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

Percentage Accurate: 83.3% → 96.6%

Time: 10.1s

Alternatives: 15

Speedup: 0.8×

• 25.5% 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: 83.3% 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, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot z\right) \cdot \left(z + 1\right)\\ \mathbf{if}\;t_0 \leq 2 \cdot 10^{-211} \lor \neg \left(t_0 \leq 2 \cdot 10^{+257}\right):\\ \;\;\;\;\frac{\frac{x}{z} \cdot \frac{y}{z}}{z + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{t_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z z) (+ z 1.0))))
   (if (or (<= t_0 2e-211) (not (<= t_0 2e+257)))
     (/ (* (/ x z) (/ y z)) (+ z 1.0))
     (/ (* x y) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (z * z) * (z + 1.0);
	double tmp;
	if ((t_0 <= 2e-211) || !(t_0 <= 2e+257)) {
		tmp = ((x / z) * (y / z)) / (z + 1.0);
	} else {
		tmp = (x * y) / t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (z * z) * (z + 1.0d0)
    if ((t_0 <= 2d-211) .or. (.not. (t_0 <= 2d+257))) then
        tmp = ((x / z) * (y / z)) / (z + 1.0d0)
    else
        tmp = (x * y) / t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * z) * (z + 1.0);
	double tmp;
	if ((t_0 <= 2e-211) || !(t_0 <= 2e+257)) {
		tmp = ((x / z) * (y / z)) / (z + 1.0);
	} else {
		tmp = (x * y) / t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * z) * (z + 1.0)
	tmp = 0
	if (t_0 <= 2e-211) or not (t_0 <= 2e+257):
		tmp = ((x / z) * (y / z)) / (z + 1.0)
	else:
		tmp = (x * y) / t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * z) * Float64(z + 1.0))
	tmp = 0.0
	if ((t_0 <= 2e-211) || !(t_0 <= 2e+257))
		tmp = Float64(Float64(Float64(x / z) * Float64(y / z)) / Float64(z + 1.0));
	else
		tmp = Float64(Float64(x * y) / t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * z) * (z + 1.0);
	tmp = 0.0;
	if ((t_0 <= 2e-211) || ~((t_0 <= 2e+257)))
		tmp = ((x / z) * (y / z)) / (z + 1.0);
	else
		tmp = (x * y) / t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * z), $MachinePrecision] * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 2e-211], N[Not[LessEqual[t$95$0, 2e+257]], $MachinePrecision]], N[(N[(N[(x / z), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision] / N[(z + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 z z) (+.f64 z 1)) < 2.00000000000000017e-211 or 2.00000000000000006e257 < (*.f64 (*.f64 z z) (+.f64 z 1))

   1. Initial program 77.0%

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

      1. associate-*l* 77.0%

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

      2. times-frac 93.0%

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

      3. associate-/r* 97.4%

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

      4. associate-*r/ 98.9%

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

   3. Simplified 98.9%

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

   if 2.00000000000000017e-211 < (*.f64 (*.f64 z z) (+.f64 z 1)) < 2.00000000000000006e257

   1. Initial program 99.4%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot z\right) \cdot \left(z + 1\right) \leq 2 \cdot 10^{-211} \lor \neg \left(\left(z \cdot z\right) \cdot \left(z + 1\right) \leq 2 \cdot 10^{+257}\right):\\ \;\;\;\;\frac{\frac{x}{z} \cdot \frac{y}{z}}{z + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\\ \end{array} \]

Alternative 2: 95.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot z\right) \cdot \left(z + 1\right)\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{y}{z}}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{-185}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z}}{z}\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+257}:\\ \;\;\;\;\frac{x \cdot y}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{z}}{z}}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z z) (+ z 1.0))))
   (if (<= t_0 -2e+15)
     (/ (/ y z) (* z (/ z x)))
     (if (<= t_0 5e-185)
       (/ (* x (/ y z)) z)
       (if (<= t_0 2e+257) (/ (* x y) t_0) (/ (/ (/ x z) z) (/ z y)))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * z) * (z + 1.0);
	double tmp;
	if (t_0 <= -2e+15) {
		tmp = (y / z) / (z * (z / x));
	} else if (t_0 <= 5e-185) {
		tmp = (x * (y / z)) / z;
	} else if (t_0 <= 2e+257) {
		tmp = (x * y) / t_0;
	} else {
		tmp = ((x / z) / z) / (z / y);
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (z * z) * (z + 1.0d0)
    if (t_0 <= (-2d+15)) then
        tmp = (y / z) / (z * (z / x))
    else if (t_0 <= 5d-185) then
        tmp = (x * (y / z)) / z
    else if (t_0 <= 2d+257) then
        tmp = (x * y) / t_0
    else
        tmp = ((x / z) / z) / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * z) * (z + 1.0);
	double tmp;
	if (t_0 <= -2e+15) {
		tmp = (y / z) / (z * (z / x));
	} else if (t_0 <= 5e-185) {
		tmp = (x * (y / z)) / z;
	} else if (t_0 <= 2e+257) {
		tmp = (x * y) / t_0;
	} else {
		tmp = ((x / z) / z) / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * z) * (z + 1.0)
	tmp = 0
	if t_0 <= -2e+15:
		tmp = (y / z) / (z * (z / x))
	elif t_0 <= 5e-185:
		tmp = (x * (y / z)) / z
	elif t_0 <= 2e+257:
		tmp = (x * y) / t_0
	else:
		tmp = ((x / z) / z) / (z / y)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * z) * Float64(z + 1.0))
	tmp = 0.0
	if (t_0 <= -2e+15)
		tmp = Float64(Float64(y / z) / Float64(z * Float64(z / x)));
	elseif (t_0 <= 5e-185)
		tmp = Float64(Float64(x * Float64(y / z)) / z);
	elseif (t_0 <= 2e+257)
		tmp = Float64(Float64(x * y) / t_0);
	else
		tmp = Float64(Float64(Float64(x / z) / z) / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * z) * (z + 1.0);
	tmp = 0.0;
	if (t_0 <= -2e+15)
		tmp = (y / z) / (z * (z / x));
	elseif (t_0 <= 5e-185)
		tmp = (x * (y / z)) / z;
	elseif (t_0 <= 2e+257)
		tmp = (x * y) / t_0;
	else
		tmp = ((x / z) / z) / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * z), $MachinePrecision] * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+15], N[(N[(y / z), $MachinePrecision] / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e-185], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[t$95$0, 2e+257], N[(N[(x * y), $MachinePrecision] / t$95$0), $MachinePrecision], N[(N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision] / N[(z / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 (*.f64 z z) (+.f64 z 1)) < -2e15

   1. Initial program 80.4%

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

      1. *-commutative 80.4%

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

      2. sqr-neg 80.4%

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

      3. times-frac 87.2%

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

      4. sqr-neg 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around inf 86.2%

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

      1. *-commutative 86.2%

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

      2. clear-num 86.2%

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

      3. associate-/r* 95.4%

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

      4. frac-times 96.7%

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

      5. *-un-lft-identity 96.7%

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

   6. Applied egg-rr 96.7%

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

   if -2e15 < (*.f64 (*.f64 z z) (+.f64 z 1)) < 5.0000000000000003e-185

   1. Initial program 75.4%

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

      1. *-commutative 75.4%

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

      2. sqr-neg 75.4%

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

      3. times-frac 78.8%

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

      4. sqr-neg 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in z around 0 78.8%

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

      1. associate-/r* 90.6%

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

      2. associate-*l/ 98.5%

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

   6. Applied egg-rr 98.5%

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

   if 5.0000000000000003e-185 < (*.f64 (*.f64 z z) (+.f64 z 1)) < 2.00000000000000006e257

   1. Initial program 99.3%

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

   if 2.00000000000000006e257 < (*.f64 (*.f64 z z) (+.f64 z 1))

   1. Initial program 81.1%

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

      1. *-commutative 81.1%

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

      2. sqr-neg 81.1%

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

      3. times-frac 91.8%

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

      4. sqr-neg 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in z around inf 91.8%

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

      1. associate-/r* 98.0%

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

      2. frac-times 91.8%

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

   6. Applied egg-rr 91.8%

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

      1. clear-num 91.8%

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

      2. inv-pow 91.8%

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

      3. *-un-lft-identity 91.8%

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

      4. times-frac 89.8%

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

      5. clear-num 89.8%

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

      6. associate-/l* 95.8%

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

      7. div-inv 95.8%

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

      8. clear-num 95.9%

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

   8. Applied egg-rr 95.9%

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

      1. unpow-1 95.9%

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

      2. *-commutative 95.9%

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

      3. associate-/r* 95.9%

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

      4. *-commutative 95.9%

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

      5. associate-/r* 95.9%

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

      6. associate-/r/ 95.8%

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

      7. *-commutative 95.8%

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

      8. associate-*l/ 95.8%

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

      9. associate-*r/ 95.9%

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

      10. *-rgt-identity 95.9%

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

   10. Simplified 95.9%

       \[\leadsto \color{blue}{\frac{\frac{\frac{x}{z}}{z}}{\frac{z}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot z\right) \cdot \left(z + 1\right) \leq -2 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{y}{z}}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;\left(z \cdot z\right) \cdot \left(z + 1\right) \leq 5 \cdot 10^{-185}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z}}{z}\\ \mathbf{elif}\;\left(z \cdot z\right) \cdot \left(z + 1\right) \leq 2 \cdot 10^{+257}:\\ \;\;\;\;\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x}{z}}{z}}{\frac{z}{y}}\\ \end{array} \]

Alternative 3: 94.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(z \cdot z\right) \cdot \left(z + 1\right)\\ \mathbf{if}\;t_0 \leq -2 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{y}{z}}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{-185}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{x}{z + 1}}{z \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* z z) (+ z 1.0))))
   (if (<= t_0 -2e+15)
     (/ (/ y z) (* z (/ z x)))
     (if (<= t_0 5e-185)
       (/ (* x (/ y z)) z)
       (/ (* y (/ x (+ z 1.0))) (* z z))))))

C

double code(double x, double y, double z) {
	double t_0 = (z * z) * (z + 1.0);
	double tmp;
	if (t_0 <= -2e+15) {
		tmp = (y / z) / (z * (z / x));
	} else if (t_0 <= 5e-185) {
		tmp = (x * (y / z)) / z;
	} else {
		tmp = (y * (x / (z + 1.0))) / (z * 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) :: t_0
    real(8) :: tmp
    t_0 = (z * z) * (z + 1.0d0)
    if (t_0 <= (-2d+15)) then
        tmp = (y / z) / (z * (z / x))
    else if (t_0 <= 5d-185) then
        tmp = (x * (y / z)) / z
    else
        tmp = (y * (x / (z + 1.0d0))) / (z * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (z * z) * (z + 1.0);
	double tmp;
	if (t_0 <= -2e+15) {
		tmp = (y / z) / (z * (z / x));
	} else if (t_0 <= 5e-185) {
		tmp = (x * (y / z)) / z;
	} else {
		tmp = (y * (x / (z + 1.0))) / (z * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (z * z) * (z + 1.0)
	tmp = 0
	if t_0 <= -2e+15:
		tmp = (y / z) / (z * (z / x))
	elif t_0 <= 5e-185:
		tmp = (x * (y / z)) / z
	else:
		tmp = (y * (x / (z + 1.0))) / (z * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(z * z) * Float64(z + 1.0))
	tmp = 0.0
	if (t_0 <= -2e+15)
		tmp = Float64(Float64(y / z) / Float64(z * Float64(z / x)));
	elseif (t_0 <= 5e-185)
		tmp = Float64(Float64(x * Float64(y / z)) / z);
	else
		tmp = Float64(Float64(y * Float64(x / Float64(z + 1.0))) / Float64(z * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (z * z) * (z + 1.0);
	tmp = 0.0;
	if (t_0 <= -2e+15)
		tmp = (y / z) / (z * (z / x));
	elseif (t_0 <= 5e-185)
		tmp = (x * (y / z)) / z;
	else
		tmp = (y * (x / (z + 1.0))) / (z * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(z * z), $MachinePrecision] * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+15], N[(N[(y / z), $MachinePrecision] / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e-185], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(N[(y * N[(x / N[(z + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 z z) (+.f64 z 1)) < -2e15

   1. Initial program 80.4%

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

      1. *-commutative 80.4%

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

      2. sqr-neg 80.4%

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

      3. times-frac 87.2%

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

      4. sqr-neg 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around inf 86.2%

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

      1. *-commutative 86.2%

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

      2. clear-num 86.2%

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

      3. associate-/r* 95.4%

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

      4. frac-times 96.7%

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

      5. *-un-lft-identity 96.7%

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

   6. Applied egg-rr 96.7%

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

   if -2e15 < (*.f64 (*.f64 z z) (+.f64 z 1)) < 5.0000000000000003e-185

   1. Initial program 75.4%

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

      1. *-commutative 75.4%

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

      2. sqr-neg 75.4%

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

      3. times-frac 78.8%

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

      4. sqr-neg 78.8%

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

   3. Simplified 78.8%

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

   4. Taylor expanded in z around 0 78.8%

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

      1. associate-/r* 90.6%

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

      2. associate-*l/ 98.5%

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

   6. Applied egg-rr 98.5%

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

   if 5.0000000000000003e-185 < (*.f64 (*.f64 z z) (+.f64 z 1))

   1. Initial program 90.0%

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

      1. *-commutative 90.0%

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

      2. sqr-neg 90.0%

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

      3. times-frac 86.7%

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

      4. sqr-neg 86.7%

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

   3. Simplified 86.7%

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

      1. associate-*l/ 92.5%

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

   5. Applied egg-rr 92.5%

      \[\leadsto \color{blue}{\frac{y \cdot \frac{x}{z + 1}}{z \cdot z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z \cdot z\right) \cdot \left(z + 1\right) \leq -2 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{y}{z}}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;\left(z \cdot z\right) \cdot \left(z + 1\right) \leq 5 \cdot 10^{-185}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{x}{z + 1}}{z \cdot z}\\ \end{array} \]

Alternative 4: 94.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-92} \lor \neg \left(z \leq 5.8 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{y}{z \cdot \left(z \cdot \frac{z + 1}{x}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{z}{y}}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.6e-92) (not (<= z 5.8e-15)))
   (/ y (* z (* z (/ (+ z 1.0) x))))
   (/ (/ x (/ z y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.6e-92) || !(z <= 5.8e-15)) {
		tmp = y / (z * (z * ((z + 1.0) / x)));
	} else {
		tmp = (x / (z / y)) / 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 <= (-2.6d-92)) .or. (.not. (z <= 5.8d-15))) then
        tmp = y / (z * (z * ((z + 1.0d0) / x)))
    else
        tmp = (x / (z / y)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.6e-92) || !(z <= 5.8e-15)) {
		tmp = y / (z * (z * ((z + 1.0) / x)));
	} else {
		tmp = (x / (z / y)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.6e-92) or not (z <= 5.8e-15):
		tmp = y / (z * (z * ((z + 1.0) / x)))
	else:
		tmp = (x / (z / y)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.6e-92) || !(z <= 5.8e-15))
		tmp = Float64(y / Float64(z * Float64(z * Float64(Float64(z + 1.0) / x))));
	else
		tmp = Float64(Float64(x / Float64(z / y)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.6e-92) || ~((z <= 5.8e-15)))
		tmp = y / (z * (z * ((z + 1.0) / x)));
	else
		tmp = (x / (z / y)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.6e-92], N[Not[LessEqual[z, 5.8e-15]], $MachinePrecision]], N[(y / N[(z * N[(z * N[(N[(z + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e-92 or 5.80000000000000037e-15 < z

   1. Initial program 84.7%

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

      1. *-commutative 84.7%

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

      2. sqr-neg 84.7%

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

      3. times-frac 87.9%

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

      4. sqr-neg 87.9%

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

   3. Simplified 87.9%

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

      1. frac-2neg 87.9%

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

      2. div-inv 87.8%

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

      3. distribute-rgt-neg-in 87.8%

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

   5. Applied egg-rr 87.8%

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

      1. associate-*r/ 87.9%

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

      2. *-rgt-identity 87.9%

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

      3. associate-/r* 94.1%

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

   7. Simplified 94.1%

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

      1. *-commutative 94.1%

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

      2. clear-num 94.1%

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

      3. distribute-frac-neg 94.1%

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

      4. frac-2neg 94.1%

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

      5. times-frac 94.2%

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

      6. *-un-lft-identity 94.2%

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

      7. associate-/l/ 89.9%

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

      8. *-commutative 89.9%

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

   9. Applied egg-rr 89.9%

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

   if -2.6e-92 < z < 5.80000000000000037e-15

   1. Initial program 77.9%

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

      1. *-commutative 77.9%

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

      2. sqr-neg 77.9%

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

      3. times-frac 78.4%

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

      4. sqr-neg 78.4%

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

   3. Simplified 78.4%

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

   4. Taylor expanded in z around 0 78.4%

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

      1. add-sqr-sqrt 31.9%

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

      2. sqrt-unprod 28.6%

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

      3. sqr-neg 28.6%

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

      4. sqrt-unprod 0.3%

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

      5. add-sqr-sqrt 1.3%

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

      6. distribute-rgt-neg-in 1.3%

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

      7. associate-/r* 1.4%

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

      8. associate-/r/ 1.4%

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

      9. clear-num 1.4%

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

      10. *-un-lft-identity 1.4%

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

      11. associate-*l/ 1.4%

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

      12. clear-num 1.4%

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

      13. associate-/r* 1.4%

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

      14. distribute-neg-frac 1.4%

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

      15. div-inv 1.4%

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

      16. clear-num 1.4%

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

      17. /-rgt-identity 1.4%

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

   6. Applied egg-rr 1.4%

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

      1. add-sqr-sqrt 1.2%

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

      2. sqrt-unprod 44.8%

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

      3. sqr-neg 44.8%

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

      4. sqrt-unprod 50.7%

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

      5. add-sqr-sqrt 96.9%

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

      6. distribute-rgt-neg-in 96.9%

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

      7. clear-num 96.8%

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

      8. associate-*l/ 98.4%

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

      9. *-un-lft-identity 98.4%

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

   8. Applied egg-rr 98.4%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-92} \lor \neg \left(z \leq 5.8 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{y}{z \cdot \left(z \cdot \frac{z + 1}{x}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{\frac{z}{y}}}{z}\\ \end{array} \]

Alternative 5: 93.1% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0)))
   (* (/ x z) (/ y (* z z)))
   (/ (* x (/ y z)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = (x / z) * (y / (z * z));
	} else {
		tmp = (x * (y / z)) / 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 <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x / z) * (y / (z * z))
    else
        tmp = (x * (y / z)) / z
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x / z), $MachinePrecision] * N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 82.6%

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

      1. *-commutative 82.6%

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

      2. sqr-neg 82.6%

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

      3. times-frac 86.9%

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

      4. sqr-neg 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in z around inf 86.4%

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

   if -1 < z < 1

   1. Initial program 80.8%

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

      1. *-commutative 80.8%

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

      2. sqr-neg 80.8%

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

      3. times-frac 80.6%

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

      4. sqr-neg 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in z around 0 77.7%

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

      1. associate-/r* 86.9%

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

      2. associate-*l/ 93.6%

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

   6. Applied egg-rr 93.6%

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

4. Final simplification 90.1%

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

Alternative 6: 92.2% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0)))
   (/ y (* (* z z) (/ z x)))
   (/ (* x (/ y z)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = y / ((z * z) * (z / x));
	} else {
		tmp = (x * (y / z)) / 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 <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = y / ((z * z) * (z / x))
    else
        tmp = (x * (y / z)) / z
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(y / N[(N[(z * z), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 82.6%

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

      1. *-commutative 82.6%

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

      2. sqr-neg 82.6%

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

      3. times-frac 86.9%

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

      4. sqr-neg 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in z around inf 86.4%

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

      1. *-commutative 86.4%

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

      2. clear-num 86.4%

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

      3. frac-times 85.5%

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

      4. *-un-lft-identity 85.5%

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

   6. Applied egg-rr 85.5%

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

   if -1 < z < 1

   1. Initial program 80.8%

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

      1. *-commutative 80.8%

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

      2. sqr-neg 80.8%

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

      3. times-frac 80.6%

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

      4. sqr-neg 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in z around 0 77.7%

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

      1. associate-/r* 86.9%

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

      2. associate-*l/ 93.6%

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

   6. Applied egg-rr 93.6%

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

4. Final simplification 89.7%

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

Alternative 7: 92.4% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0)))
   (/ y (* (* z z) (/ z x)))
   (/ (/ x (/ z y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = y / ((z * z) * (z / x));
	} else {
		tmp = (x / (z / y)) / 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 <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = y / ((z * z) * (z / x))
    else
        tmp = (x / (z / y)) / z
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(y / N[(N[(z * z), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 82.6%

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

      1. *-commutative 82.6%

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

      2. sqr-neg 82.6%

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

      3. times-frac 86.9%

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

      4. sqr-neg 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in z around inf 86.4%

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

      1. *-commutative 86.4%

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

      2. clear-num 86.4%

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

      3. frac-times 85.5%

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

      4. *-un-lft-identity 85.5%

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

   6. Applied egg-rr 85.5%

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

   if -1 < z < 1

   1. Initial program 80.8%

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

      1. *-commutative 80.8%

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

      2. sqr-neg 80.8%

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

      3. times-frac 80.6%

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

      4. sqr-neg 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in z around 0 77.7%

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

      1. add-sqr-sqrt 32.9%

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

      2. sqrt-unprod 28.7%

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

      3. sqr-neg 28.7%

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

      4. sqrt-unprod 0.3%

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

      5. add-sqr-sqrt 1.3%

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

      6. distribute-rgt-neg-in 1.3%

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

      7. associate-/r* 1.3%

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

      8. associate-/r/ 1.4%

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

      9. clear-num 1.4%

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

      10. *-un-lft-identity 1.4%

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

      11. associate-*l/ 1.4%

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

      12. clear-num 1.4%

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

      13. associate-/r* 1.4%

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

      14. distribute-neg-frac 1.4%

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

      15. div-inv 1.4%

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

      16. clear-num 1.4%

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

      17. /-rgt-identity 1.4%

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

   6. Applied egg-rr 1.4%

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

      1. add-sqr-sqrt 1.1%

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

      2. sqrt-unprod 41.9%

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

      3. sqr-neg 41.9%

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

      4. sqrt-unprod 47.2%

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

      5. add-sqr-sqrt 93.6%

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

      6. distribute-rgt-neg-in 93.6%

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

      7. clear-num 93.6%

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

      8. associate-*l/ 94.9%

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

      9. *-un-lft-identity 94.9%

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

   8. Applied egg-rr 94.9%

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

4. Final simplification 90.3%

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

Alternative 8: 95.1% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.0)))
   (/ (/ y z) (* z (/ z x)))
   (/ (/ x (/ z y)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.0)) {
		tmp = (y / z) / (z * (z / x));
	} else {
		tmp = (x / (z / y)) / 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 <= (-1.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (y / z) / (z * (z / x))
    else
        tmp = (x / (z / y)) / z
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(y / z), $MachinePrecision] / N[(z * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1 < z

   1. Initial program 82.6%

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

      1. *-commutative 82.6%

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

      2. sqr-neg 82.6%

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

      3. times-frac 86.9%

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

      4. sqr-neg 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in z around inf 86.4%

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

      1. *-commutative 86.4%

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

      2. clear-num 86.4%

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

      3. associate-/r* 93.6%

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

      4. frac-times 94.5%

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

      5. *-un-lft-identity 94.5%

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

   6. Applied egg-rr 94.5%

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

   if -1 < z < 1

   1. Initial program 80.8%

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

      1. *-commutative 80.8%

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

      2. sqr-neg 80.8%

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

      3. times-frac 80.6%

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

      4. sqr-neg 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in z around 0 77.7%

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

      1. add-sqr-sqrt 32.9%

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

      2. sqrt-unprod 28.7%

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

      3. sqr-neg 28.7%

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

      4. sqrt-unprod 0.3%

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

      5. add-sqr-sqrt 1.3%

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

      6. distribute-rgt-neg-in 1.3%

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

      7. associate-/r* 1.3%

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

      8. associate-/r/ 1.4%

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

      9. clear-num 1.4%

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

      10. *-un-lft-identity 1.4%

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

      11. associate-*l/ 1.4%

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

      12. clear-num 1.4%

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

      13. associate-/r* 1.4%

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

      14. distribute-neg-frac 1.4%

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

      15. div-inv 1.4%

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

      16. clear-num 1.4%

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

      17. /-rgt-identity 1.4%

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

   6. Applied egg-rr 1.4%

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

      1. add-sqr-sqrt 1.1%

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

      2. sqrt-unprod 41.9%

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

      3. sqr-neg 41.9%

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

      4. sqrt-unprod 47.2%

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

      5. add-sqr-sqrt 93.6%

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

      6. distribute-rgt-neg-in 93.6%

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

      7. clear-num 93.6%

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

      8. associate-*l/ 94.9%

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

      9. *-un-lft-identity 94.9%

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

   8. Applied egg-rr 94.9%

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

4. Final simplification 94.7%

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

Alternative 9: 92.7% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0)
   (/ y (* (* z z) (/ z x)))
   (if (<= z 1.0) (/ (/ x (/ z y)) z) (/ (* x (/ y z)) (* z z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = y / ((z * z) * (z / x));
	} else if (z <= 1.0) {
		tmp = (x / (z / y)) / z;
	} else {
		tmp = (x * (y / z)) / (z * 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 <= (-1.0d0)) then
        tmp = y / ((z * z) * (z / x))
    else if (z <= 1.0d0) then
        tmp = (x / (z / y)) / z
    else
        tmp = (x * (y / z)) / (z * z)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if z < -1

   1. Initial program 80.4%

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

      1. *-commutative 80.4%

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

      2. sqr-neg 80.4%

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

      3. times-frac 87.2%

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

      4. sqr-neg 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around inf 86.2%

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

      1. *-commutative 86.2%

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

      2. clear-num 86.2%

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

      3. frac-times 86.8%

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

      4. *-un-lft-identity 86.8%

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

   6. Applied egg-rr 86.8%

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

   if -1 < z < 1

   1. Initial program 80.8%

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

      1. *-commutative 80.8%

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

      2. sqr-neg 80.8%

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

      3. times-frac 80.6%

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

      4. sqr-neg 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in z around 0 77.7%

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

      1. add-sqr-sqrt 32.9%

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

      2. sqrt-unprod 28.7%

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

      3. sqr-neg 28.7%

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

      4. sqrt-unprod 0.3%

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

      5. add-sqr-sqrt 1.3%

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

      6. distribute-rgt-neg-in 1.3%

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

      7. associate-/r* 1.3%

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

      8. associate-/r/ 1.4%

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

      9. clear-num 1.4%

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

      10. *-un-lft-identity 1.4%

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

      11. associate-*l/ 1.4%

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

      12. clear-num 1.4%

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

      13. associate-/r* 1.4%

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

      14. distribute-neg-frac 1.4%

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

      15. div-inv 1.4%

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

      16. clear-num 1.4%

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

      17. /-rgt-identity 1.4%

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

   6. Applied egg-rr 1.4%

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

      1. add-sqr-sqrt 1.1%

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

      2. sqrt-unprod 41.9%

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

      3. sqr-neg 41.9%

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

      4. sqrt-unprod 47.2%

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

      5. add-sqr-sqrt 93.6%

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

      6. distribute-rgt-neg-in 93.6%

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

      7. clear-num 93.6%

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

      8. associate-*l/ 94.9%

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

      9. *-un-lft-identity 94.9%

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

   8. Applied egg-rr 94.9%

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

   if 1 < z

   1. Initial program 85.1%

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

      1. *-commutative 85.1%

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

      2. sqr-neg 85.1%

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

      3. times-frac 86.6%

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

      4. sqr-neg 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in z around inf 86.6%

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

      1. associate-/r* 91.4%

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

      2. frac-times 93.5%

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

   6. Applied egg-rr 93.5%

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

4. Final simplification 92.5%

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

Alternative 10: 93.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;\frac{\frac{y}{z}}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{\frac{x}{\frac{z}{y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\frac{z}{x}}}{z \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.0)
   (/ (/ y z) (* z (/ z x)))
   (if (<= z 1.0) (/ (/ x (/ z y)) z) (/ (/ y (/ z x)) (* z z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.0) {
		tmp = (y / z) / (z * (z / x));
	} else if (z <= 1.0) {
		tmp = (x / (z / y)) / z;
	} else {
		tmp = (y / (z / x)) / (z * 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 <= (-1.0d0)) then
        tmp = (y / z) / (z * (z / x))
    else if (z <= 1.0d0) then
        tmp = (x / (z / y)) / z
    else
        tmp = (y / (z / x)) / (z * z)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if z < -1

   1. Initial program 80.4%

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

      1. *-commutative 80.4%

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

      2. sqr-neg 80.4%

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

      3. times-frac 87.2%

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

      4. sqr-neg 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in z around inf 86.2%

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

      1. *-commutative 86.2%

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

      2. clear-num 86.2%

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

      3. associate-/r* 95.4%

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

      4. frac-times 96.7%

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

      5. *-un-lft-identity 96.7%

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

   6. Applied egg-rr 96.7%

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

   if -1 < z < 1

   1. Initial program 80.8%

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

      1. *-commutative 80.8%

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

      2. sqr-neg 80.8%

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

      3. times-frac 80.6%

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

      4. sqr-neg 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in z around 0 77.7%

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

      1. add-sqr-sqrt 32.9%

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

      2. sqrt-unprod 28.7%

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

      3. sqr-neg 28.7%

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

      4. sqrt-unprod 0.3%

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

      5. add-sqr-sqrt 1.3%

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

      6. distribute-rgt-neg-in 1.3%

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

      7. associate-/r* 1.3%

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

      8. associate-/r/ 1.4%

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

      9. clear-num 1.4%

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

      10. *-un-lft-identity 1.4%

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

      11. associate-*l/ 1.4%

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

      12. clear-num 1.4%

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

      13. associate-/r* 1.4%

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

      14. distribute-neg-frac 1.4%

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

      15. div-inv 1.4%

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

      16. clear-num 1.4%

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

      17. /-rgt-identity 1.4%

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

   6. Applied egg-rr 1.4%

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

      1. add-sqr-sqrt 1.1%

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

      2. sqrt-unprod 41.9%

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

      3. sqr-neg 41.9%

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

      4. sqrt-unprod 47.2%

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

      5. add-sqr-sqrt 93.6%

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

      6. distribute-rgt-neg-in 93.6%

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

      7. clear-num 93.6%

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

      8. associate-*l/ 94.9%

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

      9. *-un-lft-identity 94.9%

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

   8. Applied egg-rr 94.9%

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

   if 1 < z

   1. Initial program 85.1%

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

      1. *-commutative 85.1%

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

      2. sqr-neg 85.1%

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

      3. times-frac 86.6%

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

      4. sqr-neg 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in z around inf 86.6%

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

      1. associate-/r* 91.4%

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

      2. frac-times 93.5%

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

   6. Applied egg-rr 93.5%

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

      1. associate-*l/ 90.1%

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

      2. associate-/l* 88.7%

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

   8. Applied egg-rr 88.7%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;\frac{\frac{y}{z}}{z \cdot \frac{z}{x}}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{\frac{x}{\frac{z}{y}}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\frac{z}{x}}}{z \cdot z}\\ \end{array} \]

Alternative 11: 73.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \frac{y}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1e-11) (* x (/ y (* z z))) (* y (/ x (* z z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e-11) {
		tmp = x * (y / (z * z));
	} else {
		tmp = y * (x / (z * 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 (x <= (-1d-11)) then
        tmp = x * (y / (z * z))
    else
        tmp = y * (x / (z * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1e-11) {
		tmp = x * (y / (z * z));
	} else {
		tmp = y * (x / (z * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1e-11:
		tmp = x * (y / (z * z))
	else:
		tmp = y * (x / (z * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1e-11)
		tmp = Float64(x * Float64(y / Float64(z * z)));
	else
		tmp = Float64(y * Float64(x / Float64(z * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1e-11)
		tmp = x * (y / (z * z));
	else
		tmp = y * (x / (z * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1e-11], N[(x * N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.99999999999999939e-12

   1. Initial program 81.1%

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

      1. *-commutative 81.1%

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

      2. sqr-neg 81.1%

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

      3. times-frac 85.5%

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

      4. sqr-neg 85.5%

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

   3. Simplified 85.5%

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

   4. Taylor expanded in z around 0 71.5%

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

   if -9.99999999999999939e-12 < x

   1. Initial program 81.9%

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

      1. *-commutative 81.9%

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

      2. associate-*r/ 82.4%

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

      3. sqr-neg 82.4%

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

      4. associate-*l* 82.4%

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

      5. associate-*l* 82.4%

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

      6. sqr-neg 82.4%

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

      7. associate-*l* 82.4%

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

      8. distribute-lft-in 82.4%

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

      9. fma-def 82.4%

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

      10. *-rgt-identity 82.4%

          \[\leadsto y \cdot \frac{x}{z \cdot \mathsf{fma}\left(z, z, \color{blue}{z}\right)} \]

   3. Simplified 82.4%

      \[\leadsto \color{blue}{y \cdot \frac{x}{z \cdot \mathsf{fma}\left(z, z, z\right)}} \]

   4. Taylor expanded in z around 0 75.4%

      \[\leadsto y \cdot \color{blue}{\frac{x}{{z}^{2}}} \]
   5. Step-by-step derivation

      1. unpow2 75.4%

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

   6. Simplified 75.4%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \frac{y}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot z}\\ \end{array} \]

Alternative 12: 75.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \frac{y}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{x}{z}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.5e-78) (* x (/ y (* z z))) (* y (/ (/ x z) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.5e-78) {
		tmp = x * (y / (z * z));
	} else {
		tmp = y * ((x / z) / 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 (x <= (-3.5d-78)) then
        tmp = x * (y / (z * z))
    else
        tmp = y * ((x / z) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.5e-78) {
		tmp = x * (y / (z * z));
	} else {
		tmp = y * ((x / z) / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.5e-78:
		tmp = x * (y / (z * z))
	else:
		tmp = y * ((x / z) / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.5e-78)
		tmp = Float64(x * Float64(y / Float64(z * z)));
	else
		tmp = Float64(y * Float64(Float64(x / z) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.5e-78)
		tmp = x * (y / (z * z));
	else
		tmp = y * ((x / z) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.5e-78], N[(x * N[(y / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4999999999999999e-78

   1. Initial program 83.1%

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

      1. *-commutative 83.1%

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

      2. sqr-neg 83.1%

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

      3. times-frac 86.8%

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

      4. sqr-neg 86.8%

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

   3. Simplified 86.8%

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

   4. Taylor expanded in z around 0 74.4%

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

   if -3.4999999999999999e-78 < x

   1. Initial program 81.0%

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

      1. *-commutative 81.0%

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

      2. sqr-neg 81.0%

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

      3. times-frac 82.1%

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

      4. sqr-neg 82.1%

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

   3. Simplified 82.1%

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

      1. *-commutative 82.1%

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

      2. clear-num 82.1%

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

      3. associate-/r* 90.0%

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

      4. frac-times 93.8%

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

      5. *-un-lft-identity 93.8%

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

   5. Applied egg-rr 93.8%

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

   6. Taylor expanded in z around 0 69.9%

      \[\leadsto \color{blue}{\frac{x \cdot y}{{z}^{2}}} \]
   7. Step-by-step derivation

      1. unpow2 69.9%

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

      2. associate-/l* 72.4%

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

      3. associate-/r/ 74.3%

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

      4. associate-/l/ 78.7%

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

   8. Simplified 78.7%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-78}:\\ \;\;\;\;x \cdot \frac{y}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 13: 76.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{-126}:\\ \;\;\;\;\frac{x}{z \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 2.2e-126) (/ x (* z (/ z y))) (* y (/ x (* z z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.2e-126) {
		tmp = x / (z * (z / y));
	} else {
		tmp = y * (x / (z * 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 (y <= 2.2d-126) then
        tmp = x / (z * (z / y))
    else
        tmp = y * (x / (z * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.2e-126) {
		tmp = x / (z * (z / y));
	} else {
		tmp = y * (x / (z * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 2.2e-126:
		tmp = x / (z * (z / y))
	else:
		tmp = y * (x / (z * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 2.2e-126)
		tmp = Float64(x / Float64(z * Float64(z / y)));
	else
		tmp = Float64(y * Float64(x / Float64(z * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.2e-126)
		tmp = x / (z * (z / y));
	else
		tmp = y * (x / (z * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 2.2e-126], N[(x / N[(z * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.20000000000000014e-126

   1. Initial program 80.3%

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

      1. *-commutative 80.3%

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

      2. sqr-neg 80.3%

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

      3. times-frac 83.8%

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

      4. sqr-neg 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in z around 0 75.7%

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

      1. *-commutative 75.7%

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

      2. clear-num 75.7%

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

      3. associate-*l/ 81.3%

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

      4. div-inv 81.8%

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

      5. *-commutative 81.8%

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

   6. Applied egg-rr 81.8%

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

   if 2.20000000000000014e-126 < y

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

      2. associate-*r/ 87.0%

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

      3. sqr-neg 87.0%

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

      4. associate-*l* 86.9%

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

      5. associate-*l* 87.0%

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

      6. sqr-neg 87.0%

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

      7. associate-*l* 86.9%

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

      8. distribute-lft-in 86.9%

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

      9. fma-def 86.9%

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

      10. *-rgt-identity 86.9%

          \[\leadsto y \cdot \frac{x}{z \cdot \mathsf{fma}\left(z, z, \color{blue}{z}\right)} \]

   3. Simplified 86.9%

      \[\leadsto \color{blue}{y \cdot \frac{x}{z \cdot \mathsf{fma}\left(z, z, z\right)}} \]

   4. Taylor expanded in z around 0 77.0%

      \[\leadsto y \cdot \color{blue}{\frac{x}{{z}^{2}}} \]
   5. Step-by-step derivation

      1. unpow2 77.0%

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

   6. Simplified 77.0%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.2 \cdot 10^{-126}:\\ \;\;\;\;\frac{x}{z \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot z}\\ \end{array} \]

Alternative 14: 76.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{-133}:\\ \;\;\;\;\frac{x}{z \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot \frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 1.1e-133) (/ x (* z (/ z y))) (/ y (* z (/ z x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.1e-133) {
		tmp = x / (z * (z / y));
	} else {
		tmp = y / (z * (z / x));
	}
	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 (y <= 1.1d-133) then
        tmp = x / (z * (z / y))
    else
        tmp = y / (z * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.1e-133) {
		tmp = x / (z * (z / y));
	} else {
		tmp = y / (z * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 1.1e-133:
		tmp = x / (z * (z / y))
	else:
		tmp = y / (z * (z / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 1.1e-133)
		tmp = Float64(x / Float64(z * Float64(z / y)));
	else
		tmp = Float64(y / Float64(z * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 1.1e-133)
		tmp = x / (z * (z / y));
	else
		tmp = y / (z * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 1.1e-133], N[(x / 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 y < 1.1e-133

   1. Initial program 80.2%

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

      1. *-commutative 80.2%

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

      2. sqr-neg 80.2%

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

      3. times-frac 83.8%

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

      4. sqr-neg 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in z around 0 75.6%

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

      1. *-commutative 75.6%

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

      2. clear-num 75.6%

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

      3. associate-*l/ 81.2%

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

      4. div-inv 81.7%

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

      5. *-commutative 81.7%

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

   6. Applied egg-rr 81.7%

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

   if 1.1e-133 < y

   1. Initial program 85.5%

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

      1. *-commutative 85.5%

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

      2. sqr-neg 85.5%

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

      3. times-frac 83.4%

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

      4. sqr-neg 83.4%

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

   3. Simplified 83.4%

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

      1. *-commutative 83.4%

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

      2. clear-num 83.4%

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

      3. associate-/r* 88.4%

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

      4. frac-times 93.5%

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

      5. *-un-lft-identity 93.5%

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

   5. Applied egg-rr 93.5%

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

   6. Taylor expanded in z around 0 70.8%

      \[\leadsto \color{blue}{\frac{x \cdot y}{{z}^{2}}} \]
   7. Step-by-step derivation

      1. unpow2 70.8%

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

      2. *-commutative 70.8%

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

      3. associate-/l* 77.3%

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

      4. associate-*r/ 78.7%

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

   8. Simplified 78.7%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.1 \cdot 10^{-133}:\\ \;\;\;\;\frac{x}{z \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 15: 71.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ y \cdot \frac{x}{z \cdot z} \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return y * (x / (z * 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 = y * (x / (z * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.7%

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

   1. *-commutative 81.7%

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

   2. associate-*r/ 81.5%

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

   3. sqr-neg 81.5%

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

   4. associate-*l* 81.5%

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

   5. associate-*l* 81.5%

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

   6. sqr-neg 81.5%

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

   7. associate-*l* 81.5%

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

   8. distribute-lft-in 81.5%

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

   9. fma-def 81.5%

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

   10. *-rgt-identity 81.5%

       \[\leadsto y \cdot \frac{x}{z \cdot \mathsf{fma}\left(z, z, \color{blue}{z}\right)} \]

3. Simplified 81.5%

   \[\leadsto \color{blue}{y \cdot \frac{x}{z \cdot \mathsf{fma}\left(z, z, z\right)}} \]

4. Taylor expanded in z around 0 72.3%

   \[\leadsto y \cdot \color{blue}{\frac{x}{{z}^{2}}} \]
5. Step-by-step derivation

   1. unpow2 72.3%

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

6. Simplified 72.3%

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

7. Final simplification 72.3%

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

Developer target: 95.7% accurate, 0.8× 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 2023290 
(FPCore (x y z)
  :name "Statistics.Distribution.Beta:$cvariance from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (if (< z 249.6182814532307) (/ (* y (/ x z)) (+ z (* z z))) (/ (* (/ (/ y z) (+ 1.0 z)) x) z))

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