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

Percentage Accurate: 96.1% → 99.1%

Time: 5.6s

Alternatives: 6

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: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+101}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(-z\right)\\ \mathbf{elif}\;y \cdot z \leq 4 \cdot 10^{+222}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -5e+101)
   (* (* y x) (- z))
   (if (<= (* y z) 4e+222) (- x (* (* y z) x)) (* y (* z (- x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5e+101) {
		tmp = (y * x) * -z;
	} else if ((y * z) <= 4e+222) {
		tmp = x - ((y * z) * 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 ((y * z) <= (-5d+101)) then
        tmp = (y * x) * -z
    else if ((y * z) <= 4d+222) then
        tmp = x - ((y * z) * 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 ((y * z) <= -5e+101) {
		tmp = (y * x) * -z;
	} else if ((y * z) <= 4e+222) {
		tmp = x - ((y * z) * x);
	} 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) <= -5e+101:
		tmp = (y * x) * -z
	elif (y * z) <= 4e+222:
		tmp = x - ((y * z) * 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 (Float64(y * z) <= -5e+101)
		tmp = Float64(Float64(y * x) * Float64(-z));
	elseif (Float64(y * z) <= 4e+222)
		tmp = Float64(x - Float64(Float64(y * z) * 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 ((y * z) <= -5e+101)
		tmp = (y * x) * -z;
	elseif ((y * z) <= 4e+222)
		tmp = x - ((y * z) * 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[N[(y * z), $MachinePrecision], -5e+101], N[(N[(y * x), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 4e+222], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -4.99999999999999989e101

   1. Initial program 86.1%

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

   3. Taylor expanded in y around inf 86.1%

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

      1. mul-1-neg 86.1%

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

      2. associate-*r* 97.8%

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

   5. Simplified 97.8%

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

   if -4.99999999999999989e101 < (*.f64 y z) < 4.0000000000000002e222

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-rgt-in 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. distribute-rgt-neg-in 99.9%

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

   4. Applied egg-rr 99.9%

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

      1. add-sqr-sqrt 51.8%

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

      2. sqrt-unprod 78.2%

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

      3. distribute-rgt-neg-out 78.2%

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

      4. distribute-rgt-neg-out 78.2%

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

      5. sqr-neg 78.2%

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

      6. sqrt-prod 39.1%

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

      7. add-sqr-sqrt 66.2%

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

      8. cancel-sign-sub 66.2%

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

      9. distribute-rgt-neg-out 66.2%

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

      10. associate-*l* 62.2%

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

      11. add-sqr-sqrt 29.6%

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

      12. sqrt-unprod 65.7%

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

      13. sqr-neg 65.7%

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

      14. sqrt-unprod 43.5%

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

      15. add-sqr-sqrt 90.8%

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

   6. Applied egg-rr 90.8%

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

   7. Taylor expanded in y around 0 99.9%

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

   if 4.0000000000000002e222 < (*.f64 y z)

   1. Initial program 79.7%

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

   3. Taylor expanded in y around inf 79.7%

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

      1. mul-1-neg 79.7%

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

      2. associate-*r* 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-*l* 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+101}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(-z\right)\\ \mathbf{elif}\;y \cdot z \leq 4 \cdot 10^{+222}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5000000000000:\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(-z\right)\\ \mathbf{elif}\;y \cdot z \leq 0.1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 4 \cdot 10^{+222}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

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) -5000000000000.0)
   (* (* y x) (- z))
   (if (<= (* y z) 0.1)
     x
     (if (<= (* y z) 4e+222) (* (* y z) (- x)) (* y (* z (- x)))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -5000000000000.0) {
		tmp = (y * x) * -z;
	} else if ((y * z) <= 0.1) {
		tmp = x;
	} else if ((y * z) <= 4e+222) {
		tmp = (y * z) * -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 ((y * z) <= (-5000000000000.0d0)) then
        tmp = (y * x) * -z
    else if ((y * z) <= 0.1d0) then
        tmp = x
    else if ((y * z) <= 4d+222) then
        tmp = (y * z) * -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 ((y * z) <= -5000000000000.0) {
		tmp = (y * x) * -z;
	} else if ((y * z) <= 0.1) {
		tmp = x;
	} else if ((y * z) <= 4e+222) {
		tmp = (y * z) * -x;
	} 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) <= -5000000000000.0:
		tmp = (y * x) * -z
	elif (y * z) <= 0.1:
		tmp = x
	elif (y * z) <= 4e+222:
		tmp = (y * z) * -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 (Float64(y * z) <= -5000000000000.0)
		tmp = Float64(Float64(y * x) * Float64(-z));
	elseif (Float64(y * z) <= 0.1)
		tmp = x;
	elseif (Float64(y * z) <= 4e+222)
		tmp = Float64(Float64(y * z) * Float64(-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 ((y * z) <= -5000000000000.0)
		tmp = (y * x) * -z;
	elseif ((y * z) <= 0.1)
		tmp = x;
	elseif ((y * z) <= 4e+222)
		tmp = (y * z) * -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[N[(y * z), $MachinePrecision], -5000000000000.0], N[(N[(y * x), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 0.1], x, If[LessEqual[N[(y * z), $MachinePrecision], 4e+222], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 y z) < -5e12

   1. Initial program 89.8%

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

   3. Taylor expanded in y around inf 89.5%

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

      1. mul-1-neg 89.5%

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

      2. associate-*r* 95.1%

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

   5. Simplified 95.1%

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

   if -5e12 < (*.f64 y z) < 0.10000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 94.7%

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

   if 0.10000000000000001 < (*.f64 y z) < 4.0000000000000002e222

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. associate-*r* 87.9%

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

   5. Simplified 87.9%

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

   6. Taylor expanded in x around 0 99.7%

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

   if 4.0000000000000002e222 < (*.f64 y z)

   1. Initial program 79.7%

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

   3. Taylor expanded in y around inf 79.7%

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

      1. mul-1-neg 79.7%

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

      2. associate-*r* 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-*l* 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5000000000000:\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(-z\right)\\ \mathbf{elif}\;y \cdot z \leq 0.1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 4 \cdot 10^{+222}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \left(y \cdot x\right) \cdot \left(-z\right)\\ \mathbf{if}\;y \cdot z \leq -5000000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 0.1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 4 \cdot 10^{+222}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 (* (* y x) (- z))))
   (if (<= (* y z) -5000000000000.0)
     t_0
     (if (<= (* y z) 0.1) x (if (<= (* y z) 4e+222) (* (* y z) (- x)) t_0)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = (y * x) * -z;
	double tmp;
	if ((y * z) <= -5000000000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.1) {
		tmp = x;
	} else if ((y * z) <= 4e+222) {
		tmp = (y * z) * -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 = (y * x) * -z
    if ((y * z) <= (-5000000000000.0d0)) then
        tmp = t_0
    else if ((y * z) <= 0.1d0) then
        tmp = x
    else if ((y * z) <= 4d+222) then
        tmp = (y * z) * -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 = (y * x) * -z;
	double tmp;
	if ((y * z) <= -5000000000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.1) {
		tmp = x;
	} else if ((y * z) <= 4e+222) {
		tmp = (y * z) * -x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = (y * x) * -z
	tmp = 0
	if (y * z) <= -5000000000000.0:
		tmp = t_0
	elif (y * z) <= 0.1:
		tmp = x
	elif (y * z) <= 4e+222:
		tmp = (y * z) * -x
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(Float64(y * x) * Float64(-z))
	tmp = 0.0
	if (Float64(y * z) <= -5000000000000.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 0.1)
		tmp = x;
	elseif (Float64(y * z) <= 4e+222)
		tmp = Float64(Float64(y * z) * Float64(-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 = (y * x) * -z;
	tmp = 0.0;
	if ((y * z) <= -5000000000000.0)
		tmp = t_0;
	elseif ((y * z) <= 0.1)
		tmp = x;
	elseif ((y * z) <= 4e+222)
		tmp = (y * z) * -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[(N[(y * x), $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[N[(y * z), $MachinePrecision], -5000000000000.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 0.1], x, If[LessEqual[N[(y * z), $MachinePrecision], 4e+222], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -5e12 or 4.0000000000000002e222 < (*.f64 y z)

   1. Initial program 86.8%

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

   3. Taylor expanded in y around inf 86.6%

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

      1. mul-1-neg 86.6%

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

      2. associate-*r* 96.5%

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

   5. Simplified 96.5%

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

   if -5e12 < (*.f64 y z) < 0.10000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 94.7%

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

   if 0.10000000000000001 < (*.f64 y z) < 4.0000000000000002e222

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. associate-*r* 87.9%

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

   5. Simplified 87.9%

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

   6. Taylor expanded in x around 0 99.7%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5000000000000:\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(-z\right)\\ \mathbf{elif}\;y \cdot z \leq 0.1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 4 \cdot 10^{+222}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+101}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(-z\right)\\ \mathbf{elif}\;y \cdot z \leq 4 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

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) -5e+101)
   (* (* y x) (- z))
   (if (<= (* y z) 4e+222) (* 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) <= -5e+101) {
		tmp = (y * x) * -z;
	} else if ((y * z) <= 4e+222) {
		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) <= (-5d+101)) then
        tmp = (y * x) * -z
    else if ((y * z) <= 4d+222) 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) <= -5e+101) {
		tmp = (y * x) * -z;
	} else if ((y * z) <= 4e+222) {
		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) <= -5e+101:
		tmp = (y * x) * -z
	elif (y * z) <= 4e+222:
		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) <= -5e+101)
		tmp = Float64(Float64(y * x) * Float64(-z));
	elseif (Float64(y * z) <= 4e+222)
		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) <= -5e+101)
		tmp = (y * x) * -z;
	elseif ((y * z) <= 4e+222)
		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], -5e+101], N[(N[(y * x), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[N[(y * z), $MachinePrecision], 4e+222], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -4.99999999999999989e101

   1. Initial program 86.1%

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

   3. Taylor expanded in y around inf 86.1%

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

      1. mul-1-neg 86.1%

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

      2. associate-*r* 97.8%

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

   5. Simplified 97.8%

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

   if -4.99999999999999989e101 < (*.f64 y z) < 4.0000000000000002e222

   1. Initial program 99.9%

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

   if 4.0000000000000002e222 < (*.f64 y z)

   1. Initial program 79.7%

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

   3. Taylor expanded in y around inf 79.7%

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

      1. mul-1-neg 79.7%

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

      2. associate-*r* 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-*l* 100.0%

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

   5. Simplified 100.0%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -5 \cdot 10^{+101}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \left(-z\right)\\ \mathbf{elif}\;y \cdot z \leq 4 \cdot 10^{+222}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.8% accurate, 0.3× speedup

Math

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

FPCore

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

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -1.0) || !((y * z) <= 1.0)) {
		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 (((y * z) <= (-1.0d0)) .or. (.not. ((y * z) <= 1.0d0))) 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 (((y * z) <= -1.0) || !((y * z) <= 1.0)) {
		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 ((y * z) <= -1.0) or not ((y * z) <= 1.0):
		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 ((Float64(y * z) <= -1.0) || !(Float64(y * z) <= 1.0))
		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 (((y * z) <= -1.0) || ~(((y * z) <= 1.0)))
		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[N[(y * z), $MachinePrecision], -1.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 1.0]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.6%

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

   3. Taylor expanded in y around inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. associate-*r* 93.1%

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

   5. Simplified 93.1%

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

   6. Taylor expanded in x around 0 89.7%

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

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

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 96.1%

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

4. Final simplification 92.8%

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

Alternative 6: 50.6% 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 95.1%

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

3. Taylor expanded in y around 0 48.3%

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

Reproduce

herbie shell --seed 2024085 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))