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

Percentage Accurate: 96.1% → 97.9%

Time: 6.7s

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: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+240}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -1e+240) (* z (* y (- x))) (- x (* (* y z) x))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -1e+240) {
		tmp = z * (y * -x);
	} else {
		tmp = x - ((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) <= (-1d+240)) then
        tmp = z * (y * -x)
    else
        tmp = x - ((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) <= -1e+240) {
		tmp = z * (y * -x);
	} else {
		tmp = x - ((y * z) * x);
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -1e+240:
		tmp = z * (y * -x)
	else:
		tmp = x - ((y * z) * x)
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -1e+240)
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = Float64(x - Float64(Float64(y * z) * 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) <= -1e+240)
		tmp = z * (y * -x);
	else
		tmp = x - ((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], -1e+240], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1.00000000000000001e240

   1. Initial program 65.1%

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

      1. flip-- 6.1%

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

      2. associate-*r/ 6.1%

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

      3. metadata-eval 6.1%

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

      4. pow2 6.1%

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

   3. Applied egg-rr 6.1%

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

      1. associate-/l* 6.1%

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

      2. +-commutative 6.1%

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

   5. Simplified 6.1%

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

   6. Taylor expanded in y around inf 65.0%

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

      1. associate-/r/ 65.1%

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

      2. associate-*r* 99.8%

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

      3. div-inv 99.8%

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

      4. metadata-eval 99.8%

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

   8. Applied egg-rr 99.8%

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

   if -1.00000000000000001e240 < (*.f64 y z)

   1. Initial program 99.5%

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

   2. Taylor expanded in y around 0 99.5%

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

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

   4. Simplified 99.5%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+240}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \end{array} \]

Alternative 2: 97.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -((double) INFINITY)) {
		tmp = y * (z * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -Double.POSITIVE_INFINITY) {
		tmp = y * (z * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -math.inf:
		tmp = y * (z * -x)
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

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

MATLAB

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -inf.0

   1. Initial program 55.9%

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

      1. flip-- 0.0%

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

      2. associate-*r/ 0.0%

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

      3. metadata-eval 0.0%

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

      4. pow2 0.0%

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

   3. Applied egg-rr 0.0%

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

      1. associate-/l* 0.0%

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

      2. +-commutative 0.0%

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

   5. Simplified 0.0%

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

   6. Taylor expanded in y around inf 55.9%

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

   7. Taylor expanded in x around 0 55.9%

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

      1. associate-*r* 55.9%

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

      2. *-commutative 55.9%

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

      3. *-commutative 55.9%

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

      4. associate-*l* 99.7%

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

      5. *-commutative 99.7%

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

      6. associate-*l* 99.7%

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

      7. neg-mul-1 99.7%

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

   9. Simplified 99.7%

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

   if -inf.0 < (*.f64 y z)

   1. Initial program 99.5%

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

4. Final simplification 99.5%

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

Alternative 3: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+240}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) -1e+240) (* z (* y (- x))) (* x (- 1.0 (* y z)))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= -1e+240) {
		tmp = z * (y * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	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) <= (-1d+240)) then
        tmp = z * (y * -x)
    else
        tmp = x * (1.0d0 - (y * z))
    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) <= -1e+240) {
		tmp = z * (y * -x);
	} else {
		tmp = x * (1.0 - (y * z));
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y * z) <= -1e+240:
		tmp = z * (y * -x)
	else:
		tmp = x * (1.0 - (y * z))
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(y * z) <= -1e+240)
		tmp = Float64(z * Float64(y * Float64(-x)));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y * z)));
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y * z) <= -1e+240)
		tmp = z * (y * -x);
	else
		tmp = x * (1.0 - (y * z));
	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], -1e+240], N[(z * N[(y * (-x)), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -1.00000000000000001e240

   1. Initial program 65.1%

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

      1. flip-- 6.1%

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

      2. associate-*r/ 6.1%

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

      3. metadata-eval 6.1%

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

      4. pow2 6.1%

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

   3. Applied egg-rr 6.1%

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

      1. associate-/l* 6.1%

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

      2. +-commutative 6.1%

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

   5. Simplified 6.1%

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

   6. Taylor expanded in y around inf 65.0%

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

      1. associate-/r/ 65.1%

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

      2. associate-*r* 99.8%

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

      3. div-inv 99.8%

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

      4. metadata-eval 99.8%

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

   8. Applied egg-rr 99.8%

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

   if -1.00000000000000001e240 < (*.f64 y z)

   1. Initial program 99.5%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -1 \cdot 10^{+240}:\\ \;\;\;\;z \cdot \left(y \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]

Alternative 4: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+97} \lor \neg \left(y \leq 4.4 \cdot 10^{-70}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.22e+97) (not (<= y 4.4e-70))) (* (* y z) (- x)) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.22e+97) || !(y <= 4.4e-70)) {
		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 ((y <= (-1.22d+97)) .or. (.not. (y <= 4.4d-70))) 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 ((y <= -1.22e+97) || !(y <= 4.4e-70)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -1.22e+97) or not (y <= 4.4e-70):
		tmp = (y * z) * -x
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.22e+97) || !(y <= 4.4e-70))
		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 ((y <= -1.22e+97) || ~((y <= 4.4e-70)))
		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[y, -1.22e+97], N[Not[LessEqual[y, 4.4e-70]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.21999999999999997e97 or 4.3999999999999998e-70 < y

   1. Initial program 93.5%

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

   2. Taylor expanded in y around inf 64.7%

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

      1. mul-1-neg 64.7%

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

      2. distribute-rgt-neg-in 64.7%

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

      3. distribute-rgt-neg-out 64.7%

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

   4. Simplified 64.7%

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

   if -1.21999999999999997e97 < y < 4.3999999999999998e-70

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 69.9%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+97} \lor \neg \left(y \leq 4.4 \cdot 10^{-70}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 76.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+97} \lor \neg \left(y \leq 5.2 \cdot 10^{-70}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.22e+97) (not (<= y 5.2e-70))) (* y (* z (- x))) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.22e+97) || !(y <= 5.2e-70)) {
		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 ((y <= (-1.22d+97)) .or. (.not. (y <= 5.2d-70))) 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 ((y <= -1.22e+97) || !(y <= 5.2e-70)) {
		tmp = y * (z * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -1.22e+97) or not (y <= 5.2e-70):
		tmp = y * (z * -x)
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.22e+97) || !(y <= 5.2e-70))
		tmp = Float64(y * Float64(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 ((y <= -1.22e+97) || ~((y <= 5.2e-70)))
		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[y, -1.22e+97], N[Not[LessEqual[y, 5.2e-70]], $MachinePrecision]], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.21999999999999997e97 or 5.20000000000000004e-70 < y

   1. Initial program 93.5%

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

      1. flip-- 67.0%

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

      2. associate-*r/ 62.5%

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

      3. metadata-eval 62.5%

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

      4. pow2 62.5%

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

   3. Applied egg-rr 62.5%

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

      1. associate-/l* 67.0%

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

      2. +-commutative 67.0%

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

   5. Simplified 67.0%

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

   6. Taylor expanded in y around inf 64.7%

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

   7. Taylor expanded in x around 0 64.7%

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

      1. associate-*r* 64.7%

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

      2. *-commutative 64.7%

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

      3. *-commutative 64.7%

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

      4. associate-*l* 66.9%

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

      5. *-commutative 66.9%

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

      6. associate-*l* 66.9%

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

      7. neg-mul-1 66.9%

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

   9. Simplified 66.9%

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

   if -1.21999999999999997e97 < y < 5.20000000000000004e-70

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 69.9%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+97} \lor \neg \left(y \leq 5.2 \cdot 10^{-70}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 51.3% 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 96.9%

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

2. Taylor expanded in y around 0 51.9%

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

3. Final simplification 51.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023275 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))