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

Percentage Accurate: 95.9% → 99.8%

Time: 5.4s

Alternatives: 7

Speedup: 0.3×

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: 95.9% 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: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+236}\right):\\ \;\;\;\;-z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= (* y z) (- INFINITY)) (not (<= (* y z) 2e+236)))
   (- (* z (* x y)))
   (* 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)) || !((y * z) <= 2e+236)) {
		tmp = -(z * (x * y));
	} 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) || !((y * z) <= 2e+236)) {
		tmp = -(z * (x * y));
	} 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) or not ((y * z) <= 2e+236):
		tmp = -(z * (x * y))
	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)) || !(Float64(y * z) <= 2e+236))
		tmp = Float64(-Float64(z * Float64(x * y)));
	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) || ~(((y * z) <= 2e+236)))
		tmp = -(z * (x * y));
	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[Or[LessEqual[N[(y * z), $MachinePrecision], (-Infinity)], N[Not[LessEqual[N[(y * z), $MachinePrecision], 2e+236]], $MachinePrecision]], (-N[(z * N[(x * y), $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 or 2.00000000000000011e236 < (*.f64 y z)

   1. Initial program 74.3%

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

   3. Taylor expanded in y around inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. associate-*r* 99.8%

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

   5. Simplified 99.8%

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

   if -inf.0 < (*.f64 y z) < 2.00000000000000011e236

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty \lor \neg \left(y \cdot z \leq 2 \cdot 10^{+236}\right):\\ \;\;\;\;-z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := x \cdot \left(y \cdot \left(-z\right)\right)\\ t_1 := -z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \cdot z \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \cdot z \leq -200000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \cdot z \leq 0.0001:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+236}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* y (- z)))) (t_1 (- (* z (* x y)))))
   (if (<= (* y z) (- INFINITY))
     t_1
     (if (<= (* y z) -200000000.0)
       t_0
       (if (<= (* y z) 0.0001) x (if (<= (* y z) 2e+236) t_0 t_1))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = x * (y * -z);
	double t_1 = -(z * (x * y));
	double tmp;
	if ((y * z) <= -((double) INFINITY)) {
		tmp = t_1;
	} else if ((y * z) <= -200000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.0001) {
		tmp = x;
	} else if ((y * z) <= 2e+236) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = x * (y * -z);
	double t_1 = -(z * (x * y));
	double tmp;
	if ((y * z) <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if ((y * z) <= -200000000.0) {
		tmp = t_0;
	} else if ((y * z) <= 0.0001) {
		tmp = x;
	} else if ((y * z) <= 2e+236) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = x * (y * -z)
	t_1 = -(z * (x * y))
	tmp = 0
	if (y * z) <= -math.inf:
		tmp = t_1
	elif (y * z) <= -200000000.0:
		tmp = t_0
	elif (y * z) <= 0.0001:
		tmp = x
	elif (y * z) <= 2e+236:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(x * Float64(y * Float64(-z)))
	t_1 = Float64(-Float64(z * Float64(x * y)))
	tmp = 0.0
	if (Float64(y * z) <= Float64(-Inf))
		tmp = t_1;
	elseif (Float64(y * z) <= -200000000.0)
		tmp = t_0;
	elseif (Float64(y * z) <= 0.0001)
		tmp = x;
	elseif (Float64(y * z) <= 2e+236)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = x * (y * -z);
	t_1 = -(z * (x * y));
	tmp = 0.0;
	if ((y * z) <= -Inf)
		tmp = t_1;
	elseif ((y * z) <= -200000000.0)
		tmp = t_0;
	elseif ((y * z) <= 0.0001)
		tmp = x;
	elseif ((y * z) <= 2e+236)
		tmp = t_0;
	else
		tmp = t_1;
	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_] := Block[{t$95$0 = N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = (-N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[N[(y * z), $MachinePrecision], (-Infinity)], t$95$1, If[LessEqual[N[(y * z), $MachinePrecision], -200000000.0], t$95$0, If[LessEqual[N[(y * z), $MachinePrecision], 0.0001], x, If[LessEqual[N[(y * z), $MachinePrecision], 2e+236], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y z) < -inf.0 or 2.00000000000000011e236 < (*.f64 y z)

   1. Initial program 74.3%

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

   3. Taylor expanded in y around inf 74.3%

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

      1. mul-1-neg 74.3%

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

      2. associate-*r* 99.8%

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

   5. Simplified 99.8%

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

   if -inf.0 < (*.f64 y z) < -2e8 or 1.00000000000000005e-4 < (*.f64 y z) < 2.00000000000000011e236

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 97.9%

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

      1. mul-1-neg 97.9%

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

      2. associate-*r* 90.1%

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

   5. Simplified 90.1%

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

   6. Taylor expanded in x around 0 97.9%

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

   if -2e8 < (*.f64 y z) < 1.00000000000000005e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.2%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -\infty:\\ \;\;\;\;-z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \cdot z \leq -200000000:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{elif}\;y \cdot z \leq 0.0001:\\ \;\;\;\;x\\ \mathbf{elif}\;y \cdot z \leq 2 \cdot 10^{+236}:\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -200000000 \lor \neg \left(y \cdot z \leq 0.0001\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

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 z) -200000000.0) (not (<= (* y z) 0.0001)))
   (* x (* y (- z)))
   x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -200000000.0) || !((y * z) <= 0.0001)) {
		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 * z) <= (-200000000.0d0)) .or. (.not. ((y * z) <= 0.0001d0))) 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 * z) <= -200000000.0) || !((y * z) <= 0.0001)) {
		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 * z) <= -200000000.0) or not ((y * z) <= 0.0001):
		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 ((Float64(y * z) <= -200000000.0) || !(Float64(y * z) <= 0.0001))
		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 * z) <= -200000000.0) || ~(((y * z) <= 0.0001)))
		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[N[(y * z), $MachinePrecision], -200000000.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 0.0001]], $MachinePrecision]], N[(x * N[(y * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2e8 or 1.00000000000000005e-4 < (*.f64 y z)

   1. Initial program 92.8%

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

   3. Taylor expanded in y around inf 91.5%

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

      1. mul-1-neg 91.5%

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

      2. associate-*r* 92.8%

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

   5. Simplified 92.8%

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

   6. Taylor expanded in x around 0 91.5%

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

   if -2e8 < (*.f64 y z) < 1.00000000000000005e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.2%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -200000000 \lor \neg \left(y \cdot z \leq 0.0001\right):\\ \;\;\;\;x \cdot \left(y \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \cdot z \leq -200000000 \lor \neg \left(y \cdot z \leq 0.0001\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

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 z) -200000000.0) (not (<= (* y z) 0.0001)))
   (* y (* x (- z)))
   x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((y * z) <= -200000000.0) || !((y * z) <= 0.0001)) {
		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 * z) <= (-200000000.0d0)) .or. (.not. ((y * z) <= 0.0001d0))) 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 * z) <= -200000000.0) || !((y * z) <= 0.0001)) {
		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 * z) <= -200000000.0) or not ((y * z) <= 0.0001):
		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 ((Float64(y * z) <= -200000000.0) || !(Float64(y * z) <= 0.0001))
		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 * z) <= -200000000.0) || ~(((y * z) <= 0.0001)))
		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[N[(y * z), $MachinePrecision], -200000000.0], N[Not[LessEqual[N[(y * z), $MachinePrecision], 0.0001]], $MachinePrecision]], N[(y * N[(x * (-z)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y z) < -2e8 or 1.00000000000000005e-4 < (*.f64 y z)

   1. Initial program 92.8%

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

   3. Taylor expanded in y around inf 91.5%

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

      1. mul-1-neg 91.5%

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

      2. associate-*r* 92.8%

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

      3. distribute-rgt-neg-in 92.8%

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

      4. *-commutative 92.8%

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

      5. associate-*l* 91.4%

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

   5. Simplified 91.4%

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

   if -2e8 < (*.f64 y z) < 1.00000000000000005e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.2%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z \leq -200000000 \lor \neg \left(y \cdot z \leq 0.0001\right):\\ \;\;\;\;y \cdot \left(x \cdot \left(-z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq 4.2 \cdot 10^{-101}:\\ \;\;\;\;x - y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= x 4.2e-101) (- x (* y (* x z))) (* x (- 1.0 (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (x <= 4.2e-101) {
		tmp = x - (y * (x * z));
	} else {
		tmp = x * (1.0 - (y * z));
	}
	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 (x <= 4.2d-101) then
        tmp = x - (y * (x * z))
    else
        tmp = x * (1.0d0 - (y * z))
    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 (x <= 4.2e-101) {
		tmp = x - (y * (x * z));
	} 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 x <= 4.2e-101:
		tmp = x - (y * (x * z))
	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 (x <= 4.2e-101)
		tmp = Float64(x - Float64(y * Float64(x * z)));
	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 (x <= 4.2e-101)
		tmp = x - (y * (x * z));
	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[x, 4.2e-101], N[(x - N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.20000000000000031e-101

   1. Initial program 93.6%

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

      1. sub-neg 93.6%

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

      2. distribute-rgt-in 93.6%

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

      3. *-un-lft-identity 93.6%

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

      4. distribute-rgt-neg-in 93.6%

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

   4. Applied egg-rr 93.6%

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

      1. *-commutative 93.6%

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

      2. *-commutative 93.6%

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

      3. associate-*r* 94.5%

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

      4. distribute-rgt-neg-out 94.5%

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

      5. distribute-lft-neg-in 94.5%

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

      6. associate-*l* 93.6%

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

      7. *-commutative 93.6%

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

      8. add-sqr-sqrt 43.4%

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

      9. sqrt-unprod 61.2%

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

      10. sqr-neg 61.2%

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

      11. sqrt-unprod 25.1%

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

      12. add-sqr-sqrt 42.4%

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

      13. cancel-sign-sub-inv 42.4%

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

      14. *-commutative 42.4%

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

      15. *-commutative 42.4%

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

      16. associate-*r* 39.4%

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

      17. add-sqr-sqrt 22.1%

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

      18. sqrt-unprod 58.3%

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

      19. sqr-neg 58.3%

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

      20. sqrt-unprod 45.3%

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

      21. add-sqr-sqrt 93.5%

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

   6. Applied egg-rr 94.5%

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

   if 4.20000000000000031e-101 < x

   1. Initial program 99.8%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.2 \cdot 10^{-101}:\\ \;\;\;\;x - y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.58 \cdot 10^{+165}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (if (<= y -1.58e+165) (/ (* x y) y) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.58e+165) {
		tmp = (x * y) / y;
	} 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 <= (-1.58d+165)) then
        tmp = (x * y) / y
    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 <= -1.58e+165) {
		tmp = (x * y) / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -1.58e+165:
		tmp = (x * y) / y
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1.58e+165)
		tmp = Float64(Float64(x * y) / y);
	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 <= -1.58e+165)
		tmp = (x * y) / y;
	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[LessEqual[y, -1.58e+165], N[(N[(x * y), $MachinePrecision] / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.58000000000000007e165

   1. Initial program 89.5%

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

   3. Taylor expanded in y around inf 85.6%

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

   4. Taylor expanded in z around 0 6.3%

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

      1. *-commutative 6.3%

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

      2. associate-*l/ 20.3%

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

   6. Applied egg-rr 20.3%

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

   if -1.58000000000000007e165 < y

   1. Initial program 96.6%

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

   3. Taylor expanded in y around 0 48.2%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.58 \cdot 10^{+165}:\\ \;\;\;\;\frac{x \cdot y}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 95.9%

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

3. Taylor expanded in y around 0 43.7%

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

4. Final simplification 43.7%

   \[\leadsto x \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024071 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, I"
  :precision binary64
  (* x (- 1.0 (* y z))))