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

Percentage Accurate: 96.0% → 97.9%

Time: 5.2s

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: 96.0% 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: 97.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+226}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{-1}{\left(y \cdot y\right) \cdot \left(x \cdot \left(z \cdot z\right)\right)} + \frac{\frac{-1}{y}}{z \cdot x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 5e+226)
   (- x (* (* y z) x))
   (/ 1.0 (+ (/ -1.0 (* (* y y) (* x (* z z)))) (/ (/ -1.0 y) (* z x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+226) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = 1.0 / ((-1.0 / ((y * y) * (x * (z * z)))) + ((-1.0 / y) / (z * x)));
	}
	return tmp;
}

Fortran

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+226) then
        tmp = x - ((y * z) * x)
    else
        tmp = 1.0d0 / (((-1.0d0) / ((y * y) * (x * (z * z)))) + (((-1.0d0) / y) / (z * x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+226) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = 1.0 / ((-1.0 / ((y * y) * (x * (z * z)))) + ((-1.0 / y) / (z * x)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= 5e+226:
		tmp = x - ((y * z) * x)
	else:
		tmp = 1.0 / ((-1.0 / ((y * y) * (x * (z * z)))) + ((-1.0 / y) / (z * x)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 5e+226)
		tmp = Float64(x - Float64(Float64(y * z) * x));
	else
		tmp = Float64(1.0 / Float64(Float64(-1.0 / Float64(Float64(y * y) * Float64(x * Float64(z * z)))) + Float64(Float64(-1.0 / y) / Float64(z * x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 5e+226)
		tmp = x - ((y * z) * x);
	else
		tmp = 1.0 / ((-1.0 / ((y * y) * (x * (z * z)))) + ((-1.0 / y) / (z * x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 5e+226], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(-1.0 / N[(N[(y * y), $MachinePrecision] * N[(x * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-1.0 / y), $MachinePrecision] / N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 5.0000000000000005e226

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. distribute-rgt-in 98.3%

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

      3. *-un-lft-identity 98.3%

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

      4. distribute-rgt-neg-in 98.3%

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

   3. Applied egg-rr 98.3%

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

   if 5.0000000000000005e226 < (*.f64 y z)

   1. Initial program 77.4%

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

      1. add-cube-cbrt 77.3%

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

      2. pow3 77.3%

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

   3. Applied egg-rr 77.3%

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

      1. rem-cube-cbrt 77.4%

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

      2. *-commutative 77.4%

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

      3. flip-- 16.7%

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

      4. metadata-eval 16.7%

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

      5. unpow2 16.7%

         \[\leadsto \frac{1 - \color{blue}{{\left(y \cdot z\right)}^{2}}}{1 + y \cdot z} \cdot x \]

      6. associate-/r/ 16.5%

         \[\leadsto \color{blue}{\frac{1 - {\left(y \cdot z\right)}^{2}}{\frac{1 + y \cdot z}{x}}} \]

      7. clear-num 16.5%

         \[\leadsto \color{blue}{\frac{1}{\frac{\frac{1 + y \cdot z}{x}}{1 - {\left(y \cdot z\right)}^{2}}}} \]

      8. clear-num 16.5%

         \[\leadsto \frac{1}{\color{blue}{\frac{1}{\frac{1 - {\left(y \cdot z\right)}^{2}}{\frac{1 + y \cdot z}{x}}}}} \]

      9. associate-/r/ 16.7%

         \[\leadsto \frac{1}{\frac{1}{\color{blue}{\frac{1 - {\left(y \cdot z\right)}^{2}}{1 + y \cdot z} \cdot x}}} \]

      10. metadata-eval 16.7%

          \[\leadsto \frac{1}{\frac{1}{\frac{\color{blue}{1 \cdot 1} - {\left(y \cdot z\right)}^{2}}{1 + y \cdot z} \cdot x}} \]

      11. unpow2 16.7%

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

      12. flip-- 77.4%

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

      13. *-commutative 77.4%

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

   5. Applied egg-rr 77.4%

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

   6. Taylor expanded in y around inf 99.9%

      \[\leadsto \frac{1}{\color{blue}{-\left(\frac{1}{{y}^{2} \cdot \left({z}^{2} \cdot x\right)} + \frac{1}{y \cdot \left(z \cdot x\right)}\right)}} \]
   7. Step-by-step derivation

      1. unpow2 99.9%

         \[\leadsto \frac{1}{-\left(\frac{1}{\color{blue}{\left(y \cdot y\right)} \cdot \left({z}^{2} \cdot x\right)} + \frac{1}{y \cdot \left(z \cdot x\right)}\right)} \]

      2. *-commutative 99.9%

         \[\leadsto \frac{1}{-\left(\frac{1}{\left(y \cdot y\right) \cdot \color{blue}{\left(x \cdot {z}^{2}\right)}} + \frac{1}{y \cdot \left(z \cdot x\right)}\right)} \]

      3. unpow2 99.9%

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

      4. associate-/r* 99.9%

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

   8. Simplified 99.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+226}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{-1}{\left(y \cdot y\right) \cdot \left(x \cdot \left(z \cdot z\right)\right)} + \frac{\frac{-1}{y}}{z \cdot x}}\\ \end{array} \]

Alternative 2: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+226}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 5e+226) (* x (- 1.0 (* y z))) (* y (* z (- x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+226) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Fortran

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+226) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = y * (z * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+226) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= 5e+226:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = y * (z * -x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 5e+226)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(y * Float64(z * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 5e+226)
		tmp = x * (1.0 - (y * z));
	else
		tmp = y * (z * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 5e+226], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 5.0000000000000005e226

   1. Initial program 98.3%

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

   if 5.0000000000000005e226 < (*.f64 y z)

   1. Initial program 77.4%

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

   2. Taylor expanded in y around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-rgt-neg-in 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+226}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 3: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+226}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 5e+226) (- x (* (* y z) x)) (* y (* z (- x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+226) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Fortran

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+226) then
        tmp = x - ((y * z) * x)
    else
        tmp = y * (z * -x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+226) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y * z) <= 5e+226:
		tmp = x - ((y * z) * x)
	else:
		tmp = y * (z * -x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 5e+226)
		tmp = Float64(x - Float64(Float64(y * z) * x));
	else
		tmp = Float64(y * Float64(z * Float64(-x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 5e+226)
		tmp = x - ((y * z) * x);
	else
		tmp = y * (z * -x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], 5e+226], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 5.0000000000000005e226

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. distribute-rgt-in 98.3%

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

      3. *-un-lft-identity 98.3%

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

      4. distribute-rgt-neg-in 98.3%

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

   3. Applied egg-rr 98.3%

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

   if 5.0000000000000005e226 < (*.f64 y z)

   1. Initial program 77.4%

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

   2. Taylor expanded in y around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-rgt-neg-in 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+226}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 4: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-115} \lor \neg \left(z \leq 7 \cdot 10^{+100}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.3e-115) (not (<= z 7e+100))) (* (* y z) (- x)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.3e-115) || !(z <= 7e+100)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

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 <= (-3.3d-115)) .or. (.not. (z <= 7d+100))) then
        tmp = (y * z) * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.3e-115) || !(z <= 7e+100)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.3e-115) or not (z <= 7e+100):
		tmp = (y * z) * -x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.3e-115) || !(z <= 7e+100))
		tmp = Float64(Float64(y * z) * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.3e-115) || ~((z <= 7e+100)))
		tmp = (y * z) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.3e-115], N[Not[LessEqual[z, 7e+100]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999999e-115 or 6.99999999999999953e100 < z

   1. Initial program 94.8%

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

   2. Taylor expanded in y around inf 68.4%

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

      1. mul-1-neg 68.4%

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

      2. distribute-rgt-neg-out 68.4%

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

   4. Simplified 68.4%

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

   if -3.2999999999999999e-115 < z < 6.99999999999999953e100

   1. Initial program 97.7%

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

   2. Taylor expanded in y around 0 77.7%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-115} \lor \neg \left(z \leq 7 \cdot 10^{+100}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 70.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-115} \lor \neg \left(z \leq 8.5 \cdot 10^{+100}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.3e-115) (not (<= z 8.5e+100))) (* y (* z (- x))) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.3e-115) || !(z <= 8.5e+100)) {
		tmp = y * (z * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

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 <= (-3.3d-115)) .or. (.not. (z <= 8.5d+100))) then
        tmp = y * (z * -x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.3e-115) || !(z <= 8.5e+100)) {
		tmp = y * (z * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.3e-115) or not (z <= 8.5e+100):
		tmp = y * (z * -x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.3e-115) || !(z <= 8.5e+100))
		tmp = Float64(y * Float64(z * Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -3.3e-115) || ~((z <= 8.5e+100)))
		tmp = y * (z * -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.3e-115], N[Not[LessEqual[z, 8.5e+100]], $MachinePrecision]], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999999e-115 or 8.50000000000000043e100 < z

   1. Initial program 94.8%

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

   2. Taylor expanded in y around inf 68.8%

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

      1. mul-1-neg 68.8%

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

      2. distribute-rgt-neg-in 68.8%

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

      3. distribute-rgt-neg-in 68.8%

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

   4. Simplified 68.8%

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

   if -3.2999999999999999e-115 < z < 8.50000000000000043e100

   1. Initial program 97.7%

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

   2. Taylor expanded in y around 0 77.7%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{-115} \lor \neg \left(z \leq 8.5 \cdot 10^{+100}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 50.4% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

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

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
end function

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 96.2%

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

2. Taylor expanded in y around 0 53.1%

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

3. Final simplification 53.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023240 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))