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

Percentage Accurate: 96.0% → 97.9%

Time: 7.2s

Alternatives: 5

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: 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, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+218}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(z, -y, 1\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -1e+218) (* z (* y (- x))) (* x (fma z (- y) 1.0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -1e+218) {
		tmp = z * (y * -x);
	} else {
		tmp = x * fma(z, -y, 1.0);
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -1e+218)
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = Float64(x * fma(z, Float64(-y), 1.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -1e+218], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * (-y) + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1.00000000000000008e218

   1. Initial program 75.1%

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

   3. Taylor expanded in z around inf 75.1%

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

      1. add-sqr-sqrt 30.7%

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

      2. add-sqr-sqrt 0.0%

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

      3. difference-of-squares 0.0%

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

      4. inv-pow 0.0%

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

      5. sqrt-pow1 0.0%

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

      6. metadata-eval 0.0%

         \[\leadsto x \cdot \left(z \cdot \left(\left({z}^{\color{blue}{-0.5}} + \sqrt{y}\right) \cdot \left(\sqrt{\frac{1}{z}} - \sqrt{y}\right)\right)\right) \]

      7. inv-pow 0.0%

         \[\leadsto x \cdot \left(z \cdot \left(\left({z}^{-0.5} + \sqrt{y}\right) \cdot \left(\sqrt{\color{blue}{{z}^{-1}}} - \sqrt{y}\right)\right)\right) \]

      8. sqrt-pow1 0.0%

         \[\leadsto x \cdot \left(z \cdot \left(\left({z}^{-0.5} + \sqrt{y}\right) \cdot \left(\color{blue}{{z}^{\left(\frac{-1}{2}\right)}} - \sqrt{y}\right)\right)\right) \]

      9. metadata-eval 0.0%

         \[\leadsto x \cdot \left(z \cdot \left(\left({z}^{-0.5} + \sqrt{y}\right) \cdot \left({z}^{\color{blue}{-0.5}} - \sqrt{y}\right)\right)\right) \]

   5. Applied egg-rr 0.0%

      \[\leadsto x \cdot \left(z \cdot \color{blue}{\left(\left({z}^{-0.5} + \sqrt{y}\right) \cdot \left({z}^{-0.5} - \sqrt{y}\right)\right)}\right) \]

   6. Taylor expanded in y around inf 75.1%

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

      1. associate-*r* 99.6%

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

      2. associate-*r* 99.6%

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

      3. *-commutative 99.6%

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

      4. mul-1-neg 99.6%

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

      5. distribute-rgt-neg-out 99.6%

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

   8. Simplified 99.6%

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

   if -1.00000000000000008e218 < (*.f64 y z)

   1. Initial program 99.4%

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

      1. cancel-sign-sub-inv 99.4%

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

      2. +-commutative 99.4%

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

      3. *-commutative 99.4%

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

      4. fma-define 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(z, -y, 1\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+218}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(z, -y, 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 75.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-132} \lor \neg \left(z \leq 2.8 \cdot 10^{+54}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.1e-132) (not (<= z 2.8e+54))) (* (* y z) (- x)) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.1e-132) || !(z <= 2.8e+54)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.1d-132)) .or. (.not. (z <= 2.8d+54))) then
        tmp = (y * z) * -x
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.1e-132) || !(z <= 2.8e+54)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -4.1e-132) or not (z <= 2.8e+54):
		tmp = (y * z) * -x
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.1e-132) || !(z <= 2.8e+54))
		tmp = Float64(Float64(y * z) * Float64(-x));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.1e-132) || ~((z <= 2.8e+54)))
		tmp = (y * z) * -x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -4.1e-132], N[Not[LessEqual[z, 2.8e+54]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.10000000000000007e-132 or 2.80000000000000015e54 < z

   1. Initial program 94.8%

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

   3. Taylor expanded in y around inf 69.4%

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

      1. associate-*r* 69.4%

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

      2. mul-1-neg 69.4%

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

   5. Simplified 69.4%

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

   if -4.10000000000000007e-132 < z < 2.80000000000000015e54

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 77.2%

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

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-132} \lor \neg \left(z \leq 2.8 \cdot 10^{+54}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-132} \lor \neg \left(z \leq 4.9 \cdot 10^{+54}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.1e-132) (not (<= z 4.9e+54))) (* y (* z (- x))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.1e-132) || !(z <= 4.9e+54)) {
		tmp = y * (z * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.1d-132)) .or. (.not. (z <= 4.9d+54))) then
        tmp = y * (z * -x)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.1e-132) || !(z <= 4.9e+54)) {
		tmp = y * (z * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -4.1e-132) or not (z <= 4.9e+54):
		tmp = y * (z * -x)
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.1e-132) || !(z <= 4.9e+54))
		tmp = Float64(y * Float64(z * Float64(-x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.1e-132) || ~((z <= 4.9e+54)))
		tmp = y * (z * -x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -4.1e-132], N[Not[LessEqual[z, 4.9e+54]], $MachinePrecision]], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.10000000000000007e-132 or 4.90000000000000001e54 < z

   1. Initial program 94.8%

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

   3. Taylor expanded in y around inf 69.4%

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

      1. mul-1-neg 69.4%

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

      2. *-commutative 69.4%

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

      3. associate-*l* 66.9%

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

      4. *-commutative 66.9%

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

      5. distribute-rgt-neg-in 66.9%

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

      6. distribute-rgt-neg-in 66.9%

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

   5. Simplified 66.9%

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

   if -4.10000000000000007e-132 < z < 4.90000000000000001e54

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 77.2%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-132} \lor \neg \left(z \leq 4.9 \cdot 10^{+54}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+218}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -1e+218) (* z (* y (- x))) (* x (- 1.0 (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -1e+218) {
		tmp = z * (y * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y * z) <= (-1d+218)) then
        tmp = z * (y * -x)
    else
        tmp = x * (1.0d0 - (y * z))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -1e+218) {
		tmp = z * (y * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -1e+218:
		tmp = z * (y * -x)
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -1e+218)
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -1e+218)
		tmp = z * (y * -x);
	else
		tmp = x * (1.0 - (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], -1e+218], 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) < -1.00000000000000008e218

   1. Initial program 75.1%

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

   3. Taylor expanded in z around inf 75.1%

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

      1. add-sqr-sqrt 30.7%

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

      2. add-sqr-sqrt 0.0%

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

      3. difference-of-squares 0.0%

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

      4. inv-pow 0.0%

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

      5. sqrt-pow1 0.0%

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

      6. metadata-eval 0.0%

         \[\leadsto x \cdot \left(z \cdot \left(\left({z}^{\color{blue}{-0.5}} + \sqrt{y}\right) \cdot \left(\sqrt{\frac{1}{z}} - \sqrt{y}\right)\right)\right) \]

      7. inv-pow 0.0%

         \[\leadsto x \cdot \left(z \cdot \left(\left({z}^{-0.5} + \sqrt{y}\right) \cdot \left(\sqrt{\color{blue}{{z}^{-1}}} - \sqrt{y}\right)\right)\right) \]

      8. sqrt-pow1 0.0%

         \[\leadsto x \cdot \left(z \cdot \left(\left({z}^{-0.5} + \sqrt{y}\right) \cdot \left(\color{blue}{{z}^{\left(\frac{-1}{2}\right)}} - \sqrt{y}\right)\right)\right) \]

      9. metadata-eval 0.0%

         \[\leadsto x \cdot \left(z \cdot \left(\left({z}^{-0.5} + \sqrt{y}\right) \cdot \left({z}^{\color{blue}{-0.5}} - \sqrt{y}\right)\right)\right) \]

   5. Applied egg-rr 0.0%

      \[\leadsto x \cdot \left(z \cdot \color{blue}{\left(\left({z}^{-0.5} + \sqrt{y}\right) \cdot \left({z}^{-0.5} - \sqrt{y}\right)\right)}\right) \]

   6. Taylor expanded in y around inf 75.1%

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

      1. associate-*r* 99.6%

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

      2. associate-*r* 99.6%

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

      3. *-commutative 99.6%

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

      4. mul-1-neg 99.6%

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

      5. distribute-rgt-neg-out 99.6%

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

   8. Simplified 99.6%

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

   if -1.00000000000000008e218 < (*.f64 y z)

   1. Initial program 99.4%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+218}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.8% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.2%

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

3. Taylor expanded in y around 0 50.7%

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

4. Final simplification 50.7%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))