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

Percentage Accurate: 96.2% → 96.3%

Time: 4.6s

Alternatives: 5

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+207}:\\ \;\;\;\;x - y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e+207) (- x (* y (* x z))) (* x (- 1.0 (* y z)))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+207) {
		tmp = x - (y * (x * z));
	} else {
		tmp = x * (1.0 - (y * z));
	}
	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 <= (-3.8d+207)) then
        tmp = x - (y * (x * z))
    else
        tmp = x * (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e+207) {
		tmp = x - (y * (x * z));
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if y <= -3.8e+207:
		tmp = x - (y * (x * z))
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e+207)
		tmp = Float64(x - Float64(y * Float64(x * z)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.8e+207)
		tmp = x - (y * (x * z));
	else
		tmp = x * (1.0 - (y * z));
	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[y, -3.8e+207], N[(x - N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.79999999999999986e207

   1. Initial program 85.8%

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

   2. Taylor expanded in x around 0 85.8%

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

      1. *-commutative 85.8%

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

      2. distribute-rgt-out-- 85.8%

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

      3. associate-*r* 96.1%

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

      4. *-lft-identity 96.1%

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

   4. Simplified 96.1%

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

   if -3.79999999999999986e207 < y

   1. Initial program 97.9%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+207}:\\ \;\;\;\;x - y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 2: 97.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -Double.POSITIVE_INFINITY) {
		tmp = z * (y * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -math.inf:
		tmp = z * (y * -x)
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

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

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -Inf)
		tmp = z * (y * -x);
	else
		tmp = x * (1.0 - (y * z));
	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], (-Infinity)], 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) < -inf.0

   1. Initial program 79.9%

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

      1. add-cbrt-cube 79.9%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(x \cdot \left(1 - y \cdot z\right)\right) \cdot \left(x \cdot \left(1 - y \cdot z\right)\right)\right) \cdot \left(x \cdot \left(1 - y \cdot z\right)\right)}} \]

      2. pow3 79.9%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(x \cdot \left(1 - y \cdot z\right)\right)}^{3}}} \]

   3. Applied egg-rr 79.9%

      \[\leadsto \color{blue}{\sqrt[3]{{\left(x \cdot \left(1 - y \cdot z\right)\right)}^{3}}} \]

   4. Taylor expanded in y around inf 84.1%

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

      1. mul-1-neg 100.0%

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

      2. associate-*r* 79.9%

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

      3. distribute-lft-neg-in 79.9%

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

      4. distribute-rgt-neg-out 79.9%

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

      5. *-commutative 79.9%

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

   6. Simplified 79.9%

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

      1. add-sqr-sqrt 31.5%

         \[\leadsto \sqrt[3]{\color{blue}{\sqrt{{\left(x \cdot \left(y \cdot \left(-z\right)\right)\right)}^{3}} \cdot \sqrt{{\left(x \cdot \left(y \cdot \left(-z\right)\right)\right)}^{3}}}} \]

      2. sqrt-unprod 31.5%

         \[\leadsto \sqrt[3]{\color{blue}{\sqrt{{\left(x \cdot \left(y \cdot \left(-z\right)\right)\right)}^{3} \cdot {\left(x \cdot \left(y \cdot \left(-z\right)\right)\right)}^{3}}}} \]

      3. pow-prod-up 31.5%

         \[\leadsto \sqrt[3]{\sqrt{\color{blue}{{\left(x \cdot \left(y \cdot \left(-z\right)\right)\right)}^{\left(3 + 3\right)}}}} \]

      4. add-sqr-sqrt 17.6%

         \[\leadsto \sqrt[3]{\sqrt{{\left(x \cdot \left(y \cdot \color{blue}{\left(\sqrt{-z} \cdot \sqrt{-z}\right)}\right)\right)}^{\left(3 + 3\right)}}} \]

      5. sqrt-unprod 31.5%

         \[\leadsto \sqrt[3]{\sqrt{{\left(x \cdot \left(y \cdot \color{blue}{\sqrt{\left(-z\right) \cdot \left(-z\right)}}\right)\right)}^{\left(3 + 3\right)}}} \]

      6. sqr-neg 31.5%

         \[\leadsto \sqrt[3]{\sqrt{{\left(x \cdot \left(y \cdot \sqrt{\color{blue}{z \cdot z}}\right)\right)}^{\left(3 + 3\right)}}} \]

      7. sqrt-unprod 13.9%

         \[\leadsto \sqrt[3]{\sqrt{{\left(x \cdot \left(y \cdot \color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)}\right)\right)}^{\left(3 + 3\right)}}} \]

      8. add-sqr-sqrt 31.5%

         \[\leadsto \sqrt[3]{\sqrt{{\left(x \cdot \left(y \cdot \color{blue}{z}\right)\right)}^{\left(3 + 3\right)}}} \]

      9. metadata-eval 31.5%

         \[\leadsto \sqrt[3]{\sqrt{{\left(x \cdot \left(y \cdot z\right)\right)}^{\color{blue}{6}}}} \]

   8. Applied egg-rr 31.5%

      \[\leadsto \sqrt[3]{\color{blue}{\sqrt{{\left(x \cdot \left(y \cdot z\right)\right)}^{6}}}} \]
   9. Step-by-step derivation

      1. *-commutative 31.5%

         \[\leadsto \sqrt[3]{\sqrt{{\color{blue}{\left(\left(y \cdot z\right) \cdot x\right)}}^{6}}} \]

   10. Simplified 31.5%

       \[\leadsto \sqrt[3]{\color{blue}{\sqrt{{\left(\left(y \cdot z\right) \cdot x\right)}^{6}}}} \]

   11. Taylor expanded in y around -inf 100.0%

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

       1. mul-1-neg 100.0%

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

       2. *-commutative 100.0%

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

       3. associate-*l* 99.9%

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

       4. *-commutative 99.9%

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

       5. distribute-rgt-neg-in 99.9%

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

   13. Simplified 99.9%

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

   if -inf.0 < (*.f64 y z)

   1. Initial program 98.3%

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

4. Final simplification 98.4%

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

Alternative 3: 72.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+118} \lor \neg \left(y \leq 2.2 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.8e+118) (not (<= y 2.2e-85))) (* x (* y (- z))) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.8e+118) || !(y <= 2.2e-85)) {
		tmp = x * (y * -z);
	} 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 ((y <= (-6.8d+118)) .or. (.not. (y <= 2.2d-85))) then
        tmp = x * (y * -z)
    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 ((y <= -6.8e+118) || !(y <= 2.2e-85)) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -6.8e+118) or not (y <= 2.2e-85):
		tmp = x * (y * -z)
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.8e+118) || !(y <= 2.2e-85))
		tmp = Float64(x * Float64(y * Float64(-z)));
	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 ((y <= -6.8e+118) || ~((y <= 2.2e-85)))
		tmp = x * (y * -z);
	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[y, -6.8e+118], N[Not[LessEqual[y, 2.2e-85]], $MachinePrecision]], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.79999999999999973e118 or 2.2e-85 < y

   1. Initial program 94.3%

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

   2. Taylor expanded in y around inf 69.4%

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

      1. mul-1-neg 69.4%

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

      2. associate-*r* 67.2%

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

      3. distribute-lft-neg-in 67.2%

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

      4. distribute-rgt-neg-out 67.2%

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

      5. *-commutative 67.2%

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

   4. Simplified 67.2%

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

   if -6.79999999999999973e118 < y < 2.2e-85

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0 70.3%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+118} \lor \neg \left(y \leq 2.2 \cdot 10^{-85}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -2.7e+118)
   (* y (* x (- z)))
   (if (<= y 1.95e-85) x (* x (* y (- z))))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+118) {
		tmp = y * (x * -z);
	} else if (y <= 1.95e-85) {
		tmp = x;
	} else {
		tmp = x * (y * -z);
	}
	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 <= (-2.7d+118)) then
        tmp = y * (x * -z)
    else if (y <= 1.95d-85) then
        tmp = x
    else
        tmp = x * (y * -z)
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.7e+118) {
		tmp = y * (x * -z);
	} else if (y <= 1.95e-85) {
		tmp = x;
	} else {
		tmp = x * (y * -z);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if y <= -2.7e+118:
		tmp = y * (x * -z)
	elif y <= 1.95e-85:
		tmp = x
	else:
		tmp = x * (y * -z)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -2.7e+118)
		tmp = Float64(y * Float64(x * Float64(-z)));
	elseif (y <= 1.95e-85)
		tmp = x;
	else
		tmp = Float64(x * Float64(y * Float64(-z)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.7e+118)
		tmp = y * (x * -z);
	elseif (y <= 1.95e-85)
		tmp = x;
	else
		tmp = x * (y * -z);
	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[y, -2.7e+118], N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.95e-85], x, N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e118

   1. Initial program 88.7%

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

   2. Taylor expanded in y around inf 81.5%

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

      1. mul-1-neg 81.5%

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

      2. distribute-rgt-neg-in 81.5%

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

      3. distribute-lft-neg-out 81.5%

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

      4. *-commutative 81.5%

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

   4. Simplified 81.5%

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

   if -2.7e118 < y < 1.94999999999999994e-85

   1. Initial program 99.1%

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

   2. Taylor expanded in y around 0 70.3%

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

   if 1.94999999999999994e-85 < y

   1. Initial program 97.6%

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

   2. Taylor expanded in y around inf 62.2%

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

      1. mul-1-neg 62.2%

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

      2. associate-*r* 63.2%

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

      3. distribute-lft-neg-in 63.2%

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

      4. distribute-rgt-neg-out 63.2%

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

      5. *-commutative 63.2%

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

   4. Simplified 63.2%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{+118}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 5: 50.8% 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 49.6%

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

3. Final simplification 49.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023242 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))