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

Percentage Accurate: 96.2% → 98.1%

Time: 6.8s

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: 96.2% 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: 98.1% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(y * z), $MachinePrecision], (-Infinity)], 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) < -inf.0

   1. Initial program 63.3%

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

      1. sub-neg 63.3%

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

      2. distribute-rgt-in 63.3%

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

      3. *-un-lft-identity 63.3%

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

      4. distribute-rgt-neg-in 63.3%

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

   3. Applied egg-rr 63.3%

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

   4. Taylor expanded in y around 0 63.3%

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

      1. mul-1-neg 63.3%

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

      2. associate-*r* 99.8%

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

      3. *-commutative 99.8%

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

      4. distribute-lft-neg-out 99.8%

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

      5. *-commutative 99.8%

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

      6. distribute-rgt-neg-in 99.8%

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

   6. Simplified 99.8%

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

      1. distribute-rgt-neg-in 99.8%

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

      2. *-commutative 99.8%

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

      3. distribute-lft-neg-out 99.8%

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

      4. unsub-neg 99.8%

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

      5. *-commutative 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in z around inf 63.3%

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

       1. mul-1-neg 63.3%

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

       2. *-commutative 63.3%

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

       3. *-commutative 63.3%

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

       4. associate-*r* 99.8%

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

       5. distribute-rgt-neg-in 99.8%

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

       6. distribute-lft-neg-in 99.8%

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

   11. Simplified 99.8%

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

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

   1. Initial program 98.7%

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

4. Final simplification 98.8%

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

Alternative 2: 74.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+40} \lor \neg \left(y \leq 1.35 \cdot 10^{-108}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

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 -5.5e+40) (not (<= y 1.35e-108))) (* x (* y (- z))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e+40) || !(y <= 1.35e-108)) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-5.5d+40)) .or. (.not. (y <= 1.35d-108))) then
        tmp = x * (y * -z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.5e+40) || !(y <= 1.35e-108)) {
		tmp = x * (y * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -5.5e+40) or not (y <= 1.35e-108):
		tmp = x * (y * -z)
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.5e+40) || !(y <= 1.35e-108))
		tmp = Float64(x * Float64(y * Float64(-z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.5e+40) || ~((y <= 1.35e-108)))
		tmp = x * (y * -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[y, -5.5e+40], N[Not[LessEqual[y, 1.35e-108]], $MachinePrecision]], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.49999999999999974e40 or 1.35000000000000002e-108 < y

   1. Initial program 93.0%

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

   2. Taylor expanded in y around inf 71.1%

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

      1. mul-1-neg 71.1%

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

      2. distribute-rgt-neg-out 71.1%

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

   4. Simplified 71.1%

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

   if -5.49999999999999974e40 < y < 1.35000000000000002e-108

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 71.4%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+40} \lor \neg \left(y \leq 1.35 \cdot 10^{-108}\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 76.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+37} \lor \neg \left(y \leq 7 \cdot 10^{-106}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

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 -5.2e+37) (not (<= y 7e-106))) (* y (* x (- z))) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e+37) || !(y <= 7e-106)) {
		tmp = y * (x * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-5.2d+37)) .or. (.not. (y <= 7d-106))) then
        tmp = y * (x * -z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e+37) || !(y <= 7e-106)) {
		tmp = y * (x * -z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -5.2e+37) or not (y <= 7e-106):
		tmp = y * (x * -z)
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.2e+37) || !(y <= 7e-106))
		tmp = Float64(y * Float64(x * Float64(-z)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.2e+37) || ~((y <= 7e-106)))
		tmp = y * (x * -z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[y, -5.2e+37], N[Not[LessEqual[y, 7e-106]], $MachinePrecision]], N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.1999999999999998e37 or 7e-106 < y

   1. Initial program 93.0%

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

   2. Taylor expanded in y around inf 70.6%

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

      1. mul-1-neg 70.6%

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

      2. *-commutative 70.6%

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

      3. distribute-lft-neg-in 70.6%

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

      4. distribute-rgt-neg-out 70.6%

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

      5. associate-*l* 73.2%

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

      6. *-commutative 73.2%

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

   4. Simplified 73.2%

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

   if -5.1999999999999998e37 < y < 7e-106

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 71.2%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+37} \lor \neg \left(y \leq 7 \cdot 10^{-106}\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 75.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+37} \lor \neg \left(y \leq 7.4 \cdot 10^{-106}\right):\\ \;\;\;\;z \cdot \left(\left(-y\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

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 -5.2e+37) (not (<= y 7.4e-106))) (* z (* (- y) x)) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e+37) || !(y <= 7.4e-106)) {
		tmp = z * (-y * 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 <= (-5.2d+37)) .or. (.not. (y <= 7.4d-106))) then
        tmp = z * (-y * 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 <= -5.2e+37) || !(y <= 7.4e-106)) {
		tmp = z * (-y * x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -5.2e+37) or not (y <= 7.4e-106):
		tmp = z * (-y * x)
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.2e+37) || !(y <= 7.4e-106))
		tmp = Float64(z * Float64(Float64(-y) * 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 <= -5.2e+37) || ~((y <= 7.4e-106)))
		tmp = z * (-y * 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, -5.2e+37], N[Not[LessEqual[y, 7.4e-106]], $MachinePrecision]], N[(z * N[((-y) * x), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.1999999999999998e37 or 7.39999999999999959e-106 < y

   1. Initial program 93.0%

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

      1. sub-neg 93.0%

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

      2. distribute-rgt-in 93.0%

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

      3. *-un-lft-identity 93.0%

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

      4. distribute-rgt-neg-in 93.0%

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

   3. Applied egg-rr 93.0%

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

   4. Taylor expanded in y around 0 93.0%

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

      1. mul-1-neg 93.0%

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

      2. associate-*r* 94.1%

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

      3. *-commutative 94.1%

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

      4. distribute-lft-neg-out 94.1%

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

      5. *-commutative 94.1%

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

      6. distribute-rgt-neg-in 94.1%

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

   6. Simplified 94.1%

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

      1. distribute-rgt-neg-in 94.1%

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

      2. *-commutative 94.1%

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

      3. distribute-lft-neg-out 94.1%

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

      4. unsub-neg 94.1%

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

      5. *-commutative 94.1%

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

   8. Applied egg-rr 94.1%

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

   9. Taylor expanded in z around inf 70.6%

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

       1. mul-1-neg 70.6%

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

       2. *-commutative 70.6%

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

       3. *-commutative 70.6%

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

       4. associate-*r* 73.8%

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

       5. distribute-rgt-neg-in 73.8%

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

       6. distribute-lft-neg-in 73.8%

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

   11. Simplified 73.8%

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

   if -5.1999999999999998e37 < y < 7.39999999999999959e-106

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 71.2%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+37} \lor \neg \left(y \leq 7.4 \cdot 10^{-106}\right):\\ \;\;\;\;z \cdot \left(\left(-y\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 50.5% 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. Taylor expanded in y around 0 46.4%

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

3. Final simplification 46.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023330 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))