+222}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -5e+231) (not (<= (* y z) 2e+222)))
   (* z (* y (- x)))
   (- x (* x (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -5e+231) || !((y * z) <= 2e+222)) {
		tmp = z * (y * -x);
	} else {
		tmp = x - (x * (y * z));
	}
	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) <= (-5d+231)) .or. (.not. ((y * z) <= 2d+222))) then
        tmp = z * (y * -x)
    else
        tmp = x - (x * (y * z))
    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) <= -5e+231) || !((y * z) <= 2e+222)) {
		tmp = z * (y * -x);
	} else {
		tmp = x - (x * (y * z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if ((y * z) <= -5e+231) or not ((y * z) <= 2e+222):
		tmp = z * (y * -x)
	else:
		tmp = x - (x * (y * z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -5e+231) || !(Float64(y * z) <= 2e+222))
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = Float64(x - Float64(x * Float64(y * z)));
	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) <= -5e+231) || ~(((y * z) <= 2e+222)))
		tmp = z * (y * -x);
	else
		tmp = x - (x * (y * z));
	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[N[(y * z), $MachinePrecision], -5e+231], N[Not[LessEqual[N[(y * z), $MachinePrecision], 2e+222]], $MachinePrecision]], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -5.00000000000000028e231 or 2.0000000000000001e222 < (*.f64 y z)

   1. Initial program 75.6%

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

      1. sub-neg 75.6%

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

      2. distribute-rgt-in 75.6%

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

      3. *-un-lft-identity 75.6%

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

      4. distribute-rgt-neg-in 75.6%

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

   4. Applied egg-rr 75.6%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. +-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. *-commutative 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

   10. Simplified 99.8%

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

   if -5.00000000000000028e231 < (*.f64 y z) < 2.0000000000000001e222

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-rgt-in 99.8%

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

      3. *-un-lft-identity 99.8%

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

      4. distribute-rgt-neg-in 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. associate-*l* 93.0%

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

      2. add-sqr-sqrt 50.0%

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

      3. sqrt-unprod 68.6%

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

      4. sqr-neg 68.6%

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

      5. sqrt-unprod 28.1%

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

      6. add-sqr-sqrt 60.0%

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

      7. cancel-sign-sub-inv 60.0%

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

      8. associate-*l* 61.0%

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

      9. distribute-rgt-neg-out 61.0%

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

      10. distribute-lft-neg-in 61.0%

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

      11. associate-*r* 60.0%

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

      12. add-sqr-sqrt 28.1%

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

      13. sqrt-unprod 68.6%

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

      14. sqr-neg 68.6%

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

      15. sqrt-unprod 50.0%

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

      16. add-sqr-sqrt 93.0%

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

   6. Applied egg-rr 93.0%

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

   7. Taylor expanded in y around 0 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+231} \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+222}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+231} \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+222}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -5e+231) (not (<= (* y z) 2e+222)))
   (* z (* y (- x)))
   (* x (- 1.0 (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -5e+231) || !((y * z) <= 2e+222)) {
		tmp = z * (y * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	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) <= (-5d+231)) .or. (.not. ((y * z) <= 2d+222))) then
        tmp = z * (y * -x)
    else
        tmp = x * (1.0d0 - (y * z))
    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) <= -5e+231) || !((y * z) <= 2e+222)) {
		tmp = z * (y * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if ((y * z) <= -5e+231) or not ((y * z) <= 2e+222):
		tmp = z * (y * -x)
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((Float64(y * z) <= -5e+231) || !(Float64(y * z) <= 2e+222))
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	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) <= -5e+231) || ~(((y * z) <= 2e+222)))
		tmp = z * (y * -x);
	else
		tmp = x * (1.0 - (y * z));
	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[N[(y * z), $MachinePrecision], -5e+231], N[Not[LessEqual[N[(y * z), $MachinePrecision], 2e+222]], $MachinePrecision]], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -5.00000000000000028e231 or 2.0000000000000001e222 < (*.f64 y z)

   1. Initial program 75.6%

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

      1. sub-neg 75.6%

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

      2. distribute-rgt-in 75.6%

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

      3. *-un-lft-identity 75.6%

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

      4. distribute-rgt-neg-in 75.6%

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

   4. Applied egg-rr 75.6%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. +-commutative 99.8%

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

      2. mul-1-neg 99.8%

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

      3. unsub-neg 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. *-commutative 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

   10. Simplified 99.8%

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

   if -5.00000000000000028e231 < (*.f64 y z) < 2.0000000000000001e222

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+231} \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+222}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+63} \lor \neg \left(y \leq 6.8 \cdot 10^{-105}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.5e+63) (not (<= y 6.8e-105))) (* z (* y (- x))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e+63) || !(y <= 6.8e-105)) {
		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 ((y <= (-6.5d+63)) .or. (.not. (y <= 6.8d-105))) 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 ((y <= -6.5e+63) || !(y <= 6.8e-105)) {
		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 (y <= -6.5e+63) or not (y <= 6.8e-105):
		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 ((y <= -6.5e+63) || !(y <= 6.8e-105))
		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 ((y <= -6.5e+63) || ~((y <= 6.8e-105)))
		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[y, -6.5e+63], N[Not[LessEqual[y, 6.8e-105]], $MachinePrecision]], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.49999999999999992e63 or 6.79999999999999984e-105 < y

   1. Initial program 89.6%

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

      1. sub-neg 89.6%

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

      2. distribute-rgt-in 89.7%

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

      3. *-un-lft-identity 89.7%

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

      4. distribute-rgt-neg-in 89.7%

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

   4. Applied egg-rr 89.7%

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

   5. Taylor expanded in z around inf 90.7%

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

      1. +-commutative 90.7%

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

      2. mul-1-neg 90.7%

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

      3. unsub-neg 90.7%

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

   7. Simplified 90.7%

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

   8. Taylor expanded in z around inf 69.7%

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

      1. mul-1-neg 69.7%

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

      2. *-commutative 69.7%

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

      3. distribute-rgt-neg-in 69.7%

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

   10. Simplified 69.7%

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

   if -6.49999999999999992e63 < y < 6.79999999999999984e-105

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 69.8%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+63} \lor \neg \left(y \leq 6.8 \cdot 10^{-105}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+65} \lor \neg \left(y \leq 6.8 \cdot 10^{-105}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.8e+65) (not (<= y 6.8e-105))) (* x (* y (- z))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.8e+65) || !(y <= 6.8e-105)) {
		tmp = x * (y * -z);
	} 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 ((y <= (-5.8d+65)) .or. (.not. (y <= 6.8d-105))) then
        tmp = x * (y * -z)
    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 ((y <= -5.8e+65) || !(y <= 6.8e-105)) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -5.8e+65) or not (y <= 6.8e-105):
		tmp = x * (y * -z)
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.8e+65) || !(y <= 6.8e-105))
		tmp = Float64(x * Float64(y * Float64(-z)));
	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 ((y <= -5.8e+65) || ~((y <= 6.8e-105)))
		tmp = x * (y * -z);
	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[y, -5.8e+65], N[Not[LessEqual[y, 6.8e-105]], $MachinePrecision]], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.8000000000000001e65 or 6.79999999999999984e-105 < y

   1. Initial program 89.6%

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

   3. Taylor expanded in y around inf 61.9%

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

      1. mul-1-neg 61.9%

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

      2. distribute-rgt-neg-out 61.9%

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

   5. Simplified 61.9%

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

   if -5.8000000000000001e65 < y < 6.79999999999999984e-105

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 69.8%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+65} \lor \neg \left(y \leq 6.8 \cdot 10^{-105}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+66}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -3.3e+66)
   (* z (* y (- x)))
   (if (<= y 6.8e-105) x (* (- y) (* x z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.3e+66) {
		tmp = z * (y * -x);
	} else if (y <= 6.8e-105) {
		tmp = x;
	} else {
		tmp = -y * (x * z);
	}
	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 <= (-3.3d+66)) then
        tmp = z * (y * -x)
    else if (y <= 6.8d-105) then
        tmp = x
    else
        tmp = -y * (x * z)
    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 <= -3.3e+66) {
		tmp = z * (y * -x);
	} else if (y <= 6.8e-105) {
		tmp = x;
	} else {
		tmp = -y * (x * z);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -3.3e+66:
		tmp = z * (y * -x)
	elif y <= 6.8e-105:
		tmp = x
	else:
		tmp = -y * (x * z)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -3.3e+66)
		tmp = Float64(z * Float64(y * Float64(-x)));
	elseif (y <= 6.8e-105)
		tmp = x;
	else
		tmp = Float64(Float64(-y) * Float64(x * z));
	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 <= -3.3e+66)
		tmp = z * (y * -x);
	elseif (y <= 6.8e-105)
		tmp = x;
	else
		tmp = -y * (x * z);
	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[y, -3.3e+66], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e-105], x, N[((-y) * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.3000000000000001e66

   1. Initial program 91.6%

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

      1. sub-neg 91.6%

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

      2. distribute-rgt-in 91.6%

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

      3. *-un-lft-identity 91.6%

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

      4. distribute-rgt-neg-in 91.6%

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

   4. Applied egg-rr 91.6%

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

   5. Taylor expanded in z around inf 95.5%

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

      1. +-commutative 95.5%

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

      2. mul-1-neg 95.5%

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

      3. unsub-neg 95.5%

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

   7. Simplified 95.5%

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

   8. Taylor expanded in z around inf 81.4%

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

      1. mul-1-neg 81.4%

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

      2. *-commutative 81.4%

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

      3. distribute-rgt-neg-in 81.4%

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

   10. Simplified 81.4%

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

   if -3.3000000000000001e66 < y < 6.79999999999999984e-105

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 69.8%

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

   if 6.79999999999999984e-105 < y

   1. Initial program 88.6%

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

   3. Taylor expanded in y around inf 55.5%

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

      1. mul-1-neg 55.5%

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

      2. *-commutative 55.5%

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

      3. associate-*r* 65.4%

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

      4. distribute-rgt-neg-in 65.4%

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

   5. Simplified 65.4%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+66}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 95.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+102}:\\ \;\;\;\;\left(z + \frac{-1}{y}\right) \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1.1e+102) (* (+ z (/ -1.0 y)) (* y (- x))) (- x (* x (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.1e+102) {
		tmp = (z + (-1.0 / y)) * (y * -x);
	} else {
		tmp = x - (x * (y * z));
	}
	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 <= (-1.1d+102)) then
        tmp = (z + ((-1.0d0) / y)) * (y * -x)
    else
        tmp = x - (x * (y * z))
    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 <= -1.1e+102) {
		tmp = (z + (-1.0 / y)) * (y * -x);
	} else {
		tmp = x - (x * (y * z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -1.1e+102:
		tmp = (z + (-1.0 / y)) * (y * -x)
	else:
		tmp = x - (x * (y * z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1.1e+102)
		tmp = Float64(Float64(z + Float64(-1.0 / y)) * Float64(y * Float64(-x)));
	else
		tmp = Float64(x - Float64(x * Float64(y * z)));
	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 <= -1.1e+102)
		tmp = (z + (-1.0 / y)) * (y * -x);
	else
		tmp = x - (x * (y * z));
	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[y, -1.1e+102], N[(N[(z + N[(-1.0 / y), $MachinePrecision]), $MachinePrecision] * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000004e102

   1. Initial program 90.0%

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

   3. Taylor expanded in y around inf 85.3%

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

   4. Taylor expanded in x around -inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. associate-*r* 99.7%

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

      3. distribute-lft-neg-in 99.7%

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

      4. distribute-rgt-neg-in 99.7%

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

      5. sub-neg 99.7%

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

      6. distribute-neg-frac 99.7%

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

      7. metadata-eval 99.7%

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

   6. Simplified 99.7%

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

   if -1.10000000000000004e102 < y

   1. Initial program 95.5%

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

      1. sub-neg 95.5%

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

      2. distribute-rgt-in 95.6%

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

      3. *-un-lft-identity 95.6%

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

      4. distribute-rgt-neg-in 95.6%

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

   4. Applied egg-rr 95.6%

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

      1. associate-*l* 95.5%

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

      2. add-sqr-sqrt 59.8%

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

      3. sqrt-unprod 72.4%

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

      4. sqr-neg 72.4%

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

      5. sqrt-unprod 24.5%

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

      6. add-sqr-sqrt 54.3%

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

      7. cancel-sign-sub-inv 54.3%

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

      8. associate-*l* 55.2%

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

      9. distribute-rgt-neg-out 55.2%

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

      10. distribute-lft-neg-in 55.2%

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

      11. associate-*r* 54.3%

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

      12. add-sqr-sqrt 24.5%

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

      13. sqrt-unprod 72.4%

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

      14. sqr-neg 72.4%

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

      15. sqrt-unprod 59.8%

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

      16. add-sqr-sqrt 95.5%

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

   6. Applied egg-rr 95.5%

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

   7. Taylor expanded in y around 0 95.6%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+102}:\\ \;\;\;\;\left(z + \frac{-1}{y}\right) \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 53.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+168}:\\ \;\;\;\;\frac{y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (if (<= y -1.7e+168) (/ (* y x) y) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.7e+168) {
		tmp = (y * x) / y;
	} 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 (y <= (-1.7d+168)) then
        tmp = (y * x) / y
    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 (y <= -1.7e+168) {
		tmp = (y * x) / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -1.7e+168:
		tmp = (y * x) / y
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1.7e+168)
		tmp = Float64(Float64(y * x) / y);
	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 (y <= -1.7e+168)
		tmp = (y * x) / y;
	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[LessEqual[y, -1.7e+168], N[(N[(y * x), $MachinePrecision] / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.70000000000000001e168

   1. Initial program 93.7%

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

   3. Taylor expanded in y around inf 84.6%

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

   4. Taylor expanded in z around 0 6.6%

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

      1. associate-*r/ 34.9%

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

   6. Applied egg-rr 34.9%

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

   if -1.70000000000000001e168 < y

   1. Initial program 94.8%

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

   3. Taylor expanded in y around 0 54.9%

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

Alternative 8: 51.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+102}:\\ \;\;\;\;\frac{x \cdot z}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (if (<= y -1.2e+102) (/ (* x z) z) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.2e+102) {
		tmp = (x * z) / z;
	} 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 (y <= (-1.2d+102)) then
        tmp = (x * z) / z
    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 (y <= -1.2e+102) {
		tmp = (x * z) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -1.2e+102:
		tmp = (x * z) / z
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1.2e+102)
		tmp = Float64(Float64(x * z) / z);
	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 (y <= -1.2e+102)
		tmp = (x * z) / z;
	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[LessEqual[y, -1.2e+102], N[(N[(x * z), $MachinePrecision] / z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.19999999999999997e102

   1. Initial program 90.0%

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

      1. sub-neg 90.0%

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

      2. distribute-rgt-in 90.0%

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

      3. *-un-lft-identity 90.0%

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

      4. distribute-rgt-neg-in 90.0%

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

   4. Applied egg-rr 90.0%

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

   5. Taylor expanded in z around inf 97.1%

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

      1. +-commutative 97.1%

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

      2. mul-1-neg 97.1%

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

      3. unsub-neg 97.1%

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

   7. Simplified 97.1%

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

   8. Taylor expanded in z around 0 13.8%

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

      1. *-commutative 13.8%

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

      2. associate-*l/ 15.6%

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

   10. Applied egg-rr 15.6%

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

   if -1.19999999999999997e102 < y

   1. Initial program 95.5%

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

   3. Taylor expanded in y around 0 56.4%

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

Alternative 9: 51.1% 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 94.7%

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

3. Taylor expanded in y around 0 49.5%

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