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

Percentage Accurate: 96.2% → 99.5%

Time: 6.5s

Alternatives: 5

Speedup: 0.3×

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: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot y \leq -1 \cdot 10^{+146}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \cdot y \leq 10^{+260}:\\ \;\;\;\;x \cdot \left(1 - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* z y) -1e+146)
   (* z (* y (- x)))
   (if (<= (* z y) 1e+260) (* x (- 1.0 (* z y))) (* y (* x (- z))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z * y) <= -1e+146) {
		tmp = z * (y * -x);
	} else if ((z * y) <= 1e+260) {
		tmp = x * (1.0 - (z * y));
	} else {
		tmp = y * (x * -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 ((z * y) <= (-1d+146)) then
        tmp = z * (y * -x)
    else if ((z * y) <= 1d+260) then
        tmp = x * (1.0d0 - (z * y))
    else
        tmp = y * (x * -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 ((z * y) <= -1e+146) {
		tmp = z * (y * -x);
	} else if ((z * y) <= 1e+260) {
		tmp = x * (1.0 - (z * y));
	} else {
		tmp = y * (x * -z);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z * y) <= -1e+146:
		tmp = z * (y * -x)
	elif (z * y) <= 1e+260:
		tmp = x * (1.0 - (z * y))
	else:
		tmp = y * (x * -z)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(z * y) <= -1e+146)
		tmp = Float64(z * Float64(y * Float64(-x)));
	elseif (Float64(z * y) <= 1e+260)
		tmp = Float64(x * Float64(1.0 - Float64(z * y)));
	else
		tmp = Float64(y * Float64(x * Float64(-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 ((z * y) <= -1e+146)
		tmp = z * (y * -x);
	elseif ((z * y) <= 1e+260)
		tmp = x * (1.0 - (z * y));
	else
		tmp = y * (x * -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[(z * y), $MachinePrecision], -1e+146], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * y), $MachinePrecision], 1e+260], N[(x * N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -9.99999999999999934e145

   1. Initial program 84.9%

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

      1. flip-- 27.8%

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

      2. associate-*r/ 27.8%

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

      3. metadata-eval 27.8%

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

      4. pow2 27.8%

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

      5. +-commutative 27.8%

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

      6. fma-def 27.8%

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

   4. Applied egg-rr 27.8%

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

      1. associate-/l* 27.8%

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

   6. Simplified 27.8%

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

   7. Taylor expanded in y around inf 84.9%

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

      1. div-inv 84.8%

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

      2. frac-2neg 84.8%

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

      3. metadata-eval 84.8%

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

      4. remove-double-div 84.9%

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

      5. distribute-rgt-neg-in 84.9%

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

      6. associate-*r* 97.7%

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

      7. *-commutative 97.7%

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

      8. distribute-rgt-neg-in 97.7%

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

      9. *-commutative 97.7%

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

   9. Applied egg-rr 97.7%

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

   if -9.99999999999999934e145 < (*.f64 y z) < 1.00000000000000007e260

   1. Initial program 99.9%

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

   if 1.00000000000000007e260 < (*.f64 y z)

   1. Initial program 78.0%

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

   3. Taylor expanded in y around inf 78.0%

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

      1. mul-1-neg 78.0%

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

      2. associate-*r* 99.9%

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

      3. distribute-rgt-neg-in 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-*r* 99.9%

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

      6. distribute-rgt-neg-out 99.9%

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

   5. Simplified 99.9%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot y \leq -1 \cdot 10^{+146}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \cdot y \leq 10^{+260}:\\ \;\;\;\;x \cdot \left(1 - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+56} \lor \neg \left(y \leq 2.15 \cdot 10^{-101}\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.1e+56) (not (<= y 2.15e-101))) (* x (* z (- y))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.1e+56) || !(y <= 2.15e-101)) {
		tmp = x * (z * -y);
	} 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 ((y <= (-3.1d+56)) .or. (.not. (y <= 2.15d-101))) then
        tmp = x * (z * -y)
    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 ((y <= -3.1e+56) || !(y <= 2.15e-101)) {
		tmp = x * (z * -y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -3.1e+56) or not (y <= 2.15e-101):
		tmp = x * (z * -y)
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.1e+56) || !(y <= 2.15e-101))
		tmp = Float64(x * Float64(z * Float64(-y)));
	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 ((y <= -3.1e+56) || ~((y <= 2.15e-101)))
		tmp = x * (z * -y);
	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[y, -3.1e+56], N[Not[LessEqual[y, 2.15e-101]], $MachinePrecision]], N[(x * N[(z * (-y)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000005e56 or 2.1499999999999999e-101 < y

   1. Initial program 91.5%

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

   3. Taylor expanded in y around inf 68.2%

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

      1. mul-1-neg 68.2%

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

      2. distribute-rgt-neg-in 68.2%

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

      3. distribute-rgt-neg-out 68.2%

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

   5. Simplified 68.2%

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

   if -3.10000000000000005e56 < y < 2.1499999999999999e-101

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 76.2%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+56} \lor \neg \left(y \leq 2.15 \cdot 10^{-101}\right):\\ \;\;\;\;x \cdot \left(z \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+56} \lor \neg \left(y \leq 6 \cdot 10^{-70}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.5e+56) (not (<= y 6e-70))) (* y (* x (- z))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.5e+56) || !(y <= 6e-70)) {
		tmp = y * (x * -z);
	} 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 ((y <= (-3.5d+56)) .or. (.not. (y <= 6d-70))) then
        tmp = y * (x * -z)
    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 ((y <= -3.5e+56) || !(y <= 6e-70)) {
		tmp = y * (x * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -3.5e+56) or not (y <= 6e-70):
		tmp = y * (x * -z)
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.5e+56) || !(y <= 6e-70))
		tmp = Float64(y * Float64(x * Float64(-z)));
	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 ((y <= -3.5e+56) || ~((y <= 6e-70)))
		tmp = y * (x * -z);
	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[y, -3.5e+56], N[Not[LessEqual[y, 6e-70]], $MachinePrecision]], N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.49999999999999999e56 or 6.0000000000000003e-70 < y

   1. Initial program 91.0%

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

   3. Taylor expanded in y around inf 69.5%

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

      1. mul-1-neg 69.5%

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

      2. associate-*r* 75.4%

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

      3. distribute-rgt-neg-in 75.4%

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

      4. *-commutative 75.4%

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

      5. associate-*r* 75.3%

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

      6. distribute-rgt-neg-out 75.3%

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

   5. Simplified 75.3%

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

   if -3.49999999999999999e56 < y < 6.0000000000000003e-70

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 75.3%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+56} \lor \neg \left(y \leq 6 \cdot 10^{-70}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 2.15 \cdot 10^{-160}:\\ \;\;\;\;x - z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z \cdot y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= x 2.15e-160) (- x (* z (* x y))) (* x (- 1.0 (* z y)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (x <= 2.15e-160) {
		tmp = x - (z * (x * y));
	} else {
		tmp = x * (1.0 - (z * y));
	}
	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 (x <= 2.15d-160) then
        tmp = x - (z * (x * y))
    else
        tmp = x * (1.0d0 - (z * y))
    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 (x <= 2.15e-160) {
		tmp = x - (z * (x * y));
	} else {
		tmp = x * (1.0 - (z * y));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if x <= 2.15e-160:
		tmp = x - (z * (x * y))
	else:
		tmp = x * (1.0 - (z * y))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (x <= 2.15e-160)
		tmp = Float64(x - Float64(z * Float64(x * y)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(z * y)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= 2.15e-160)
		tmp = x - (z * (x * y));
	else
		tmp = x * (1.0 - (z * y));
	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[x, 2.15e-160], N[(x - N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.15000000000000007e-160

   1. Initial program 93.0%

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

      1. sub-neg 93.0%

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

      2. distribute-rgt-in 92.9%

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

      3. *-un-lft-identity 92.9%

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

      4. distribute-rgt-neg-in 92.9%

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

   4. Applied egg-rr 92.9%

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

      1. *-commutative 92.9%

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

      2. *-commutative 92.9%

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

      3. associate-*r* 93.9%

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

      4. distribute-rgt-neg-in 93.9%

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

      5. distribute-lft-neg-in 93.9%

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

      6. associate-*l* 92.9%

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

      7. *-commutative 92.9%

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

      8. add-sqr-sqrt 53.3%

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

      9. sqrt-prod 68.8%

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

      10. sqr-neg 68.8%

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

      11. distribute-rgt-neg-out 68.8%

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

      12. distribute-rgt-neg-out 68.8%

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

      13. sqrt-unprod 32.2%

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

      14. add-sqr-sqrt 50.7%

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

      15. cancel-sign-sub-inv 50.7%

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

      16. add-sqr-sqrt 32.2%

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

      17. sqrt-unprod 68.8%

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

      18. distribute-rgt-neg-out 68.8%

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

      19. distribute-rgt-neg-out 68.8%

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

      20. sqr-neg 68.8%

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

   6. Applied egg-rr 92.9%

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

      1. expm1-log1p-u 71.5%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. expm1-udef 60.6%

         \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)} - 1\right)} \]

   8. Applied egg-rr 60.6%

      \[\leadsto x - \color{blue}{\left(e^{\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)} - 1\right)} \]
   9. Step-by-step derivation

      1. expm1-def 71.5%

         \[\leadsto x - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x \cdot \left(y \cdot z\right)\right)\right)} \]

      2. expm1-log1p 92.9%

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

      3. associate-*r* 96.4%

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

      4. *-commutative 96.4%

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

   10. Simplified 96.4%

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

   if 2.15000000000000007e-160 < x

   1. Initial program 100.0%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.15 \cdot 10^{-160}:\\ \;\;\;\;x - z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.3% 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 95.4%

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

3. Taylor expanded in y around 0 49.2%

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

4. Final simplification 49.2%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024020 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))