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

Percentage Accurate: 95.9% → 99.6%

Time: 6.9s

Alternatives: 6

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: 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: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+185} \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+182}\right):\\ \;\;\;\;y \cdot \left(-x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) -1e+185) (not (<= (* y z) 2e+182)))
   (* y (- (* x z)))
   (* 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+185) || !((y * z) <= 2e+182)) {
		tmp = y * -(x * z);
	} 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+185)) .or. (.not. ((y * z) <= 2d+182))) then
        tmp = y * -(x * z)
    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+185) || !((y * z) <= 2e+182)) {
		tmp = y * -(x * z);
	} 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+185) or not ((y * z) <= 2e+182):
		tmp = y * -(x * z)
	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+185) || !(Float64(y * z) <= 2e+182))
		tmp = Float64(y * Float64(-Float64(x * z)));
	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+185) || ~(((y * z) <= 2e+182)))
		tmp = y * -(x * z);
	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[Or[LessEqual[N[(y * z), $MachinePrecision], -1e+185], N[Not[LessEqual[N[(y * z), $MachinePrecision], 2e+182]], $MachinePrecision]], N[(y * (-N[(x * z), $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) < -9.9999999999999998e184 or 2.0000000000000001e182 < (*.f64 y z)

   1. Initial program 81.4%

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

   3. Taylor expanded in y around inf 81.4%

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

      1. mul-1-neg 81.4%

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

      2. associate-*r* 99.8%

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

      3. distribute-rgt-neg-in 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-*r* 99.7%

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

      6. distribute-rgt-neg-out 99.7%

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

   5. Simplified 99.7%

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

   if -9.9999999999999998e184 < (*.f64 y z) < 2.0000000000000001e182

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+185} \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+182}\right):\\ \;\;\;\;y \cdot \left(-x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{+42} \lor \neg \left(y \leq 1.5 \cdot 10^{-88}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.38e+42) (not (<= y 1.5e-88))) (* (* y z) (- x)) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.38e+42) || !(y <= 1.5e-88)) {
		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 ((y <= (-1.38d+42)) .or. (.not. (y <= 1.5d-88))) 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 ((y <= -1.38e+42) || !(y <= 1.5e-88)) {
		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 (y <= -1.38e+42) or not (y <= 1.5e-88):
		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 ((y <= -1.38e+42) || !(y <= 1.5e-88))
		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 ((y <= -1.38e+42) || ~((y <= 1.5e-88)))
		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[y, -1.38e+42], N[Not[LessEqual[y, 1.5e-88]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.3800000000000001e42 or 1.5e-88 < y

   1. Initial program 90.2%

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

   3. Taylor expanded in y around inf 66.0%

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

      1. mul-1-neg 66.0%

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

      2. distribute-rgt-neg-in 66.0%

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

      3. distribute-rgt-neg-out 66.0%

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

   5. Simplified 66.0%

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

   if -1.3800000000000001e42 < y < 1.5e-88

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.0%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{+42} \lor \neg \left(y \leq 1.5 \cdot 10^{-88}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{+42} \lor \neg \left(y \leq 1.25 \cdot 10^{-86}\right):\\ \;\;\;\;y \cdot \left(-x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

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 -1.18e+42) (not (<= y 1.25e-86))) (* y (- (* x z))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.18e+42) || !(y <= 1.25e-86)) {
		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 <= (-1.18d+42)) .or. (.not. (y <= 1.25d-86))) 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 <= -1.18e+42) || !(y <= 1.25e-86)) {
		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 <= -1.18e+42) or not (y <= 1.25e-86):
		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 <= -1.18e+42) || !(y <= 1.25e-86))
		tmp = Float64(y * Float64(-Float64(x * 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 <= -1.18e+42) || ~((y <= 1.25e-86)))
		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, -1.18e+42], N[Not[LessEqual[y, 1.25e-86]], $MachinePrecision]], N[(y * (-N[(x * z), $MachinePrecision])), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.18e42 or 1.25e-86 < y

   1. Initial program 90.2%

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

   3. Taylor expanded in y around inf 66.0%

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

      1. mul-1-neg 66.0%

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

      2. associate-*r* 75.0%

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

      3. distribute-rgt-neg-in 75.0%

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

      4. *-commutative 75.0%

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

      5. associate-*r* 72.5%

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

      6. distribute-rgt-neg-out 72.5%

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

   5. Simplified 72.5%

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

   if -1.18e42 < y < 1.25e-86

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.0%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.18 \cdot 10^{+42} \lor \neg \left(y \leq 1.25 \cdot 10^{-86}\right):\\ \;\;\;\;y \cdot \left(-x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 8 \cdot 10^{+107}:\\ \;\;\;\;x - y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= x 8e+107) (- x (* y (* x z))) (- x (* x (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (x <= 8e+107) {
		tmp = x - (y * (x * z));
	} else {
		tmp = x - (x * (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 (x <= 8d+107) then
        tmp = x - (y * (x * z))
    else
        tmp = x - (x * (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 (x <= 8e+107) {
		tmp = x - (y * (x * z));
	} else {
		tmp = x - (x * (y * z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if x <= 8e+107:
		tmp = x - (y * (x * z))
	else:
		tmp = x - (x * (y * z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (x <= 8e+107)
		tmp = Float64(x - Float64(y * Float64(x * z)));
	else
		tmp = Float64(x - Float64(x * 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 (x <= 8e+107)
		tmp = x - (y * (x * z));
	else
		tmp = x - (x * (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[x, 8e+107], N[(x - N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.9999999999999998e107

   1. Initial program 93.3%

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

      1. sub-neg 93.3%

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

      2. distribute-rgt-in 93.3%

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

      3. *-un-lft-identity 93.3%

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

      4. distribute-rgt-neg-in 93.3%

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

   4. Applied egg-rr 93.3%

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

      1. distribute-rgt-neg-out 93.3%

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

      2. distribute-lft-neg-out 93.3%

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

      3. associate-*r* 93.8%

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

      4. *-commutative 93.8%

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

      5. distribute-lft-neg-in 93.8%

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

      6. add-sqr-sqrt 51.9%

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

      7. sqrt-unprod 58.7%

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

      8. sqr-neg 58.7%

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

      9. sqrt-unprod 27.2%

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

      10. add-sqr-sqrt 45.2%

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

      11. *-commutative 45.2%

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

      12. distribute-lft-neg-in 45.2%

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

      13. cancel-sign-sub-inv 45.2%

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

      14. associate-*l* 47.6%

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

      15. *-commutative 47.6%

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

      16. *-commutative 47.6%

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

      17. associate-*r* 45.2%

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

   6. Applied egg-rr 93.8%

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

   if 7.9999999999999998e107 < x

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-rgt-in 100.0%

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

      3. *-un-lft-identity 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

   4. Applied egg-rr 100.0%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 8 \cdot 10^{+107}:\\ \;\;\;\;x - y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{+83}:\\ \;\;\;\;x - y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= x 5e+83) (- x (* y (* x z))) (* x (- 1.0 (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (x <= 5e+83) {
		tmp = x - (y * (x * z));
	} 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 (x <= 5d+83) then
        tmp = x - (y * (x * z))
    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 (x <= 5e+83) {
		tmp = x - (y * (x * z));
	} 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 x <= 5e+83:
		tmp = x - (y * (x * z))
	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 (x <= 5e+83)
		tmp = Float64(x - Float64(y * Float64(x * z)));
	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 (x <= 5e+83)
		tmp = x - (y * (x * z));
	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[x, 5e+83], N[(x - N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 5.00000000000000029e83

   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 93.0%

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

      3. *-un-lft-identity 93.0%

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

      4. distribute-rgt-neg-in 93.0%

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

   4. Applied egg-rr 93.0%

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

      1. distribute-rgt-neg-out 93.0%

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

      2. distribute-lft-neg-out 93.0%

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

      3. associate-*r* 93.5%

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

      4. *-commutative 93.5%

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

      5. distribute-lft-neg-in 93.5%

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

      6. add-sqr-sqrt 51.7%

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

      7. sqrt-unprod 56.9%

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

      8. sqr-neg 56.9%

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

      9. sqrt-unprod 26.5%

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

      10. add-sqr-sqrt 43.7%

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

      11. *-commutative 43.7%

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

      12. distribute-lft-neg-in 43.7%

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

      13. cancel-sign-sub-inv 43.7%

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

      14. associate-*l* 46.3%

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

      15. *-commutative 46.3%

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

      16. *-commutative 46.3%

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

      17. associate-*r* 43.7%

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

   6. Applied egg-rr 93.5%

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

   if 5.00000000000000029e83 < 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 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5 \cdot 10^{+83}:\\ \;\;\;\;x - y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.2% 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 94.4%

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

3. Taylor expanded in y around 0 46.8%

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

4. Final simplification 46.8%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024029 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))