Statistics.Distribution.Beta:$cvariance from math-functions-0.1.5.2

Percentage Accurate: 82.9% → 96.6%

Time: 9.6s

Alternatives: 8

Speedup: 1.0×

• 25.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z) :precision binary64 (/ (* x y) (* (* z z) (+ z 1.0))))

C

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

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 * y) / ((z * z) * (z + 1.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 82.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (/ (* x y) (* (* z z) (+ z 1.0))))

C

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

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 * y) / ((z * z) * (z + 1.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \frac{y}{z} \cdot \frac{\frac{x}{z + 1}}{z} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* (/ y z) (/ (/ x (+ z 1.0)) z)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return (y / z) * ((x / (z + 1.0)) / z);
}

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 = (y / z) * ((x / (z + 1.0d0)) / z)
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return (y / z) * ((x / (z + 1.0)) / z);
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return (y / z) * ((x / (z + 1.0)) / z)

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(Float64(y / z) * Float64(Float64(x / Float64(z + 1.0)) / z))
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = (y / z) * ((x / (z + 1.0)) / z);
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(N[(y / z), $MachinePrecision] * N[(N[(x / N[(z + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.7%

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

   1. *-commutative 83.7%

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

   2. frac-times 88.3%

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

   3. associate-*l/ 86.9%

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

   4. times-frac 98.2%

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

4. Applied egg-rr 98.2%

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

5. Final simplification 98.2%

   \[\leadsto \frac{y}{z} \cdot \frac{\frac{x}{z + 1}}{z} \]
6. Add Preprocessing

Alternative 2: 92.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.043\right):\\ \;\;\;\;\frac{y}{z} \cdot \frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.043)))
   (* (/ y z) (/ (/ x z) z))
   (/ y (* z (/ z x)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.043)) {
		tmp = (y / z) * ((x / z) / z);
	} else {
		tmp = y / (z * (z / x));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 0.043d0))) then
        tmp = (y / z) * ((x / z) / z)
    else
        tmp = y / (z * (z / x))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.043)) {
		tmp = (y / z) * ((x / z) / z);
	} else {
		tmp = y / (z * (z / x));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 0.043):
		tmp = (y / z) * ((x / z) / z)
	else:
		tmp = y / (z * (z / x))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 0.043))
		tmp = Float64(Float64(y / z) * Float64(Float64(x / z) / z));
	else
		tmp = Float64(y / Float64(z * Float64(z / 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 ((z <= -1.0) || ~((z <= 0.043)))
		tmp = (y / z) * ((x / z) / z);
	else
		tmp = y / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 0.043]], $MachinePrecision]], N[(N[(y / z), $MachinePrecision] * N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 0.042999999999999997 < z

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

      2. frac-times 93.9%

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

      3. associate-*l/ 93.9%

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

      4. times-frac 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in z around inf 95.7%

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

   if -1 < z < 0.042999999999999997

   1. Initial program 80.0%

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

      1. *-commutative 80.0%

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

      2. associate-/l* 81.3%

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

      3. sqr-neg 81.3%

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

      4. associate-/r* 81.3%

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

      5. sqr-neg 81.3%

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

   3. Simplified 81.3%

      \[\leadsto \color{blue}{y \cdot \frac{\frac{x}{z \cdot z}}{z + 1}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 81.3%

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

      2. clear-num 81.2%

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

      3. associate-*l/ 81.2%

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

      4. associate-/r/ 82.0%

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

      5. frac-times 82.9%

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

      6. associate-/r* 88.8%

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

      7. frac-times 98.2%

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

      8. *-un-lft-identity 98.2%

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

   6. Applied egg-rr 98.2%

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

      1. associate-/r* 97.9%

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

      2. div-inv 97.9%

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

      3. clear-num 98.0%

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

      4. associate-*r/ 98.2%

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

      5. associate-*l/ 96.6%

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

      6. associate-/l* 89.6%

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

      7. associate-/l/ 89.6%

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

   8. Applied egg-rr 89.6%

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

   9. Taylor expanded in z around 0 87.5%

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

       1. clear-num 87.5%

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

       2. un-div-inv 88.2%

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

       3. div-inv 88.2%

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

       4. clear-num 88.2%

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

   11. Applied egg-rr 88.2%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.043\right):\\ \;\;\;\;\frac{y}{z} \cdot \frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot \frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.043\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.043)))
   (/ (/ x z) (* z (/ z y)))
   (/ y (* z (/ z x)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.043)) {
		tmp = (x / z) / (z * (z / y));
	} else {
		tmp = y / (z * (z / x));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 0.043d0))) then
        tmp = (x / z) / (z * (z / y))
    else
        tmp = y / (z * (z / x))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.043)) {
		tmp = (x / z) / (z * (z / y));
	} else {
		tmp = y / (z * (z / x));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 0.043):
		tmp = (x / z) / (z * (z / y))
	else:
		tmp = y / (z * (z / x))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 0.043))
		tmp = Float64(Float64(x / z) / Float64(z * Float64(z / y)));
	else
		tmp = Float64(y / Float64(z * Float64(z / 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 ((z <= -1.0) || ~((z <= 0.043)))
		tmp = (x / z) / (z * (z / y));
	else
		tmp = y / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 0.043]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / N[(z * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 0.042999999999999997 < z

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

      2. frac-times 93.9%

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

      3. associate-*l/ 93.9%

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

      4. times-frac 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in z around inf 95.7%

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

      1. clear-num 95.7%

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

      2. frac-times 94.5%

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

      3. *-un-lft-identity 94.5%

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

   7. Applied egg-rr 94.5%

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

   if -1 < z < 0.042999999999999997

   1. Initial program 80.0%

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

      1. *-commutative 80.0%

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

      2. associate-/l* 81.3%

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

      3. sqr-neg 81.3%

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

      4. associate-/r* 81.3%

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

      5. sqr-neg 81.3%

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

   3. Simplified 81.3%

      \[\leadsto \color{blue}{y \cdot \frac{\frac{x}{z \cdot z}}{z + 1}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 81.3%

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

      2. clear-num 81.2%

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

      3. associate-*l/ 81.2%

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

      4. associate-/r/ 82.0%

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

      5. frac-times 82.9%

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

      6. associate-/r* 88.8%

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

      7. frac-times 98.2%

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

      8. *-un-lft-identity 98.2%

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

   6. Applied egg-rr 98.2%

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

      1. associate-/r* 97.9%

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

      2. div-inv 97.9%

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

      3. clear-num 98.0%

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

      4. associate-*r/ 98.2%

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

      5. associate-*l/ 96.6%

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

      6. associate-/l* 89.6%

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

      7. associate-/l/ 89.6%

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

   8. Applied egg-rr 89.6%

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

   9. Taylor expanded in z around 0 87.5%

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

       1. clear-num 87.5%

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

       2. un-div-inv 88.2%

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

       3. div-inv 88.2%

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

       4. clear-num 88.2%

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

   11. Applied egg-rr 88.2%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.043\right):\\ \;\;\;\;\frac{\frac{x}{z}}{z \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot \frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 91.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.043\right):\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{z}{\frac{y}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 0.043)))
   (/ (/ x z) (/ z (/ y z)))
   (/ y (* z (/ z x)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.043)) {
		tmp = (x / z) / (z / (y / z));
	} else {
		tmp = y / (z * (z / x));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.0d0)) .or. (.not. (z <= 0.043d0))) then
        tmp = (x / z) / (z / (y / z))
    else
        tmp = y / (z * (z / x))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 0.043)) {
		tmp = (x / z) / (z / (y / z));
	} else {
		tmp = y / (z * (z / x));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -1.0) or not (z <= 0.043):
		tmp = (x / z) / (z / (y / z))
	else:
		tmp = y / (z * (z / x))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 0.043))
		tmp = Float64(Float64(x / z) / Float64(z / Float64(y / z)));
	else
		tmp = Float64(y / Float64(z * Float64(z / 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 ((z <= -1.0) || ~((z <= 0.043)))
		tmp = (x / z) / (z / (y / z));
	else
		tmp = y / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 0.043]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] / N[(z / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 0.042999999999999997 < z

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

      2. frac-times 93.9%

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

      3. associate-*l/ 93.9%

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

      4. times-frac 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in z around inf 95.7%

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

      1. clear-num 95.7%

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

      2. frac-times 94.5%

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

      3. *-un-lft-identity 94.5%

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

   7. Applied egg-rr 94.5%

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

      1. *-commutative 94.5%

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

      2. clear-num 94.5%

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

      3. un-div-inv 94.6%

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

   9. Applied egg-rr 94.6%

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

   if -1 < z < 0.042999999999999997

   1. Initial program 80.0%

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

      1. *-commutative 80.0%

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

      2. associate-/l* 81.3%

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

      3. sqr-neg 81.3%

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

      4. associate-/r* 81.3%

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

      5. sqr-neg 81.3%

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

   3. Simplified 81.3%

      \[\leadsto \color{blue}{y \cdot \frac{\frac{x}{z \cdot z}}{z + 1}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 81.3%

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

      2. clear-num 81.2%

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

      3. associate-*l/ 81.2%

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

      4. associate-/r/ 82.0%

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

      5. frac-times 82.9%

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

      6. associate-/r* 88.8%

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

      7. frac-times 98.2%

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

      8. *-un-lft-identity 98.2%

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

   6. Applied egg-rr 98.2%

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

      1. associate-/r* 97.9%

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

      2. div-inv 97.9%

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

      3. clear-num 98.0%

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

      4. associate-*r/ 98.2%

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

      5. associate-*l/ 96.6%

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

      6. associate-/l* 89.6%

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

      7. associate-/l/ 89.6%

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

   8. Applied egg-rr 89.6%

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

   9. Taylor expanded in z around 0 87.5%

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

       1. clear-num 87.5%

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

       2. un-div-inv 88.2%

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

       3. div-inv 88.2%

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

       4. clear-num 88.2%

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

   11. Applied egg-rr 88.2%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 0.043\right):\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{z}{\frac{y}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot \frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-137}:\\ \;\;\;\;y \cdot \frac{\frac{x}{z \cdot z}}{z + 1}\\ \mathbf{elif}\;z \leq 0.043:\\ \;\;\;\;\frac{y \cdot \frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{z}{\frac{y}{z}}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= z -1e-137)
   (* y (/ (/ x (* z z)) (+ z 1.0)))
   (if (<= z 0.043) (/ (* y (/ x z)) z) (/ (/ x z) (/ z (/ y z))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (z <= -1e-137) {
		tmp = y * ((x / (z * z)) / (z + 1.0));
	} else if (z <= 0.043) {
		tmp = (y * (x / z)) / z;
	} else {
		tmp = (x / z) / (z / (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 (z <= (-1d-137)) then
        tmp = y * ((x / (z * z)) / (z + 1.0d0))
    else if (z <= 0.043d0) then
        tmp = (y * (x / z)) / z
    else
        tmp = (x / z) / (z / (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 (z <= -1e-137) {
		tmp = y * ((x / (z * z)) / (z + 1.0));
	} else if (z <= 0.043) {
		tmp = (y * (x / z)) / z;
	} else {
		tmp = (x / z) / (z / (y / z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if z <= -1e-137:
		tmp = y * ((x / (z * z)) / (z + 1.0))
	elif z <= 0.043:
		tmp = (y * (x / z)) / z
	else:
		tmp = (x / z) / (z / (y / z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (z <= -1e-137)
		tmp = Float64(y * Float64(Float64(x / Float64(z * z)) / Float64(z + 1.0)));
	elseif (z <= 0.043)
		tmp = Float64(Float64(y * Float64(x / z)) / z);
	else
		tmp = Float64(Float64(x / z) / Float64(z / 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 (z <= -1e-137)
		tmp = y * ((x / (z * z)) / (z + 1.0));
	elseif (z <= 0.043)
		tmp = (y * (x / z)) / z;
	else
		tmp = (x / z) / (z / (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[z, -1e-137], N[(y * N[(N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision] / N[(z + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.043], N[(N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.99999999999999978e-138

   1. Initial program 88.5%

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

      1. *-commutative 88.5%

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

      2. associate-/l* 90.2%

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

      3. sqr-neg 90.2%

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

      4. associate-/r* 92.3%

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

      5. sqr-neg 92.3%

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

   3. Simplified 92.3%

      \[\leadsto \color{blue}{y \cdot \frac{\frac{x}{z \cdot z}}{z + 1}} \]
   4. Add Preprocessing

   if -9.99999999999999978e-138 < z < 0.042999999999999997

   1. Initial program 77.3%

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

      1. *-commutative 77.3%

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

      2. sqr-neg 77.3%

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

      3. times-frac 79.4%

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

      4. sqr-neg 79.4%

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

   3. Simplified 79.4%

      \[\leadsto \color{blue}{\frac{y}{z \cdot z} \cdot \frac{x}{z + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 78.5%

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

      1. associate-*l/ 76.4%

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

      2. *-commutative 76.4%

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

      3. associate-/r* 85.7%

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

      4. *-commutative 85.7%

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

      5. associate-*r/ 97.1%

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

   7. Applied egg-rr 97.1%

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

   if 0.042999999999999997 < z

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

      2. frac-times 93.8%

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

      3. associate-*l/ 94.0%

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

      4. times-frac 98.3%

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

   4. Applied egg-rr 98.3%

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

   5. Taylor expanded in z around inf 96.0%

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

      1. clear-num 96.0%

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

      2. frac-times 93.1%

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

      3. *-un-lft-identity 93.1%

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

   7. Applied egg-rr 93.1%

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

      1. *-commutative 93.1%

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

      2. clear-num 93.1%

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

      3. un-div-inv 93.2%

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

   9. Applied egg-rr 93.2%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-137}:\\ \;\;\;\;y \cdot \frac{\frac{x}{z \cdot z}}{z + 1}\\ \mathbf{elif}\;z \leq 0.043:\\ \;\;\;\;\frac{y \cdot \frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{z}{\frac{y}{z}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 800000000000:\\ \;\;\;\;y \cdot \frac{\frac{x}{z \cdot \left(z + 1\right)}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{z}{\frac{y}{z}}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= z 800000000000.0)
   (* y (/ (/ x (* z (+ z 1.0))) z))
   (/ (/ x z) (/ z (/ y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (z <= 800000000000.0) {
		tmp = y * ((x / (z * (z + 1.0))) / z);
	} else {
		tmp = (x / z) / (z / (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 (z <= 800000000000.0d0) then
        tmp = y * ((x / (z * (z + 1.0d0))) / z)
    else
        tmp = (x / z) / (z / (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 (z <= 800000000000.0) {
		tmp = y * ((x / (z * (z + 1.0))) / z);
	} else {
		tmp = (x / z) / (z / (y / z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if z <= 800000000000.0:
		tmp = y * ((x / (z * (z + 1.0))) / z)
	else:
		tmp = (x / z) / (z / (y / z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (z <= 800000000000.0)
		tmp = Float64(y * Float64(Float64(x / Float64(z * Float64(z + 1.0))) / z));
	else
		tmp = Float64(Float64(x / z) / Float64(z / 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 (z <= 800000000000.0)
		tmp = y * ((x / (z * (z + 1.0))) / z);
	else
		tmp = (x / z) / (z / (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[z, 800000000000.0], N[(y * N[(N[(x / N[(z * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] / N[(z / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8e11

   1. Initial program 82.9%

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

      1. *-commutative 82.9%

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

      2. associate-/l* 85.2%

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

      3. sqr-neg 85.2%

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

      4. associate-/r* 86.2%

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

      5. sqr-neg 86.2%

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

   3. Simplified 86.2%

      \[\leadsto \color{blue}{y \cdot \frac{\frac{x}{z \cdot z}}{z + 1}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 86.2%

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

      2. clear-num 86.1%

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

      3. associate-*l/ 86.1%

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

      4. associate-/r/ 86.6%

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

      5. frac-times 86.8%

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

      6. associate-/r* 92.2%

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

      7. frac-times 98.1%

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

      8. *-un-lft-identity 98.1%

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

   6. Applied egg-rr 98.1%

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

      1. associate-/r* 98.1%

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

      2. div-inv 98.1%

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

      3. clear-num 98.2%

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

      4. associate-*r/ 98.2%

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

      5. associate-*l/ 97.6%

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

      6. associate-/l* 91.6%

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

      7. associate-/l/ 91.5%

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

   8. Applied egg-rr 91.5%

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

   if 8e11 < z

   1. Initial program 86.6%

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

      1. *-commutative 86.6%

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

      2. frac-times 93.5%

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

      3. associate-*l/ 93.7%

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

      4. times-frac 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in z around inf 98.2%

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

      1. clear-num 98.2%

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

      2. frac-times 95.1%

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

      3. *-un-lft-identity 95.1%

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

   7. Applied egg-rr 95.1%

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

      1. *-commutative 95.1%

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

      2. clear-num 95.1%

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

      3. un-div-inv 95.2%

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

   9. Applied egg-rr 95.2%

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

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 800000000000:\\ \;\;\;\;y \cdot \frac{\frac{x}{z \cdot \left(z + 1\right)}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{z}{\frac{y}{z}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ y \cdot \frac{\frac{x}{z}}{z} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* y (/ (/ x z) z)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return y * ((x / z) / z);
}

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 = y * ((x / z) / z)
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return y * ((x / z) / z);
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return y * ((x / z) / z)

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(y * Float64(Float64(x / z) / z))
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = y * ((x / z) / z);
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(y * N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.7%

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

   1. *-commutative 83.7%

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

   2. associate-/l* 86.3%

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

   3. sqr-neg 86.3%

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

   4. associate-/r* 87.8%

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

   5. sqr-neg 87.8%

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

3. Simplified 87.8%

   \[\leadsto \color{blue}{y \cdot \frac{\frac{x}{z \cdot z}}{z + 1}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. *-commutative 87.8%

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

   2. clear-num 87.7%

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

   3. associate-*l/ 87.7%

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

   4. associate-/r/ 88.1%

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

   5. frac-times 88.3%

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

   6. associate-/r* 93.1%

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

   7. frac-times 98.1%

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

   8. *-un-lft-identity 98.1%

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

6. Applied egg-rr 98.1%

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

   1. associate-/r* 97.8%

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

   2. div-inv 97.8%

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

   3. clear-num 97.9%

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

   4. associate-*r/ 98.2%

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

   5. associate-*l/ 97.4%

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

   6. associate-/l* 92.3%

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

   7. associate-/l/ 92.0%

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

8. Applied egg-rr 92.0%

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

9. Taylor expanded in z around 0 74.0%

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

10. Final simplification 74.0%

    \[\leadsto y \cdot \frac{\frac{x}{z}}{z} \]
11. Add Preprocessing

Alternative 8: 74.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \frac{y}{z \cdot \frac{z}{x}} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (/ y (* z (/ z x))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return y / (z * (z / 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 = y / (z * (z / x))
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return y / (z * (z / x));
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return y / (z * (z / x))

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(y / Float64(z * Float64(z / x)))
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = y / (z * (z / x));
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(y / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.7%

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

   1. *-commutative 83.7%

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

   2. associate-/l* 86.3%

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

   3. sqr-neg 86.3%

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

   4. associate-/r* 87.8%

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

   5. sqr-neg 87.8%

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

3. Simplified 87.8%

   \[\leadsto \color{blue}{y \cdot \frac{\frac{x}{z \cdot z}}{z + 1}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. *-commutative 87.8%

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

   2. clear-num 87.7%

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

   3. associate-*l/ 87.7%

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

   4. associate-/r/ 88.1%

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

   5. frac-times 88.3%

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

   6. associate-/r* 93.1%

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

   7. frac-times 98.1%

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

   8. *-un-lft-identity 98.1%

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

6. Applied egg-rr 98.1%

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

   1. associate-/r* 97.8%

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

   2. div-inv 97.8%

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

   3. clear-num 97.9%

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

   4. associate-*r/ 98.2%

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

   5. associate-*l/ 97.4%

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

   6. associate-/l* 92.3%

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

   7. associate-/l/ 92.0%

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

8. Applied egg-rr 92.0%

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

9. Taylor expanded in z around 0 74.0%

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

    1. clear-num 74.6%

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

    2. un-div-inv 75.0%

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

    3. div-inv 75.0%

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

    4. clear-num 75.0%

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

11. Applied egg-rr 75.0%

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

12. Final simplification 75.0%

    \[\leadsto \frac{y}{z \cdot \frac{z}{x}} \]
13. Add Preprocessing

Developer target: 95.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z < 249.6182814532307:\\ \;\;\;\;\frac{y \cdot \frac{x}{z}}{z + z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{y}{z}}{1 + z} \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< z 249.6182814532307)
   (/ (* y (/ x z)) (+ z (* z z)))
   (/ (* (/ (/ y z) (+ 1.0 z)) x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z < 249.6182814532307) {
		tmp = (y * (x / z)) / (z + (z * z));
	} else {
		tmp = (((y / z) / (1.0 + z)) * x) / z;
	}
	return tmp;
}

Fortran

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 < 249.6182814532307d0) then
        tmp = (y * (x / z)) / (z + (z * z))
    else
        tmp = (((y / z) / (1.0d0 + z)) * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z < 249.6182814532307) {
		tmp = (y * (x / z)) / (z + (z * z));
	} else {
		tmp = (((y / z) / (1.0 + z)) * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z < 249.6182814532307:
		tmp = (y * (x / z)) / (z + (z * z))
	else:
		tmp = (((y / z) / (1.0 + z)) * x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z < 249.6182814532307)
		tmp = Float64(Float64(y * Float64(x / z)) / Float64(z + Float64(z * z)));
	else
		tmp = Float64(Float64(Float64(Float64(y / z) / Float64(1.0 + z)) * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z < 249.6182814532307)
		tmp = (y * (x / z)) / (z + (z * z));
	else
		tmp = (((y / z) / (1.0 + z)) * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[z, 249.6182814532307], N[(N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision] / N[(z + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y / z), $MachinePrecision] / N[(1.0 + z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]]

Reproduce

herbie shell --seed 2024079 
(FPCore (x y z)
  :name "Statistics.Distribution.Beta:$cvariance from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (if (< z 249.6182814532307) (/ (* y (/ x z)) (+ z (* z z))) (/ (* (/ (/ y z) (+ 1.0 z)) x) z))

  (/ (* x y) (* (* z z) (+ z 1.0))))