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

Percentage Accurate: 95.7% → 96.8%

Time: 4.1s

Alternatives: 7

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.7% 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: 96.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 2 \cdot 10^{+59}:\\ \;\;\;\;x + \left(y \cdot \left(-z\right)\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-1 \cdot \left(x \cdot z\right)\right)\\ \end{array} \end{array} \]

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) 2e+59) (+ x (* (* y (- z)) x)) (* y (* -1.0 (* x z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 2e+59) {
		tmp = x + ((y * -z) * x);
	} else {
		tmp = y * (-1.0 * (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 * z) <= 2d+59) then
        tmp = x + ((y * -z) * x)
    else
        tmp = y * ((-1.0d0) * (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 * z) <= 2e+59) {
		tmp = x + ((y * -z) * x);
	} else {
		tmp = y * (-1.0 * (x * z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 2e+59:
		tmp = x + ((y * -z) * x)
	else:
		tmp = y * (-1.0 * (x * z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 2e+59)
		tmp = Float64(x + Float64(Float64(y * Float64(-z)) * x));
	else
		tmp = Float64(y * Float64(-1.0 * 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 * z) <= 2e+59)
		tmp = x + ((y * -z) * x);
	else
		tmp = y * (-1.0 * (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[N[(y * z), $MachinePrecision], 2e+59], N[(x + N[(N[(y * (-z)), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(y * N[(-1.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 1.99999999999999994e59

   1. Initial program 98.0%

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

      1. sub-neg 98.0%

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

      2. distribute-rgt-in 98.1%

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

      3. *-un-lft-identity 98.1%

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

      4. distribute-rgt-neg-in 98.1%

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

   4. Applied egg-rr 98.1%

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

   if 1.99999999999999994e59 < (*.f64 y z)

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 96.3%

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

   4. Taylor expanded in z around inf 98.1%

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

Alternative 2: 95.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := -z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \cdot z \leq -1000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 0.5:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 5 \cdot 10^{+187}:\\ \;\;\;\;-x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* z (* x y)))))
   (if (<= (* y z) -1000000000.0)
     t_0
     (if (<= (* y z) 0.5) x (if (<= (* y z) 5e+187) (- (* x (* y z))) t_0)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = -(z * (x * y));
	double tmp;
	if ((y * z) <= -1000000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.5) {
		tmp = x;
	} else if ((y * z) <= 5e+187) {
		tmp = -(x * (y * z));
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = -(z * (x * y))
    if ((y * z) <= (-1000000000.0d0)) then
        tmp = t_0
    else if ((y * z) <= 0.5d0) then
        tmp = x
    else if ((y * z) <= 5d+187) then
        tmp = -(x * (y * z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = -(z * (x * y));
	double tmp;
	if ((y * z) <= -1000000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.5) {
		tmp = x;
	} else if ((y * z) <= 5e+187) {
		tmp = -(x * (y * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = -(z * (x * y))
	tmp = 0
	if (y * z) <= -1000000000.0:
		tmp = t_0
	elif (y * z) <= 0.5:
		tmp = x
	elif (y * z) <= 5e+187:
		tmp = -(x * (y * z))
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(-Float64(z * Float64(x * y)))
	tmp = 0.0
	if (Float64(y * z) <= -1000000000.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 0.5)
		tmp = x;
	elseif (Float64(y * z) <= 5e+187)
		tmp = Float64(-Float64(x * Float64(y * z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = -(z * (x * y));
	tmp = 0.0;
	if ((y * z) <= -1000000000.0)
		tmp = t_0;
	elseif ((y * z) <= 0.5)
		tmp = x;
	elseif ((y * z) <= 5e+187)
		tmp = -(x * (y * z));
	else
		tmp = t_0;
	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_] := Block[{t$95$0 = (-N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[N[(y * z), $MachinePrecision], -1000000000.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 0.5], x, If[LessEqual[N[(y * z), $MachinePrecision], 5e+187], (-N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -1e9 or 5.0000000000000001e187 < (*.f64 y z)

   1. Initial program 87.4%

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

   3. Taylor expanded in y around inf 95.6%

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

   4. Taylor expanded in z around inf 96.3%

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

      1. *-commutative 96.3%

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

      2. mul-1-neg 96.3%

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

      3. distribute-lft-neg-out 96.3%

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

      4. add-sqr-sqrt 41.2%

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

      5. sqrt-unprod 37.6%

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

      6. sqr-neg 37.6%

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

      7. mul-1-neg 37.6%

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

      8. mul-1-neg 37.6%

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

      9. sqrt-unprod 0.3%

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

      10. add-sqr-sqrt 0.6%

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

      11. mul-1-neg 0.6%

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

      12. *-commutative 0.6%

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

      13. distribute-rgt-neg-in 0.6%

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

      14. associate-*r* 0.6%

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

      15. distribute-lft-neg-in 0.6%

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

      16. mul-1-neg 0.6%

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

      17. add-sqr-sqrt 0.3%

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

      18. sqrt-unprod 44.9%

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

      19. mul-1-neg 44.9%

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

      20. *-commutative 44.9%

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

      21. mul-1-neg 44.9%

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

      22. *-commutative 44.9%

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

      23. sqr-neg 44.9%

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

   6. Applied egg-rr 95.2%

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

   if -1e9 < (*.f64 y z) < 0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.4%

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

   if 0.5 < (*.f64 y z) < 5.0000000000000001e187

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf 93.3%

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

   4. Taylor expanded in z around inf 91.9%

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

      1. *-commutative 91.9%

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

      2. mul-1-neg 91.9%

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

      3. distribute-lft-neg-out 91.9%

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

      4. add-sqr-sqrt 47.9%

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

      5. sqrt-unprod 33.8%

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

      6. sqr-neg 33.8%

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

      7. mul-1-neg 33.8%

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

      8. mul-1-neg 33.8%

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

      9. sqrt-unprod 0.9%

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

      10. add-sqr-sqrt 1.5%

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

      11. mul-1-neg 1.5%

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

      12. *-commutative 1.5%

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

      13. distribute-rgt-neg-in 1.5%

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

      14. associate-*r* 1.6%

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

      15. distribute-lft-neg-in 1.6%

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

      16. mul-1-neg 1.6%

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

      17. add-sqr-sqrt 1.0%

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

      18. sqrt-unprod 27.7%

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

      19. mul-1-neg 27.7%

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

      20. *-commutative 27.7%

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

      21. mul-1-neg 27.7%

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

      22. *-commutative 27.7%

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

      23. sqr-neg 27.7%

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

   6. Applied egg-rr 86.0%

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

   7. Taylor expanded in z around 0 98.1%

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

Alternative 3: 93.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := -x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \cdot z \leq -1000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 0.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x (* y z)))))
   (if (<= (* y z) -1000000000.0) t_0 (if (<= (* y z) 0.5) x t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = -(x * (y * z));
	double tmp;
	if ((y * z) <= -1000000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.5) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = -(x * (y * z))
    if ((y * z) <= (-1000000000.0d0)) then
        tmp = t_0
    else if ((y * z) <= 0.5d0) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = -(x * (y * z));
	double tmp;
	if ((y * z) <= -1000000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.5) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = -(x * (y * z))
	tmp = 0
	if (y * z) <= -1000000000.0:
		tmp = t_0
	elif (y * z) <= 0.5:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(-Float64(x * Float64(y * z)))
	tmp = 0.0
	if (Float64(y * z) <= -1000000000.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 0.5)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = -(x * (y * z));
	tmp = 0.0;
	if ((y * z) <= -1000000000.0)
		tmp = t_0;
	elseif ((y * z) <= 0.5)
		tmp = x;
	else
		tmp = t_0;
	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_] := Block[{t$95$0 = (-N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[N[(y * z), $MachinePrecision], -1000000000.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 0.5], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1e9 or 0.5 < (*.f64 y z)

   1. Initial program 90.5%

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

   3. Taylor expanded in y around inf 95.0%

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

   4. Taylor expanded in z around inf 95.2%

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

      1. *-commutative 95.2%

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

      2. mul-1-neg 95.2%

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

      3. distribute-lft-neg-out 95.2%

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

      4. add-sqr-sqrt 42.9%

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

      5. sqrt-unprod 36.6%

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

      6. sqr-neg 36.6%

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

      7. mul-1-neg 36.6%

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

      8. mul-1-neg 36.6%

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

      9. sqrt-unprod 0.5%

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

      10. add-sqr-sqrt 0.8%

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

      11. mul-1-neg 0.8%

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

      12. *-commutative 0.8%

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

      13. distribute-rgt-neg-in 0.8%

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

      14. associate-*r* 0.8%

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

      15. distribute-lft-neg-in 0.8%

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

      16. mul-1-neg 0.8%

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

      17. add-sqr-sqrt 0.5%

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

      18. sqrt-unprod 40.5%

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

      19. mul-1-neg 40.5%

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

      20. *-commutative 40.5%

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

      21. mul-1-neg 40.5%

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

      22. *-commutative 40.5%

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

      23. sqr-neg 40.5%

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

   6. Applied egg-rr 92.8%

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

   7. Taylor expanded in z around 0 89.9%

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

   if -1e9 < (*.f64 y z) < 0.5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 97.4%

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

Alternative 4: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+187}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

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) 5e+187) (* x (- 1.0 (* y z))) (- (* z (* x y)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+187) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = -(z * (x * y));
	}
	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+187) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = -(z * (x * y))
    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+187) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = -(z * (x * y));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 5e+187:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = -(z * (x * y))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 5e+187)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(-Float64(z * Float64(x * y)));
	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+187)
		tmp = x * (1.0 - (y * z));
	else
		tmp = -(z * (x * y));
	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], 5e+187], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 5.0000000000000001e187

   1. Initial program 98.2%

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

   if 5.0000000000000001e187 < (*.f64 y z)

   1. Initial program 77.7%

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

   3. Taylor expanded in y around inf 96.9%

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

   4. Taylor expanded in z around inf 99.9%

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

      1. *-commutative 99.9%

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

      2. mul-1-neg 99.9%

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

      3. distribute-lft-neg-out 99.9%

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

      4. add-sqr-sqrt 49.7%

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

      5. sqrt-unprod 44.5%

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

      6. sqr-neg 44.5%

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

      7. mul-1-neg 44.5%

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

      8. mul-1-neg 44.5%

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

      9. sqrt-unprod 0.1%

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

      10. add-sqr-sqrt 0.4%

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

      11. mul-1-neg 0.4%

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

      12. *-commutative 0.4%

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

      13. distribute-rgt-neg-in 0.4%

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

      14. associate-*r* 0.4%

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

      15. distribute-lft-neg-in 0.4%

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

      16. mul-1-neg 0.4%

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

      17. add-sqr-sqrt 0.1%

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

      18. sqrt-unprod 47.1%

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

      19. mul-1-neg 47.1%

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

      20. *-commutative 47.1%

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

      21. mul-1-neg 47.1%

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

      22. *-commutative 47.1%

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

      23. sqr-neg 47.1%

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

   6. Applied egg-rr 99.8%

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

Alternative 5: 96.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 2 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-1 \cdot \left(x \cdot z\right)\right)\\ \end{array} \end{array} \]

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) 2e+59) (* x (- 1.0 (* y z))) (* y (* -1.0 (* x z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 2e+59) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (-1.0 * (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 * z) <= 2d+59) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = y * ((-1.0d0) * (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 * z) <= 2e+59) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (-1.0 * (x * z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 2e+59:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = y * (-1.0 * (x * z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 2e+59)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(y * Float64(-1.0 * 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 * z) <= 2e+59)
		tmp = x * (1.0 - (y * z));
	else
		tmp = y * (-1.0 * (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[N[(y * z), $MachinePrecision], 2e+59], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(-1.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 1.99999999999999994e59

   1. Initial program 98.0%

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

   if 1.99999999999999994e59 < (*.f64 y z)

   1. Initial program 86.3%

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

   3. Taylor expanded in y around inf 96.3%

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

   4. Taylor expanded in z around inf 98.1%

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

Alternative 6: 51.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (if (<= y -1.8e+117) (/ (* x y) y) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.8e+117) {
		tmp = (x * y) / 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 <= (-1.8d+117)) then
        tmp = (x * y) / 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 <= -1.8e+117) {
		tmp = (x * y) / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -1.8e+117:
		tmp = (x * y) / y
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1.8e+117)
		tmp = Float64(Float64(x * y) / 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 <= -1.8e+117)
		tmp = (x * y) / 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, -1.8e+117], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.80000000000000006e117

   1. Initial program 89.2%

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

   3. Taylor expanded in y around inf 96.0%

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

   4. Taylor expanded in z around 0 12.9%

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

      1. associate-*r/ 16.3%

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

      2. *-commutative 16.3%

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

   6. Applied egg-rr 16.3%

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

   if -1.80000000000000006e117 < y

   1. Initial program 96.5%

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

   3. Taylor expanded in y around 0 58.8%

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

Alternative 7: 49.2% 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 95.5%

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

3. Taylor expanded in y around 0 52.6%

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

Reproduce

herbie shell --seed 2024050 -o generate:simplify
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))