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

Percentage Accurate: 95.8% → 97.7%

Time: 7.7s

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: 95.8% 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: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 10^{+242}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 1e+242) (- x (* (* y z) x)) (* y (* z (- x)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 1e+242) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = y * (z * -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 * z) <= 1d+242) then
        tmp = x - ((y * z) * x)
    else
        tmp = y * (z * -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 * z) <= 1e+242) {
		tmp = x - ((y * z) * x);
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 1e+242:
		tmp = x - ((y * z) * x)
	else:
		tmp = y * (z * -x)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 1e+242)
		tmp = Float64(x - Float64(Float64(y * z) * x));
	else
		tmp = Float64(y * Float64(z * Float64(-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 * z) <= 1e+242)
		tmp = x - ((y * z) * x);
	else
		tmp = y * (z * -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[LessEqual[N[(y * z), $MachinePrecision], 1e+242], 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) < 1.00000000000000005e242

   1. Initial program 98.7%

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

      1. sub-neg 98.7%

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

      2. +-commutative 98.7%

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

      3. add-sqr-sqrt 52.9%

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

      4. distribute-rgt-neg-in 52.9%

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

      5. fma-define 52.9%

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

   4. Applied egg-rr 52.9%

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

      1. *-commutative 52.9%

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

      2. fma-undefine 52.9%

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

      3. distribute-rgt-neg-in 52.9%

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

      4. add-sqr-sqrt 98.7%

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

      5. distribute-rgt-neg-out 98.7%

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

      6. distribute-rgt1-in 98.7%

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

      7. distribute-rgt-neg-out 98.7%

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

      8. cancel-sign-sub-inv 98.7%

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

      9. *-commutative 98.7%

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

   6. Applied egg-rr 98.7%

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

   if 1.00000000000000005e242 < (*.f64 y z)

   1. Initial program 72.9%

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

      1. sub-neg 72.9%

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

      2. +-commutative 72.9%

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

      3. add-sqr-sqrt 72.8%

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

      4. distribute-rgt-neg-in 72.8%

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

      5. fma-define 72.8%

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

   4. Applied egg-rr 72.8%

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

   6. Applied egg-rr 8.2%

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

   7. Taylor expanded in y around inf 62.2%

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

   8. Taylor expanded in x around 0 99.7%

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

      1. distribute-rgt1-in 99.7%

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

      2. metadata-eval 99.7%

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

      3. neg-mul-1 99.7%

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

   10. Simplified 99.7%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 10^{+242}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+87} \lor \neg \left(y \leq 1.25 \cdot 10^{-82}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

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 -6.8e+87) (not (<= y 1.25e-82))) (* (* y z) (- x)) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.8e+87) || !(y <= 1.25e-82)) {
		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 <= (-6.8d+87)) .or. (.not. (y <= 1.25d-82))) 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 <= -6.8e+87) || !(y <= 1.25e-82)) {
		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 <= -6.8e+87) or not (y <= 1.25e-82):
		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 <= -6.8e+87) || !(y <= 1.25e-82))
		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 <= -6.8e+87) || ~((y <= 1.25e-82)))
		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, -6.8e+87], N[Not[LessEqual[y, 1.25e-82]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.8000000000000004e87 or 1.25e-82 < y

   1. Initial program 93.0%

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

   3. Taylor expanded in y around inf 58.0%

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

      1. mul-1-neg 58.0%

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

      2. distribute-rgt-neg-in 58.0%

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

      3. distribute-rgt-neg-in 58.0%

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

   5. Simplified 58.0%

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

   if -6.8000000000000004e87 < y < 1.25e-82

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 77.7%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+87} \lor \neg \left(y \leq 1.25 \cdot 10^{-82}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+87}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -2.5e+87)
   (* (* y z) (- x))
   (if (<= y 2.1e-51) x (* y (* z (- x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.5e+87) {
		tmp = (y * z) * -x;
	} else if (y <= 2.1e-51) {
		tmp = x;
	} else {
		tmp = y * (z * -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 <= (-2.5d+87)) then
        tmp = (y * z) * -x
    else if (y <= 2.1d-51) then
        tmp = x
    else
        tmp = y * (z * -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 <= -2.5e+87) {
		tmp = (y * z) * -x;
	} else if (y <= 2.1e-51) {
		tmp = x;
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -2.5e+87:
		tmp = (y * z) * -x
	elif y <= 2.1e-51:
		tmp = x
	else:
		tmp = y * (z * -x)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -2.5e+87)
		tmp = Float64(Float64(y * z) * Float64(-x));
	elseif (y <= 2.1e-51)
		tmp = x;
	else
		tmp = Float64(y * Float64(z * Float64(-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 <= -2.5e+87)
		tmp = (y * z) * -x;
	elseif (y <= 2.1e-51)
		tmp = x;
	else
		tmp = y * (z * -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[LessEqual[y, -2.5e+87], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], If[LessEqual[y, 2.1e-51], x, N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.4999999999999999e87

   1. Initial program 95.6%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. mul-1-neg 68.9%

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

      2. distribute-rgt-neg-in 68.9%

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

      3. distribute-rgt-neg-in 68.9%

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

   5. Simplified 68.9%

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

   if -2.4999999999999999e87 < y < 2.10000000000000002e-51

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 77.8%

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

   if 2.10000000000000002e-51 < y

   1. Initial program 90.9%

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

      1. sub-neg 90.9%

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

      2. +-commutative 90.9%

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

      3. add-sqr-sqrt 43.1%

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

      4. distribute-rgt-neg-in 43.1%

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

      5. fma-define 43.1%

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

   4. Applied egg-rr 43.1%

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

   6. Applied egg-rr 62.9%

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

   7. Taylor expanded in y around inf 48.8%

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

   8. Taylor expanded in x around 0 63.1%

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

      1. distribute-rgt1-in 63.1%

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

      2. metadata-eval 63.1%

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

      3. neg-mul-1 63.1%

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

   10. Simplified 63.1%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+87}:\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 10^{+242}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 1e+242) (* x (- 1.0 (* y z))) (* y (* z (- x)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 1e+242) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (z * -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 * z) <= 1d+242) then
        tmp = x * (1.0d0 - (y * z))
    else
        tmp = y * (z * -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 * z) <= 1e+242) {
		tmp = x * (1.0 - (y * z));
	} else {
		tmp = y * (z * -x);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= 1e+242:
		tmp = x * (1.0 - (y * z))
	else:
		tmp = y * (z * -x)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= 1e+242)
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	else
		tmp = Float64(y * Float64(z * Float64(-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 * z) <= 1e+242)
		tmp = x * (1.0 - (y * z));
	else
		tmp = y * (z * -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[LessEqual[N[(y * z), $MachinePrecision], 1e+242], 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) < 1.00000000000000005e242

   1. Initial program 98.7%

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

   if 1.00000000000000005e242 < (*.f64 y z)

   1. Initial program 72.9%

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

      1. sub-neg 72.9%

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

      2. +-commutative 72.9%

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

      3. add-sqr-sqrt 72.8%

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

      4. distribute-rgt-neg-in 72.8%

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

      5. fma-define 72.8%

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

   4. Applied egg-rr 72.8%

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

   6. Applied egg-rr 8.2%

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

   7. Taylor expanded in y around inf 62.2%

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

   8. Taylor expanded in x around 0 99.7%

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

      1. distribute-rgt1-in 99.7%

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

      2. metadata-eval 99.7%

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

      3. neg-mul-1 99.7%

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

   10. Simplified 99.7%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 10^{+242}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.6% 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 96.2%

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

3. Taylor expanded in y around 0 55.7%

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

4. Final simplification 55.7%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024053 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))