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

Percentage Accurate: 95.6% → 97.4%

Time: 6.0s

Alternatives: 5

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: 95.6% 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: 97.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 2 \cdot 10^{+157}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 2e+157) (- x (* (* y z) x)) (* y (* z (- x)))))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y * z) <= 2e+157) {
		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) <= 2d+157) 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) <= 2e+157) {
		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) <= 2e+157:
		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) <= 2e+157)
		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) <= 2e+157)
		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], 2e+157], 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) < 1.99999999999999997e157

   1. Initial program 98.6%

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

   2. Taylor expanded in y around 0 98.6%

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

      1. mul-1-neg 98.6%

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

   4. Simplified 98.6%

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

      1. unsub-neg 98.6%

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

      2. associate-*r* 90.8%

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

      3. *-commutative 90.8%

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

   6. Applied egg-rr 90.8%

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

   7. Taylor expanded in z around 0 98.6%

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

   if 1.99999999999999997e157 < (*.f64 y z)

   1. Initial program 74.3%

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

   2. Taylor expanded in y around 0 74.3%

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

      1. mul-1-neg 74.3%

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

   4. Simplified 74.3%

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

   5. Taylor expanded in y around inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. associate-*r* 97.1%

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

      3. *-commutative 97.1%

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

      4. distribute-lft-neg-in 97.1%

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

   7. Simplified 97.1%

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

   8. Taylor expanded in z around 0 74.3%

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

      1. mul-1-neg 74.3%

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

      2. *-commutative 74.3%

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

      3. associate-*r* 97.5%

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

      4. distribute-rgt-neg-in 97.5%

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

      5. *-commutative 97.5%

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

   10. Simplified 97.5%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 2 \cdot 10^{+157}:\\ \;\;\;\;x - \left(y \cdot z\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 2: 97.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq 2 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* y z) 2e+157) (* 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) <= 2e+157) {
		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) <= 2d+157) 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) <= 2e+157) {
		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) <= 2e+157:
		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) <= 2e+157)
		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) <= 2e+157)
		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], 2e+157], 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) < 1.99999999999999997e157

   1. Initial program 98.6%

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

   if 1.99999999999999997e157 < (*.f64 y z)

   1. Initial program 74.3%

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

   2. Taylor expanded in y around 0 74.3%

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

      1. mul-1-neg 74.3%

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

   4. Simplified 74.3%

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

   5. Taylor expanded in y around inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. associate-*r* 97.1%

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

      3. *-commutative 97.1%

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

      4. distribute-lft-neg-in 97.1%

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

   7. Simplified 97.1%

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

   8. Taylor expanded in z around 0 74.3%

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

      1. mul-1-neg 74.3%

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

      2. *-commutative 74.3%

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

      3. associate-*r* 97.5%

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

      4. distribute-rgt-neg-in 97.5%

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

      5. *-commutative 97.5%

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

   10. Simplified 97.5%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq 2 \cdot 10^{+157}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \end{array} \]

Alternative 3: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-86} \lor \neg \left(z \leq 2.9 \cdot 10^{+30}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.5e-86) (not (<= z 2.9e+30))) (* (* y z) (- x)) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.5e-86) || !(z <= 2.9e+30)) {
		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 <= (-4.5d-86)) .or. (.not. (z <= 2.9d+30))) 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 <= -4.5e-86) || !(z <= 2.9e+30)) {
		tmp = (y * z) * -x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -4.5e-86) or not (z <= 2.9e+30):
		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 <= -4.5e-86) || !(z <= 2.9e+30))
		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 <= -4.5e-86) || ~((z <= 2.9e+30)))
		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, -4.5e-86], N[Not[LessEqual[z, 2.9e+30]], $MachinePrecision]], N[(N[(y * z), $MachinePrecision] * (-x)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.4999999999999998e-86 or 2.8999999999999998e30 < z

   1. Initial program 90.6%

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

   2. Taylor expanded in y around inf 67.7%

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

      1. mul-1-neg 67.7%

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

      2. distribute-rgt-neg-in 67.7%

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

      3. distribute-rgt-neg-in 67.7%

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

   4. Simplified 67.7%

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

   if -4.4999999999999998e-86 < z < 2.8999999999999998e30

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 73.0%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-86} \lor \neg \left(z \leq 2.9 \cdot 10^{+30}\right):\\ \;\;\;\;\left(y \cdot z\right) \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 75.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-86} \lor \neg \left(z \leq 6.2 \cdot 10^{+29}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.7e-86) (not (<= z 6.2e+29))) (* y (* z (- x))) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.7e-86) || !(z <= 6.2e+29)) {
		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 <= (-1.7d-86)) .or. (.not. (z <= 6.2d+29))) 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 <= -1.7e-86) || !(z <= 6.2e+29)) {
		tmp = y * (z * -x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -1.7e-86) or not (z <= 6.2e+29):
		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 <= -1.7e-86) || !(z <= 6.2e+29))
		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 ((z <= -1.7e-86) || ~((z <= 6.2e+29)))
		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, -1.7e-86], N[Not[LessEqual[z, 6.2e+29]], $MachinePrecision]], N[(y * N[(z * (-x)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.7e-86 or 6.1999999999999998e29 < z

   1. Initial program 90.6%

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

   2. Taylor expanded in y around 0 90.6%

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

      1. mul-1-neg 90.6%

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

   4. Simplified 90.6%

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

   5. Taylor expanded in y around inf 67.7%

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

      1. mul-1-neg 67.7%

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

      2. associate-*r* 71.2%

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

      3. *-commutative 71.2%

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

      4. distribute-lft-neg-in 71.2%

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

   7. Simplified 71.2%

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

   8. Taylor expanded in z around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. *-commutative 67.7%

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

      3. associate-*r* 71.3%

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

      4. distribute-rgt-neg-in 71.3%

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

      5. *-commutative 71.3%

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

   10. Simplified 71.3%

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

   if -1.7e-86 < z < 6.1999999999999998e29

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 73.0%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-86} \lor \neg \left(z \leq 6.2 \cdot 10^{+29}\right):\\ \;\;\;\;y \cdot \left(z \cdot \left(-x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 50.1% 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 95.1%

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

2. Taylor expanded in y around 0 48.3%

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

3. Final simplification 48.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023310 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))