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

Percentage Accurate: 96.1% → 98.0%

Time: 4.0s

Alternatives: 6

Speedup: 0.6×

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: 98.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+203}:\\ \;\;\;\;x + \frac{x}{\frac{\frac{-1}{y}}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 5e+203) (+ x (/ x (/ (/ -1.0 y) z))) (* z (* y (- x)))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+203) {
		tmp = x + (x / ((-1.0 / y) / z));
	} else {
		tmp = z * (y * -x);
	}
	return tmp;
}

Fortran

NOTE: 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+203) then
        tmp = x + (x / (((-1.0d0) / y) / z))
    else
        tmp = z * (y * -x)
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+203) {
		tmp = x + (x / ((-1.0 / y) / z));
	} else {
		tmp = z * (y * -x);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 5e+203:
		tmp = x + (x / ((-1.0 / y) / z))
	else:
		tmp = z * (y * -x)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 5e+203)
		tmp = Float64(x + Float64(x / Float64(Float64(-1.0 / y) / z)));
	else
		tmp = Float64(z * Float64(y * Float64(-x)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 5e+203)
		tmp = x + (x / ((-1.0 / y) / z));
	else
		tmp = z * (y * -x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 5e+203], N[(x + N[(x / N[(N[(-1.0 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 4.99999999999999994e203

   1. Initial program 98.7%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around 0 98.7%

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

      1. mul-1-neg 98.7%

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

      2. associate-*r* 94.0%

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

   4. Simplified 94.0%

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

      1. unsub-neg 94.0%

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

      2. associate-*l* 98.7%

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

   6. Applied egg-rr 98.7%

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

      1. add-sqr-sqrt 55.7%

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

      2. sqrt-unprod 71.2%

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

      3. sqr-neg 71.2%

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

      4. sqrt-unprod 25.4%

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

      5. add-sqr-sqrt 62.5%

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

      6. distribute-lft-neg-in 62.5%

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

      7. neg-mul-1 62.5%

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

      8. metadata-eval 62.5%

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

      9. associate-/r/ 62.5%

         \[\leadsto x - x \cdot \color{blue}{\frac{1}{\frac{-1}{y \cdot z}}} \]

      10. div-inv 62.5%

          \[\leadsto x - \color{blue}{\frac{x}{\frac{-1}{y \cdot z}}} \]

      11. frac-2neg 62.5%

          \[\leadsto x - \color{blue}{\frac{-x}{-\frac{-1}{y \cdot z}}} \]

      12. distribute-neg-frac 62.5%

          \[\leadsto x - \frac{-x}{\color{blue}{\frac{--1}{y \cdot z}}} \]

      13. metadata-eval 62.5%

          \[\leadsto x - \frac{-x}{\frac{\color{blue}{1}}{y \cdot z}} \]

      14. associate-/r* 62.5%

          \[\leadsto x - \frac{-x}{\color{blue}{\frac{\frac{1}{y}}{z}}} \]

      15. metadata-eval 62.5%

          \[\leadsto x - \frac{-x}{\frac{\frac{\color{blue}{--1}}{y}}{z}} \]

      16. add-sqr-sqrt 37.0%

          \[\leadsto x - \frac{-x}{\frac{\frac{--1}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}}}{z}} \]

      17. sqrt-unprod 72.1%

          \[\leadsto x - \frac{-x}{\frac{\frac{--1}{\color{blue}{\sqrt{y \cdot y}}}}{z}} \]

      18. sqr-neg 72.1%

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

      19. sqrt-unprod 42.8%

          \[\leadsto x - \frac{-x}{\frac{\frac{--1}{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}}}{z}} \]

      20. add-sqr-sqrt 99.0%

          \[\leadsto x - \frac{-x}{\frac{\frac{--1}{\color{blue}{-y}}}{z}} \]

      21. frac-2neg 99.0%

          \[\leadsto x - \frac{-x}{\frac{\color{blue}{\frac{-1}{y}}}{z}} \]

   8. Applied egg-rr 99.0%

      \[\leadsto x - \color{blue}{\frac{-x}{\frac{\frac{-1}{y}}{z}}} \]

   if 4.99999999999999994e203 < (*.f64 y z)

   1. Initial program 82.4%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around inf 82.4%

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

      1. mul-1-neg 82.4%

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

      2. associate-*r* 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+203}:\\ \;\;\;\;x + \frac{x}{\frac{\frac{-1}{y}}{z}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 2: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 5e+203) (* x (- 1.0 (* y z))) (* z (* y (- x)))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+203) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = z * (y * -x);
	}
	return tmp;
}

Fortran

NOTE: 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+203) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = z * (y * -x)
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+203) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = z * (y * -x);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 5e+203:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = z * (y * -x)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 5e+203)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(z * Float64(y * Float64(-x)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 5e+203)
		tmp = x * (1.0 - (y * z));
	else
		tmp = z * (y * -x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 5e+203], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 4.99999999999999994e203

   1. Initial program 98.7%

      \[x \cdot \left(1 - y \cdot z\right) \]

   if 4.99999999999999994e203 < (*.f64 y z)

   1. Initial program 82.4%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around inf 82.4%

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

      1. mul-1-neg 82.4%

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

      2. associate-*r* 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+203}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 3: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+203}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 5e+203) (- x (* (* y z) x)) (* z (* y (- x)))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+203) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = z * (y * -x);
	}
	return tmp;
}

Fortran

NOTE: 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+203) then
        tmp = x - ((y * z) * x)
    else
        tmp = z * (y * -x)
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+203) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = z * (y * -x);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 5e+203:
		tmp = x - ((y * z) * x)
	else:
		tmp = z * (y * -x)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 5e+203)
		tmp = Float64(x - Float64(Float64(y * z) * x));
	else
		tmp = Float64(z * Float64(y * Float64(-x)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 5e+203)
		tmp = x - ((y * z) * x);
	else
		tmp = z * (y * -x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 5e+203], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 4.99999999999999994e203

   1. Initial program 98.7%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around 0 98.7%

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

      1. mul-1-neg 98.7%

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

      2. associate-*r* 94.0%

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

   4. Simplified 94.0%

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

      1. unsub-neg 94.0%

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

      2. associate-*l* 98.7%

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

   6. Applied egg-rr 98.7%

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

   if 4.99999999999999994e203 < (*.f64 y z)

   1. Initial program 82.4%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around inf 82.4%

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

      1. mul-1-neg 82.4%

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

      2. associate-*r* 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+203}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 4: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-71} \lor \neg \left(z \leq 2.25 \cdot 10^{+151}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.3e-71) (not (<= z 2.25e+151))) (* z (* y (- x))) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.3e-71) || !(z <= 2.25e+151)) {
		tmp = z * (y * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.3d-71)) .or. (.not. (z <= 2.25d+151))) then
        tmp = z * (y * -x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.3e-71) || !(z <= 2.25e+151)) {
		tmp = z * (y * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -2.3e-71) or not (z <= 2.25e+151):
		tmp = z * (y * -x)
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.3e-71) || !(z <= 2.25e+151))
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.3e-71) || ~((z <= 2.25e+151)))
		tmp = z * (y * -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -2.3e-71], N[Not[LessEqual[z, 2.25e+151]], $MachinePrecision]], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999998e-71 or 2.2499999999999999e151 < z

   1. Initial program 93.7%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around inf 72.0%

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

      1. mul-1-neg 72.0%

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

      2. associate-*r* 74.6%

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

   4. Simplified 74.6%

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

   if -2.2999999999999998e-71 < z < 2.2499999999999999e151

   1. Initial program 98.7%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around 0 78.5%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-71} \lor \neg \left(z \leq 2.25 \cdot 10^{+151}\right):\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 75.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-71}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= z -2.4e-71) (* z (* y (- x))) (if (<= z 5e+91) x (* y (* z (- x))))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.4e-71) {
		tmp = z * (y * -x);
	} else if (z <= 5e+91) {
		tmp = x;
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Fortran

NOTE: y and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.4d-71)) then
        tmp = z * (y * -x)
    else if (z <= 5d+91) then
        tmp = x
    else
        tmp = y * (z * -x)
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.4e-71) {
		tmp = z * (y * -x);
	} else if (z <= 5e+91) {
		tmp = x;
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if z <= -2.4e-71:
		tmp = z * (y * -x)
	elif z <= 5e+91:
		tmp = x
	else:
		tmp = y * (z * -x)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (z <= -2.4e-71)
		tmp = Float64(z * Float64(y * Float64(-x)));
	elseif (z <= 5e+91)
		tmp = x;
	else
		tmp = Float64(y * Float64(z * Float64(-x)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.4e-71)
		tmp = z * (y * -x);
	elseif (z <= 5e+91)
		tmp = x;
	else
		tmp = y * (z * -x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[z, -2.4e-71], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e+91], x, N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4e-71

   1. Initial program 97.3%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around inf 70.3%

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

      1. mul-1-neg 70.3%

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

      2. associate-*r* 69.2%

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

   4. Simplified 69.2%

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

   if -2.4e-71 < z < 5.0000000000000002e91

   1. Initial program 98.6%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around 0 79.8%

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

   if 5.0000000000000002e91 < z

   1. Initial program 88.7%

      \[x \cdot \left(1 - y \cdot z\right) \]

   2. Taylor expanded in y around inf 67.8%

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

      1. mul-1-neg 67.8%

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

      2. associate-*r* 72.0%

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

      3. distribute-rgt-neg-in 72.0%

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

      4. *-commutative 72.0%

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

      5. associate-*r* 76.7%

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

      6. distribute-rgt-neg-out 76.7%

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

   4. Simplified 76.7%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-71}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 6: 50.1% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: 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 y < z;
public static double code(double x, double y, double z) {
	return x;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.6%

   \[x \cdot \left(1 - y \cdot z\right) \]

2. Taylor expanded in y around 0 55.8%

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

3. Final simplification 55.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023298 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))