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

Percentage Accurate: 96.0% → 98.0%

Time: 4.4s

Alternatives: 6

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 96.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+257}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 5e+257) (- x (* (* y z) x)) (* y (* z (- x)))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+257) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = y * (z * -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 * z) <= 5d+257) then
        tmp = x - ((y * z) * x)
    else
        tmp = y * (z * -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 * z) <= 5e+257) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 5e+257:
		tmp = x - ((y * z) * x)
	else:
		tmp = y * (z * -x)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 5e+257)
		tmp = Float64(x - Float64(Float64(y * z) * x));
	else
		tmp = Float64(y * Float64(z * Float64(-x)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 5e+257)
		tmp = x - ((y * z) * x);
	else
		tmp = y * (z * -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[LessEqual[N[(y * z), $MachinePrecision], 5e+257], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 5.00000000000000028e257

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. distribute-rgt-in 98.3%

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

      3. *-un-lft-identity 98.3%

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

      4. distribute-rgt-neg-in 98.3%

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

   3. Applied egg-rr 98.3%

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

   if 5.00000000000000028e257 < (*.f64 y z)

   1. Initial program 73.3%

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

   2. Taylor expanded in y around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-rgt-neg-in 99.7%

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

      3. distribute-lft-neg-out 99.7%

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

      4. *-commutative 99.7%

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

   4. Simplified 99.7%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+257}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 2: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-115} \lor \neg \left(z \leq 1.75 \cdot 10^{-11} \lor \neg \left(z \leq 4.9 \cdot 10^{+17}\right) \land z \leq 6 \cdot 10^{+38}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.4e-115)
         (not (or (<= z 1.75e-11) (and (not (<= z 4.9e+17)) (<= z 6e+38)))))
   (* (* y z) (- x))
   x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.4e-115) || !((z <= 1.75e-11) || (!(z <= 4.9e+17) && (z <= 6e+38)))) {
		tmp = (y * z) * -x;
	} 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 ((z <= (-2.4d-115)) .or. (.not. (z <= 1.75d-11) .or. (.not. (z <= 4.9d+17)) .and. (z <= 6d+38))) then
        tmp = (y * z) * -x
    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 ((z <= -2.4e-115) || !((z <= 1.75e-11) || (!(z <= 4.9e+17) && (z <= 6e+38)))) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -2.4e-115) or not ((z <= 1.75e-11) or (not (z <= 4.9e+17) and (z <= 6e+38))):
		tmp = (y * z) * -x
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.4e-115) || !((z <= 1.75e-11) || (!(z <= 4.9e+17) && (z <= 6e+38))))
		tmp = Float64(Float64(y * z) * Float64(-x));
	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 ((z <= -2.4e-115) || ~(((z <= 1.75e-11) || (~((z <= 4.9e+17)) && (z <= 6e+38)))))
		tmp = (y * z) * -x;
	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[z, -2.4e-115], N[Not[Or[LessEqual[z, 1.75e-11], And[N[Not[LessEqual[z, 4.9e+17]], $MachinePrecision], LessEqual[z, 6e+38]]]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.40000000000000021e-115 or 1.7500000000000001e-11 < z < 4.9e17 or 6.0000000000000002e38 < z

   1. Initial program 94.1%

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

   2. Taylor expanded in y around inf 66.1%

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

      1. mul-1-neg 66.1%

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

      2. associate-*r* 66.7%

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

      3. distribute-lft-neg-in 66.7%

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

      4. distribute-rgt-neg-out 66.7%

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

      5. *-commutative 66.7%

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

   4. Simplified 66.7%

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

   if -2.40000000000000021e-115 < z < 1.7500000000000001e-11 or 4.9e17 < z < 6.0000000000000002e38

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 86.8%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-115} \lor \neg \left(z \leq 1.75 \cdot 10^{-11} \lor \neg \left(z \leq 4.9 \cdot 10^{+17}\right) \land z \leq 6 \cdot 10^{+38}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 74.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_0 := y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{-115}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+17}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* z (- x)))))
   (if (<= z -2.4e-115)
     t_0
     (if (<= z 5.9e-12)
       x
       (if (<= z 8.2e+17) (* (* y z) (- x)) (if (<= z 5.5e+38) x t_0))))))

C

assert(y < z);
double code(double x, double y, double z) {
	double t_0 = y * (z * -x);
	double tmp;
	if (z <= -2.4e-115) {
		tmp = t_0;
	} else if (z <= 5.9e-12) {
		tmp = x;
	} else if (z <= 8.2e+17) {
		tmp = (y * z) * -x;
	} else if (z <= 5.5e+38) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	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 = y * (z * -x)
    if (z <= (-2.4d-115)) then
        tmp = t_0
    else if (z <= 5.9d-12) then
        tmp = x
    else if (z <= 8.2d+17) then
        tmp = (y * z) * -x
    else if (z <= 5.5d+38) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double t_0 = y * (z * -x);
	double tmp;
	if (z <= -2.4e-115) {
		tmp = t_0;
	} else if (z <= 5.9e-12) {
		tmp = x;
	} else if (z <= 8.2e+17) {
		tmp = (y * z) * -x;
	} else if (z <= 5.5e+38) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	t_0 = y * (z * -x)
	tmp = 0
	if z <= -2.4e-115:
		tmp = t_0
	elif z <= 5.9e-12:
		tmp = x
	elif z <= 8.2e+17:
		tmp = (y * z) * -x
	elif z <= 5.5e+38:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	t_0 = Float64(y * Float64(z * Float64(-x)))
	tmp = 0.0
	if (z <= -2.4e-115)
		tmp = t_0;
	elseif (z <= 5.9e-12)
		tmp = x;
	elseif (z <= 8.2e+17)
		tmp = Float64(Float64(y * z) * Float64(-x));
	elseif (z <= 5.5e+38)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = y * (z * -x);
	tmp = 0.0;
	if (z <= -2.4e-115)
		tmp = t_0;
	elseif (z <= 5.9e-12)
		tmp = x;
	elseif (z <= 8.2e+17)
		tmp = (y * z) * -x;
	elseif (z <= 5.5e+38)
		tmp = x;
	else
		tmp = t_0;
	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[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e-115], t$95$0, If[LessEqual[z, 5.9e-12], x, If[LessEqual[z, 8.2e+17], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[z, 5.5e+38], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.40000000000000021e-115 or 5.5000000000000003e38 < z

   1. Initial program 93.7%

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

   2. Taylor expanded in y around inf 64.3%

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

      1. mul-1-neg 64.3%

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

      2. distribute-rgt-neg-in 64.3%

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

      3. distribute-lft-neg-out 64.3%

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

      4. *-commutative 64.3%

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

   4. Simplified 64.3%

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

   if -2.40000000000000021e-115 < z < 5.9e-12 or 8.2e17 < z < 5.5000000000000003e38

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 86.8%

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

   if 5.9e-12 < z < 8.2e17

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 91.0%

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

      1. mul-1-neg 91.0%

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

      2. associate-*r* 91.1%

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

      3. distribute-lft-neg-in 91.1%

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

      4. distribute-rgt-neg-out 91.1%

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

      5. *-commutative 91.1%

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

   4. Simplified 91.1%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+17}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 4: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} t_0 := z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{-82}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+16}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* y (- x)))))
   (if (<= z -7.8e-82)
     t_0
     (if (<= z 9.8e-11)
       x
       (if (<= z 7.6e+16) (* (* y z) (- x)) (if (<= z 4.8e+38) x t_0))))))

C

assert(y < z);
double code(double x, double y, double z) {
	double t_0 = z * (y * -x);
	double tmp;
	if (z <= -7.8e-82) {
		tmp = t_0;
	} else if (z <= 9.8e-11) {
		tmp = x;
	} else if (z <= 7.6e+16) {
		tmp = (y * z) * -x;
	} else if (z <= 4.8e+38) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	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 = z * (y * -x)
    if (z <= (-7.8d-82)) then
        tmp = t_0
    else if (z <= 9.8d-11) then
        tmp = x
    else if (z <= 7.6d+16) then
        tmp = (y * z) * -x
    else if (z <= 4.8d+38) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double t_0 = z * (y * -x);
	double tmp;
	if (z <= -7.8e-82) {
		tmp = t_0;
	} else if (z <= 9.8e-11) {
		tmp = x;
	} else if (z <= 7.6e+16) {
		tmp = (y * z) * -x;
	} else if (z <= 4.8e+38) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	t_0 = z * (y * -x)
	tmp = 0
	if z <= -7.8e-82:
		tmp = t_0
	elif z <= 9.8e-11:
		tmp = x
	elif z <= 7.6e+16:
		tmp = (y * z) * -x
	elif z <= 4.8e+38:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	t_0 = Float64(z * Float64(y * Float64(-x)))
	tmp = 0.0
	if (z <= -7.8e-82)
		tmp = t_0;
	elseif (z <= 9.8e-11)
		tmp = x;
	elseif (z <= 7.6e+16)
		tmp = Float64(Float64(y * z) * Float64(-x));
	elseif (z <= 4.8e+38)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = z * (y * -x);
	tmp = 0.0;
	if (z <= -7.8e-82)
		tmp = t_0;
	elseif (z <= 9.8e-11)
		tmp = x;
	elseif (z <= 7.6e+16)
		tmp = (y * z) * -x;
	elseif (z <= 4.8e+38)
		tmp = x;
	else
		tmp = t_0;
	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[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.8e-82], t$95$0, If[LessEqual[z, 9.8e-11], x, If[LessEqual[z, 7.6e+16], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[z, 4.8e+38], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.79999999999999947e-82 or 4.80000000000000035e38 < z

   1. Initial program 93.4%

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

      1. *-commutative 93.4%

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

      2. flip-- 64.4%

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

      3. associate-*l/ 60.6%

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

      4. metadata-eval 60.6%

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

      5. pow2 60.6%

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

   3. Applied egg-rr 60.6%

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

      1. unpow2 60.6%

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

      2. *-commutative 60.6%

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

      3. associate-*r* 56.6%

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

   5. Applied egg-rr 56.6%

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

   6. Taylor expanded in y around 0 44.0%

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

      1. unpow2 44.0%

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

   8. Simplified 44.0%

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

   9. Taylor expanded in y around inf 66.3%

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

       1. mul-1-neg 66.3%

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

       2. *-commutative 66.3%

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

       3. *-commutative 66.3%

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

       4. *-commutative 66.3%

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

       5. associate-*l* 70.8%

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

       6. distribute-rgt-neg-in 70.8%

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

       7. *-commutative 70.8%

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

       8. distribute-lft-neg-out 70.8%

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

   11. Simplified 70.8%

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

   if -7.79999999999999947e-82 < z < 9.7999999999999998e-11 or 7.6e16 < z < 4.80000000000000035e38

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 87.5%

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

   if 9.7999999999999998e-11 < z < 7.6e16

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 91.0%

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

      1. mul-1-neg 91.0%

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

      2. associate-*r* 91.1%

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

      3. distribute-lft-neg-in 91.1%

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

      4. distribute-rgt-neg-out 91.1%

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

      5. *-commutative 91.1%

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

   4. Simplified 91.1%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{-82}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-11}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+16}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 5: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+257}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 5e+257) (* x (- 1.0 (* y z))) (* y (* z (- x)))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 5e+257) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (z * -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 * z) <= 5d+257) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = y * (z * -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 * z) <= 5e+257) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 5e+257:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = y * (z * -x)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 5e+257)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(y * Float64(z * Float64(-x)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= 5e+257)
		tmp = x * (1.0 - (y * z));
	else
		tmp = y * (z * -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[LessEqual[N[(y * z), $MachinePrecision], 5e+257], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < 5.00000000000000028e257

   1. Initial program 98.3%

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

   if 5.00000000000000028e257 < (*.f64 y z)

   1. Initial program 73.3%

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

   2. Taylor expanded in y around inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. distribute-rgt-neg-in 99.7%

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

      3. distribute-lft-neg-out 99.7%

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

      4. *-commutative 99.7%

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

   4. Simplified 99.7%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 5 \cdot 10^{+257}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 6: 50.7% 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 96.2%

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

2. Taylor expanded in y around 0 49.7%

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

3. Final simplification 49.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023221 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))