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

Percentage Accurate: 95.9% → 96.8%

Time: 7.5s

Alternatives: 6

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - y \cdot z\right) \leq 5 \cdot 10^{+281}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{\frac{-1}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* x (- 1.0 (* y z))) 5e+281)
   (- x (* x (* y z)))
   (* z (/ x (/ -1.0 y)))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((x * (1.0 - (y * z))) <= 5e+281) {
		tmp = x - (x * (y * z));
	} else {
		tmp = z * (x / (-1.0 / y));
	}
	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 ((x * (1.0d0 - (y * z))) <= 5d+281) then
        tmp = x - (x * (y * z))
    else
        tmp = z * (x / ((-1.0d0) / y))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((x * (1.0 - (y * z))) <= 5e+281) {
		tmp = x - (x * (y * z));
	} else {
		tmp = z * (x / (-1.0 / y));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (x * (1.0 - (y * z))) <= 5e+281:
		tmp = x - (x * (y * z))
	else:
		tmp = z * (x / (-1.0 / y))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(x * Float64(1.0 - Float64(y * z))) <= 5e+281)
		tmp = Float64(x - Float64(x * Float64(y * z)));
	else
		tmp = Float64(z * Float64(x / Float64(-1.0 / y)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x * (1.0 - (y * z))) <= 5e+281)
		tmp = x - (x * (y * z));
	else
		tmp = z * (x / (-1.0 / y));
	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[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 5e+281], N[(x - N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(x / N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 y z))) < 5.00000000000000016e281

   1. Initial program 99.0%

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

      1. flip-- 84.0%

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

      2. associate-*r/ 80.7%

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

      3. metadata-eval 80.7%

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

      4. pow2 80.7%

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

   3. Applied egg-rr 80.7%

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

      1. associate-/l* 84.0%

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

   5. Simplified 84.0%

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

   6. Taylor expanded in x around 0 67.5%

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

      1. fma-def 67.5%

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

      2. associate-/l* 67.1%

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

      3. div-sub 67.1%

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

      4. unpow2 67.1%

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

      5. unpow2 67.1%

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

      6. swap-sqr 81.9%

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

      7. unpow2 81.9%

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

      8. div-sub 81.9%

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

      9. unpow2 81.9%

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

      10. swap-sqr 67.1%

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

   8. Simplified 67.1%

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

   9. Taylor expanded in y around 0 94.6%

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

       1. +-commutative 94.6%

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

       2. neg-mul-1 94.6%

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

       3. unsub-neg 94.6%

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

       4. associate-*r* 99.0%

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

       5. *-commutative 99.0%

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

   11. Simplified 99.0%

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

   if 5.00000000000000016e281 < (*.f64 x (-.f64 1 (*.f64 y z)))

   1. Initial program 81.1%

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

      1. flip-- 41.7%

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

      2. associate-*r/ 41.7%

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

      3. metadata-eval 41.7%

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

      4. pow2 41.7%

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

   3. Applied egg-rr 41.7%

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

      1. associate-/l* 41.7%

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

   5. Simplified 41.7%

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

   6. Taylor expanded in y around inf 81.1%

      \[\leadsto \frac{x}{\color{blue}{\frac{-1}{y \cdot z}}} \]
   7. Step-by-step derivation

      1. associate-/r* 81.1%

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

   8. Simplified 81.1%

      \[\leadsto \frac{x}{\color{blue}{\frac{\frac{-1}{y}}{z}}} \]
   9. Step-by-step derivation

      1. add-cube-cbrt 81.1%

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

      2. div-inv 81.1%

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

      3. times-frac 99.4%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{-1}{y}} \cdot \frac{\sqrt[3]{x}}{\frac{1}{z}}} \]

      4. pow2 99.4%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{\frac{-1}{y}} \cdot \frac{\sqrt[3]{x}}{\frac{1}{z}} \]

   10. Applied egg-rr 99.4%

       \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{\frac{-1}{y}} \cdot \frac{\sqrt[3]{x}}{\frac{1}{z}}} \]
   11. Step-by-step derivation

       1. associate-/r/ 99.3%

          \[\leadsto \frac{{\left(\sqrt[3]{x}\right)}^{2}}{\frac{-1}{y}} \cdot \color{blue}{\left(\frac{\sqrt[3]{x}}{1} \cdot z\right)} \]

       2. /-rgt-identity 99.3%

          \[\leadsto \frac{{\left(\sqrt[3]{x}\right)}^{2}}{\frac{-1}{y}} \cdot \left(\color{blue}{\sqrt[3]{x}} \cdot z\right) \]

       3. associate-*r* 99.3%

          \[\leadsto \color{blue}{\left(\frac{{\left(\sqrt[3]{x}\right)}^{2}}{\frac{-1}{y}} \cdot \sqrt[3]{x}\right) \cdot z} \]

       4. associate-*l/ 99.3%

          \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\frac{-1}{y}}} \cdot z \]

       5. unpow2 99.3%

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

       6. rem-3cbrt-lft 99.8%

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

   12. Simplified 99.8%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - y \cdot z\right) \leq 5 \cdot 10^{+281}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{\frac{-1}{y}}\\ \end{array} \]

Alternative 2: 97.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_0 := x \cdot \left(1 - y \cdot z\right)\\ \mathbf{if}\;t_0 \leq 4 \cdot 10^{+287}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* y z)))))
   (if (<= t_0 4e+287) t_0 (* y (* x (- z))))))

C

assert(y < z);
double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double tmp;
	if (t_0 <= 4e+287) {
		tmp = t_0;
	} else {
		tmp = y * (x * -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) :: t_0
    real(8) :: tmp
    t_0 = x * (1.0d0 - (y * z))
    if (t_0 <= 4d+287) then
        tmp = t_0
    else
        tmp = y * (x * -z)
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double tmp;
	if (t_0 <= 4e+287) {
		tmp = t_0;
	} else {
		tmp = y * (x * -z);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	t_0 = x * (1.0 - (y * z))
	tmp = 0
	if t_0 <= 4e+287:
		tmp = t_0
	else:
		tmp = y * (x * -z)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(y * z)))
	tmp = 0.0
	if (t_0 <= 4e+287)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(x * Float64(-z)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - (y * z));
	tmp = 0.0;
	if (t_0 <= 4e+287)
		tmp = t_0;
	else
		tmp = y * (x * -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_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 4e+287], t$95$0, N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 y z))) < 4.0000000000000003e287

   1. Initial program 99.0%

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

   if 4.0000000000000003e287 < (*.f64 x (-.f64 1 (*.f64 y z)))

   1. Initial program 80.5%

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

   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-lft-neg-out 99.9%

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

      4. *-commutative 99.9%

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

   4. Simplified 99.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - y \cdot z\right) \leq 4 \cdot 10^{+287}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 3: 96.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_0 := x \cdot \left(1 - y \cdot z\right)\\ \mathbf{if}\;t_0 \leq 5 \cdot 10^{+281}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{\frac{-1}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* y z)))))
   (if (<= t_0 5e+281) t_0 (* z (/ x (/ -1.0 y))))))

C

assert(y < z);
double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double tmp;
	if (t_0 <= 5e+281) {
		tmp = t_0;
	} else {
		tmp = z * (x / (-1.0 / y));
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x * (1.0d0 - (y * z))
    if (t_0 <= 5d+281) then
        tmp = t_0
    else
        tmp = z * (x / ((-1.0d0) / y))
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - (y * z));
	double tmp;
	if (t_0 <= 5e+281) {
		tmp = t_0;
	} else {
		tmp = z * (x / (-1.0 / y));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	t_0 = x * (1.0 - (y * z))
	tmp = 0
	if t_0 <= 5e+281:
		tmp = t_0
	else:
		tmp = z * (x / (-1.0 / y))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(y * z)))
	tmp = 0.0
	if (t_0 <= 5e+281)
		tmp = t_0;
	else
		tmp = Float64(z * Float64(x / Float64(-1.0 / y)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - (y * z));
	tmp = 0.0;
	if (t_0 <= 5e+281)
		tmp = t_0;
	else
		tmp = z * (x / (-1.0 / y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e+281], t$95$0, N[(z * N[(x / N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 y z))) < 5.00000000000000016e281

   1. Initial program 99.0%

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

   if 5.00000000000000016e281 < (*.f64 x (-.f64 1 (*.f64 y z)))

   1. Initial program 81.1%

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

      1. flip-- 41.7%

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

      2. associate-*r/ 41.7%

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

      3. metadata-eval 41.7%

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

      4. pow2 41.7%

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

   3. Applied egg-rr 41.7%

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

      1. associate-/l* 41.7%

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

   5. Simplified 41.7%

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

   6. Taylor expanded in y around inf 81.1%

      \[\leadsto \frac{x}{\color{blue}{\frac{-1}{y \cdot z}}} \]
   7. Step-by-step derivation

      1. associate-/r* 81.1%

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

   8. Simplified 81.1%

      \[\leadsto \frac{x}{\color{blue}{\frac{\frac{-1}{y}}{z}}} \]
   9. Step-by-step derivation

      1. add-cube-cbrt 81.1%

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

      2. div-inv 81.1%

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

      3. times-frac 99.4%

         \[\leadsto \color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\frac{-1}{y}} \cdot \frac{\sqrt[3]{x}}{\frac{1}{z}}} \]

      4. pow2 99.4%

         \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}}}{\frac{-1}{y}} \cdot \frac{\sqrt[3]{x}}{\frac{1}{z}} \]

   10. Applied egg-rr 99.4%

       \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2}}{\frac{-1}{y}} \cdot \frac{\sqrt[3]{x}}{\frac{1}{z}}} \]
   11. Step-by-step derivation

       1. associate-/r/ 99.3%

          \[\leadsto \frac{{\left(\sqrt[3]{x}\right)}^{2}}{\frac{-1}{y}} \cdot \color{blue}{\left(\frac{\sqrt[3]{x}}{1} \cdot z\right)} \]

       2. /-rgt-identity 99.3%

          \[\leadsto \frac{{\left(\sqrt[3]{x}\right)}^{2}}{\frac{-1}{y}} \cdot \left(\color{blue}{\sqrt[3]{x}} \cdot z\right) \]

       3. associate-*r* 99.3%

          \[\leadsto \color{blue}{\left(\frac{{\left(\sqrt[3]{x}\right)}^{2}}{\frac{-1}{y}} \cdot \sqrt[3]{x}\right) \cdot z} \]

       4. associate-*l/ 99.3%

          \[\leadsto \color{blue}{\frac{{\left(\sqrt[3]{x}\right)}^{2} \cdot \sqrt[3]{x}}{\frac{-1}{y}}} \cdot z \]

       5. unpow2 99.3%

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

       6. rem-3cbrt-lft 99.8%

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

   12. Simplified 99.8%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - y \cdot z\right) \leq 5 \cdot 10^{+281}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x}{\frac{-1}{y}}\\ \end{array} \]

Alternative 4: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+79} \lor \neg \left(y \leq 7 \cdot 10^{-151}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.7e+79) (not (<= y 7e-151))) (* x (* y (- z))) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.7e+79) || !(y <= 7e-151)) {
		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 <= (-1.7d+79)) .or. (.not. (y <= 7d-151))) 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 <= -1.7e+79) || !(y <= 7e-151)) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -1.7e+79) or not (y <= 7e-151):
		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 <= -1.7e+79) || !(y <= 7e-151))
		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 <= -1.7e+79) || ~((y <= 7e-151)))
		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, -1.7e+79], N[Not[LessEqual[y, 7e-151]], $MachinePrecision]], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.70000000000000016e79 or 6.99999999999999991e-151 < y

   1. Initial program 94.6%

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

   2. Taylor expanded in y around inf 59.3%

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

      1. mul-1-neg 59.3%

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

      2. associate-*r* 60.4%

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

      3. distribute-lft-neg-in 60.4%

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

      4. distribute-rgt-neg-out 60.4%

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

      5. *-commutative 60.4%

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

   4. Simplified 60.4%

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

   if -1.70000000000000016e79 < y < 6.99999999999999991e-151

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 75.4%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+79} \lor \neg \left(y \leq 7 \cdot 10^{-151}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 74.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-145}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -5e+78)
   (* x (* y (- z)))
   (if (<= y 1.55e-145) x (* y (* x (- z))))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e+78) {
		tmp = x * (y * -z);
	} else if (y <= 1.55e-145) {
		tmp = x;
	} else {
		tmp = y * (x * -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 <= (-5d+78)) then
        tmp = x * (y * -z)
    else if (y <= 1.55d-145) then
        tmp = x
    else
        tmp = y * (x * -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 <= -5e+78) {
		tmp = x * (y * -z);
	} else if (y <= 1.55e-145) {
		tmp = x;
	} else {
		tmp = y * (x * -z);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if y <= -5e+78:
		tmp = x * (y * -z)
	elif y <= 1.55e-145:
		tmp = x
	else:
		tmp = y * (x * -z)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -5e+78)
		tmp = Float64(x * Float64(y * Float64(-z)));
	elseif (y <= 1.55e-145)
		tmp = x;
	else
		tmp = Float64(y * Float64(x * 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 <= -5e+78)
		tmp = x * (y * -z);
	elseif (y <= 1.55e-145)
		tmp = x;
	else
		tmp = y * (x * -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, -5e+78], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e-145], x, N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.99999999999999984e78

   1. Initial program 94.5%

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

   2. Taylor expanded in y around inf 72.7%

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

      1. mul-1-neg 72.7%

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

      2. associate-*r* 77.0%

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

      3. distribute-lft-neg-in 77.0%

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

      4. distribute-rgt-neg-out 77.0%

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

      5. *-commutative 77.0%

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

   4. Simplified 77.0%

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

   if -4.99999999999999984e78 < y < 1.55e-145

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 75.4%

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

   if 1.55e-145 < y

   1. Initial program 94.4%

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

   2. Taylor expanded in y around inf 54.3%

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

      1. mul-1-neg 54.3%

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

      2. distribute-rgt-neg-in 54.3%

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

      3. distribute-lft-neg-out 54.3%

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

      4. *-commutative 54.3%

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

   4. Simplified 54.3%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-145}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]

Alternative 6: 50.6% 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 97.0%

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

2. Taylor expanded in y around 0 54.2%

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

3. Final simplification 54.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))