Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, G

Percentage Accurate: 84.2% → 99.0%

Time: 10.0s

Alternatives: 8

Speedup: 42.2×

Specification

Math

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

FPCore

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

C

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

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 + (exp((y * log((y / (z + y))))) / y)
end function

Java

public static double code(double x, double y, double z) {
	return x + (Math.exp((y * Math.log((y / (z + y))))) / y);
}

Python

def code(x, y, z):
	return x + (math.exp((y * math.log((y / (z + y))))) / y)

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (exp((y * log((y / (z + y))))) / y)
end function

Java

public static double code(double x, double y, double z) {
	return x + (Math.exp((y * Math.log((y / (z + y))))) / y);
}

Python

def code(x, y, z):
	return x + (math.exp((y * math.log((y / (z + y))))) / y)

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+94} \lor \neg \left(y \leq 4 \cdot 10^{-29}\right):\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.4e+94) (not (<= y 4e-29)))
   (+ x (/ (exp (- z)) y))
   (+ x (/ (pow (exp y) (log (/ y (+ y z)))) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e+94) || !(y <= 4e-29)) {
		tmp = x + (exp(-z) / y);
	} else {
		tmp = x + (pow(exp(y), log((y / (y + 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) :: tmp
    if ((y <= (-1.4d+94)) .or. (.not. (y <= 4d-29))) then
        tmp = x + (exp(-z) / y)
    else
        tmp = x + ((exp(y) ** log((y / (y + z)))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.4e+94) || !(y <= 4e-29)) {
		tmp = x + (Math.exp(-z) / y);
	} else {
		tmp = x + (Math.pow(Math.exp(y), Math.log((y / (y + z)))) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.4e+94) or not (y <= 4e-29):
		tmp = x + (math.exp(-z) / y)
	else:
		tmp = x + (math.pow(math.exp(y), math.log((y / (y + z)))) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.4e+94) || !(y <= 4e-29))
		tmp = Float64(x + Float64(exp(Float64(-z)) / y));
	else
		tmp = Float64(x + Float64((exp(y) ^ log(Float64(y / Float64(y + z)))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.4e+94) || ~((y <= 4e-29)))
		tmp = x + (exp(-z) / y);
	else
		tmp = x + ((exp(y) ^ log((y / (y + z)))) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.4e+94], N[Not[LessEqual[y, 4e-29]], $MachinePrecision]], N[(x + N[(N[Exp[(-z)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Power[N[Exp[y], $MachinePrecision], N[Log[N[(y / N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.39999999999999999e94 or 3.99999999999999977e-29 < y

   1. Initial program 81.8%

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

      1. *-commutative 81.8%

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

      2. exp-to-pow 81.8%

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

      3. +-commutative 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

   if -1.39999999999999999e94 < y < 3.99999999999999977e-29

   1. Initial program 83.2%

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

      1. exp-prod 100.0%

         \[\leadsto x + \frac{\color{blue}{{\left(e^{y}\right)}^{\log \left(\frac{y}{z + y}\right)}}}{y} \]

      2. +-commutative 100.0%

         \[\leadsto x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{\color{blue}{y + z}}\right)}}{y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+94} \lor \neg \left(y \leq 4 \cdot 10^{-29}\right):\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}\\ \end{array} \]

Alternative 2: 99.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \lor \neg \left(y \leq 1.4 \cdot 10^{-27}\right):\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.1) (not (<= y 1.4e-27)))
   (+ x (/ (exp (- z)) y))
   (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.1) || !(y <= 1.4e-27)) {
		tmp = x + (exp(-z) / y);
	} else {
		tmp = x + (1.0 / 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) :: tmp
    if ((y <= (-1.1d0)) .or. (.not. (y <= 1.4d-27))) then
        tmp = x + (exp(-z) / y)
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.1) || !(y <= 1.4e-27)) {
		tmp = x + (Math.exp(-z) / y);
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.1) or not (y <= 1.4e-27):
		tmp = x + (math.exp(-z) / y)
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.1) || !(y <= 1.4e-27))
		tmp = Float64(x + Float64(exp(Float64(-z)) / y));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.1) || ~((y <= 1.4e-27)))
		tmp = x + (exp(-z) / y);
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.1], N[Not[LessEqual[y, 1.4e-27]], $MachinePrecision]], N[(x + N[(N[Exp[(-z)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.1000000000000001 or 1.4e-27 < y

   1. Initial program 83.9%

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

      1. *-commutative 83.9%

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

      2. exp-to-pow 83.9%

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

      3. +-commutative 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

   if -1.1000000000000001 < y < 1.4e-27

   1. Initial program 79.9%

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

      1. exp-prod 100.0%

         \[\leadsto x + \frac{\color{blue}{{\left(e^{y}\right)}^{\log \left(\frac{y}{z + y}\right)}}}{y} \]

      2. +-commutative 100.0%

         \[\leadsto x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{\color{blue}{y + z}}\right)}}{y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}} \]

   4. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{\frac{1}{y} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \lor \neg \left(y \leq 1.4 \cdot 10^{-27}\right):\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]

Alternative 3: 88.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1050:\\ \;\;\;\;\frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1050.0) (/ (exp (- z)) y) (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1050.0) {
		tmp = exp(-z) / y;
	} else {
		tmp = x + (1.0 / 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) :: tmp
    if (z <= (-1050.0d0)) then
        tmp = exp(-z) / y
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1050.0) {
		tmp = Math.exp(-z) / y;
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1050.0:
		tmp = math.exp(-z) / y
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1050.0)
		tmp = Float64(exp(Float64(-z)) / y);
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1050.0)
		tmp = exp(-z) / y;
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1050.0], N[(N[Exp[(-z)], $MachinePrecision] / y), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1050

   1. Initial program 43.6%

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

      1. *-commutative 43.6%

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

      2. exp-to-pow 43.6%

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

      3. +-commutative 43.6%

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

   3. Simplified 43.6%

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

   4. Taylor expanded in y around inf 70.7%

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

      1. mul-1-neg 70.7%

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

   6. Simplified 70.7%

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

   7. Taylor expanded in x around 0 70.7%

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

   if -1050 < z

   1. Initial program 93.8%

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

      1. exp-prod 98.2%

         \[\leadsto x + \frac{\color{blue}{{\left(e^{y}\right)}^{\log \left(\frac{y}{z + y}\right)}}}{y} \]

      2. +-commutative 98.2%

         \[\leadsto x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{\color{blue}{y + z}}\right)}}{y} \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}} \]

   4. Taylor expanded in y around inf 97.7%

      \[\leadsto \color{blue}{\frac{1}{y} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1050:\\ \;\;\;\;\frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]

Alternative 4: 87.0% accurate, 14.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.345:\\ \;\;\;\;x + \frac{1 + \left(0.5 \cdot \left(z \cdot z\right) - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -0.345) (+ x (/ (+ 1.0 (- (* 0.5 (* z z)) z)) y)) (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.345) {
		tmp = x + ((1.0 + ((0.5 * (z * z)) - z)) / y);
	} else {
		tmp = x + (1.0 / 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) :: tmp
    if (y <= (-0.345d0)) then
        tmp = x + ((1.0d0 + ((0.5d0 * (z * z)) - z)) / y)
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -0.345) {
		tmp = x + ((1.0 + ((0.5 * (z * z)) - z)) / y);
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -0.345:
		tmp = x + ((1.0 + ((0.5 * (z * z)) - z)) / y)
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -0.345)
		tmp = Float64(x + Float64(Float64(1.0 + Float64(Float64(0.5 * Float64(z * z)) - z)) / y));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -0.345)
		tmp = x + ((1.0 + ((0.5 * (z * z)) - z)) / y);
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -0.345], N[(x + N[(N[(1.0 + N[(N[(0.5 * N[(z * z), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.34499999999999997

   1. Initial program 82.0%

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

      1. *-commutative 82.0%

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

      2. exp-to-pow 82.0%

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

      3. +-commutative 82.0%

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

   3. Simplified 82.0%

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

   4. Taylor expanded in z around 0 79.6%

      \[\leadsto x + \color{blue}{\left(\frac{1}{y} + \left(-1 \cdot \frac{z}{y} + \left(0.5 \cdot \frac{1}{y} + 0.5 \cdot \frac{1}{{y}^{2}}\right) \cdot {z}^{2}\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 79.6%

         \[\leadsto x + \left(\frac{1}{y} + \color{blue}{\left(\left(0.5 \cdot \frac{1}{y} + 0.5 \cdot \frac{1}{{y}^{2}}\right) \cdot {z}^{2} + -1 \cdot \frac{z}{y}\right)}\right) \]

      2. mul-1-neg 79.6%

         \[\leadsto x + \left(\frac{1}{y} + \left(\left(0.5 \cdot \frac{1}{y} + 0.5 \cdot \frac{1}{{y}^{2}}\right) \cdot {z}^{2} + \color{blue}{\left(-\frac{z}{y}\right)}\right)\right) \]

      3. unsub-neg 79.6%

         \[\leadsto x + \left(\frac{1}{y} + \color{blue}{\left(\left(0.5 \cdot \frac{1}{y} + 0.5 \cdot \frac{1}{{y}^{2}}\right) \cdot {z}^{2} - \frac{z}{y}\right)}\right) \]

      4. *-commutative 79.6%

         \[\leadsto x + \left(\frac{1}{y} + \left(\color{blue}{{z}^{2} \cdot \left(0.5 \cdot \frac{1}{y} + 0.5 \cdot \frac{1}{{y}^{2}}\right)} - \frac{z}{y}\right)\right) \]

      5. unpow2 79.6%

         \[\leadsto x + \left(\frac{1}{y} + \left(\color{blue}{\left(z \cdot z\right)} \cdot \left(0.5 \cdot \frac{1}{y} + 0.5 \cdot \frac{1}{{y}^{2}}\right) - \frac{z}{y}\right)\right) \]

      6. associate-*r/ 79.6%

         \[\leadsto x + \left(\frac{1}{y} + \left(\left(z \cdot z\right) \cdot \left(\color{blue}{\frac{0.5 \cdot 1}{y}} + 0.5 \cdot \frac{1}{{y}^{2}}\right) - \frac{z}{y}\right)\right) \]

      7. metadata-eval 79.6%

         \[\leadsto x + \left(\frac{1}{y} + \left(\left(z \cdot z\right) \cdot \left(\frac{\color{blue}{0.5}}{y} + 0.5 \cdot \frac{1}{{y}^{2}}\right) - \frac{z}{y}\right)\right) \]

      8. associate-*r/ 79.6%

         \[\leadsto x + \left(\frac{1}{y} + \left(\left(z \cdot z\right) \cdot \left(\frac{0.5}{y} + \color{blue}{\frac{0.5 \cdot 1}{{y}^{2}}}\right) - \frac{z}{y}\right)\right) \]

      9. metadata-eval 79.6%

         \[\leadsto x + \left(\frac{1}{y} + \left(\left(z \cdot z\right) \cdot \left(\frac{0.5}{y} + \frac{\color{blue}{0.5}}{{y}^{2}}\right) - \frac{z}{y}\right)\right) \]

      10. unpow2 79.6%

          \[\leadsto x + \left(\frac{1}{y} + \left(\left(z \cdot z\right) \cdot \left(\frac{0.5}{y} + \frac{0.5}{\color{blue}{y \cdot y}}\right) - \frac{z}{y}\right)\right) \]

   6. Simplified 79.6%

      \[\leadsto x + \color{blue}{\left(\frac{1}{y} + \left(\left(z \cdot z\right) \cdot \left(\frac{0.5}{y} + \frac{0.5}{y \cdot y}\right) - \frac{z}{y}\right)\right)} \]

   7. Taylor expanded in y around inf 79.6%

      \[\leadsto x + \left(\frac{1}{y} + \color{blue}{\frac{0.5 \cdot {z}^{2} - z}{y}}\right) \]
   8. Step-by-step derivation

      1. unpow2 79.6%

         \[\leadsto x + \left(\frac{1}{y} + \frac{0.5 \cdot \color{blue}{\left(z \cdot z\right)} - z}{y}\right) \]

      2. *-commutative 79.6%

         \[\leadsto x + \left(\frac{1}{y} + \frac{\color{blue}{\left(z \cdot z\right) \cdot 0.5} - z}{y}\right) \]

      3. associate-*l* 79.6%

         \[\leadsto x + \left(\frac{1}{y} + \frac{\color{blue}{z \cdot \left(z \cdot 0.5\right)} - z}{y}\right) \]

   9. Simplified 79.6%

      \[\leadsto x + \left(\frac{1}{y} + \color{blue}{\frac{z \cdot \left(z \cdot 0.5\right) - z}{y}}\right) \]

   10. Taylor expanded in y around 0 79.6%

       \[\leadsto x + \color{blue}{\frac{\left(1 + 0.5 \cdot {z}^{2}\right) - z}{y}} \]
   11. Step-by-step derivation

       1. associate--l+ 79.6%

          \[\leadsto x + \frac{\color{blue}{1 + \left(0.5 \cdot {z}^{2} - z\right)}}{y} \]

       2. unpow2 79.6%

          \[\leadsto x + \frac{1 + \left(0.5 \cdot \color{blue}{\left(z \cdot z\right)} - z\right)}{y} \]

   12. Simplified 79.6%

       \[\leadsto x + \color{blue}{\frac{1 + \left(0.5 \cdot \left(z \cdot z\right) - z\right)}{y}} \]

   if -0.34499999999999997 < y

   1. Initial program 82.6%

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

      1. exp-prod 93.2%

         \[\leadsto x + \frac{\color{blue}{{\left(e^{y}\right)}^{\log \left(\frac{y}{z + y}\right)}}}{y} \]

      2. +-commutative 93.2%

         \[\leadsto x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{\color{blue}{y + z}}\right)}}{y} \]

   3. Simplified 93.2%

      \[\leadsto \color{blue}{x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}} \]

   4. Taylor expanded in y around inf 92.1%

      \[\leadsto \color{blue}{\frac{1}{y} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.345:\\ \;\;\;\;x + \frac{1 + \left(0.5 \cdot \left(z \cdot z\right) - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]

Alternative 5: 85.3% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+185}:\\ \;\;\;\;x + 0.5 \cdot \frac{z \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.8e+185) (+ x (* 0.5 (/ (* z z) y))) (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.8e+185) {
		tmp = x + (0.5 * ((z * z) / y));
	} else {
		tmp = x + (1.0 / 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) :: tmp
    if (z <= (-2.8d+185)) then
        tmp = x + (0.5d0 * ((z * z) / y))
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.8e+185) {
		tmp = x + (0.5 * ((z * z) / y));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.8e+185:
		tmp = x + (0.5 * ((z * z) / y))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.8e+185)
		tmp = Float64(x + Float64(0.5 * Float64(Float64(z * z) / y)));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.8e+185)
		tmp = x + (0.5 * ((z * z) / y));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.8e+185], N[(x + N[(0.5 * N[(N[(z * z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.79999999999999982e185

   1. Initial program 51.6%

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

      1. *-commutative 51.6%

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

      2. exp-to-pow 51.6%

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

      3. +-commutative 51.6%

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

   3. Simplified 51.6%

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

   4. Taylor expanded in z around 0 73.1%

      \[\leadsto x + \color{blue}{\left(\frac{1}{y} + \left(-1 \cdot \frac{z}{y} + \left(0.5 \cdot \frac{1}{y} + 0.5 \cdot \frac{1}{{y}^{2}}\right) \cdot {z}^{2}\right)\right)} \]
   5. Step-by-step derivation

      1. +-commutative 73.1%

         \[\leadsto x + \left(\frac{1}{y} + \color{blue}{\left(\left(0.5 \cdot \frac{1}{y} + 0.5 \cdot \frac{1}{{y}^{2}}\right) \cdot {z}^{2} + -1 \cdot \frac{z}{y}\right)}\right) \]

      2. mul-1-neg 73.1%

         \[\leadsto x + \left(\frac{1}{y} + \left(\left(0.5 \cdot \frac{1}{y} + 0.5 \cdot \frac{1}{{y}^{2}}\right) \cdot {z}^{2} + \color{blue}{\left(-\frac{z}{y}\right)}\right)\right) \]

      3. unsub-neg 73.1%

         \[\leadsto x + \left(\frac{1}{y} + \color{blue}{\left(\left(0.5 \cdot \frac{1}{y} + 0.5 \cdot \frac{1}{{y}^{2}}\right) \cdot {z}^{2} - \frac{z}{y}\right)}\right) \]

      4. *-commutative 73.1%

         \[\leadsto x + \left(\frac{1}{y} + \left(\color{blue}{{z}^{2} \cdot \left(0.5 \cdot \frac{1}{y} + 0.5 \cdot \frac{1}{{y}^{2}}\right)} - \frac{z}{y}\right)\right) \]

      5. unpow2 73.1%

         \[\leadsto x + \left(\frac{1}{y} + \left(\color{blue}{\left(z \cdot z\right)} \cdot \left(0.5 \cdot \frac{1}{y} + 0.5 \cdot \frac{1}{{y}^{2}}\right) - \frac{z}{y}\right)\right) \]

      6. associate-*r/ 73.1%

         \[\leadsto x + \left(\frac{1}{y} + \left(\left(z \cdot z\right) \cdot \left(\color{blue}{\frac{0.5 \cdot 1}{y}} + 0.5 \cdot \frac{1}{{y}^{2}}\right) - \frac{z}{y}\right)\right) \]

      7. metadata-eval 73.1%

         \[\leadsto x + \left(\frac{1}{y} + \left(\left(z \cdot z\right) \cdot \left(\frac{\color{blue}{0.5}}{y} + 0.5 \cdot \frac{1}{{y}^{2}}\right) - \frac{z}{y}\right)\right) \]

      8. associate-*r/ 73.1%

         \[\leadsto x + \left(\frac{1}{y} + \left(\left(z \cdot z\right) \cdot \left(\frac{0.5}{y} + \color{blue}{\frac{0.5 \cdot 1}{{y}^{2}}}\right) - \frac{z}{y}\right)\right) \]

      9. metadata-eval 73.1%

         \[\leadsto x + \left(\frac{1}{y} + \left(\left(z \cdot z\right) \cdot \left(\frac{0.5}{y} + \frac{\color{blue}{0.5}}{{y}^{2}}\right) - \frac{z}{y}\right)\right) \]

      10. unpow2 73.1%

          \[\leadsto x + \left(\frac{1}{y} + \left(\left(z \cdot z\right) \cdot \left(\frac{0.5}{y} + \frac{0.5}{\color{blue}{y \cdot y}}\right) - \frac{z}{y}\right)\right) \]

   6. Simplified 73.1%

      \[\leadsto x + \color{blue}{\left(\frac{1}{y} + \left(\left(z \cdot z\right) \cdot \left(\frac{0.5}{y} + \frac{0.5}{y \cdot y}\right) - \frac{z}{y}\right)\right)} \]

   7. Taylor expanded in y around inf 74.3%

      \[\leadsto x + \left(\frac{1}{y} + \color{blue}{\frac{0.5 \cdot {z}^{2} - z}{y}}\right) \]
   8. Step-by-step derivation

      1. unpow2 74.3%

         \[\leadsto x + \left(\frac{1}{y} + \frac{0.5 \cdot \color{blue}{\left(z \cdot z\right)} - z}{y}\right) \]

      2. *-commutative 74.3%

         \[\leadsto x + \left(\frac{1}{y} + \frac{\color{blue}{\left(z \cdot z\right) \cdot 0.5} - z}{y}\right) \]

      3. associate-*l* 74.3%

         \[\leadsto x + \left(\frac{1}{y} + \frac{\color{blue}{z \cdot \left(z \cdot 0.5\right)} - z}{y}\right) \]

   9. Simplified 74.3%

      \[\leadsto x + \left(\frac{1}{y} + \color{blue}{\frac{z \cdot \left(z \cdot 0.5\right) - z}{y}}\right) \]

   10. Taylor expanded in y around 0 74.3%

       \[\leadsto x + \color{blue}{\frac{\left(1 + 0.5 \cdot {z}^{2}\right) - z}{y}} \]
   11. Step-by-step derivation

       1. associate--l+ 74.3%

          \[\leadsto x + \frac{\color{blue}{1 + \left(0.5 \cdot {z}^{2} - z\right)}}{y} \]

       2. unpow2 74.3%

          \[\leadsto x + \frac{1 + \left(0.5 \cdot \color{blue}{\left(z \cdot z\right)} - z\right)}{y} \]

   12. Simplified 74.3%

       \[\leadsto x + \color{blue}{\frac{1 + \left(0.5 \cdot \left(z \cdot z\right) - z\right)}{y}} \]

   13. Taylor expanded in z around inf 74.3%

       \[\leadsto x + \color{blue}{0.5 \cdot \frac{{z}^{2}}{y}} \]
   14. Step-by-step derivation

       1. unpow2 74.3%

          \[\leadsto x + 0.5 \cdot \frac{\color{blue}{z \cdot z}}{y} \]

   15. Simplified 74.3%

       \[\leadsto x + \color{blue}{0.5 \cdot \frac{z \cdot z}{y}} \]

   if -2.79999999999999982e185 < z

   1. Initial program 85.9%

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

      1. exp-prod 92.1%

         \[\leadsto x + \frac{\color{blue}{{\left(e^{y}\right)}^{\log \left(\frac{y}{z + y}\right)}}}{y} \]

      2. +-commutative 92.1%

         \[\leadsto x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{\color{blue}{y + z}}\right)}}{y} \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}} \]

   4. Taylor expanded in y around inf 89.2%

      \[\leadsto \color{blue}{\frac{1}{y} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+185}:\\ \;\;\;\;x + 0.5 \cdot \frac{z \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]

Alternative 6: 67.6% accurate, 29.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{-79}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-27}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.28e-79) x (if (<= y 1.4e-27) (/ 1.0 y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.28e-79) {
		tmp = x;
	} else if (y <= 1.4e-27) {
		tmp = 1.0 / y;
	} else {
		tmp = 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 <= (-1.28d-79)) then
        tmp = x
    else if (y <= 1.4d-27) then
        tmp = 1.0d0 / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.28e-79) {
		tmp = x;
	} else if (y <= 1.4e-27) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.28e-79:
		tmp = x
	elif y <= 1.4e-27:
		tmp = 1.0 / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.28e-79)
		tmp = x;
	elseif (y <= 1.4e-27)
		tmp = Float64(1.0 / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.28e-79)
		tmp = x;
	elseif (y <= 1.4e-27)
		tmp = 1.0 / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.28e-79], x, If[LessEqual[y, 1.4e-27], N[(1.0 / y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.28e-79 or 1.4e-27 < y

   1. Initial program 85.3%

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

      1. exp-prod 85.3%

         \[\leadsto x + \frac{\color{blue}{{\left(e^{y}\right)}^{\log \left(\frac{y}{z + y}\right)}}}{y} \]

      2. +-commutative 85.3%

         \[\leadsto x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{\color{blue}{y + z}}\right)}}{y} \]

   3. Simplified 85.3%

      \[\leadsto \color{blue}{x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}} \]

   4. Taylor expanded in x around inf 63.3%

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

   if -1.28e-79 < y < 1.4e-27

   1. Initial program 76.1%

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

      1. exp-prod 100.0%

         \[\leadsto x + \frac{\color{blue}{{\left(e^{y}\right)}^{\log \left(\frac{y}{z + y}\right)}}}{y} \]

      2. +-commutative 100.0%

         \[\leadsto x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{\color{blue}{y + z}}\right)}}{y} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}} \]

   4. Taylor expanded in y around 0 82.2%

      \[\leadsto \color{blue}{\frac{1}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{-79}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-27}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 84.4% accurate, 42.2× speedup

Math

\[\begin{array}{l} \\ x + \frac{1}{y} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (1.0d0 / y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.4%

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

   1. exp-prod 89.9%

      \[\leadsto x + \frac{\color{blue}{{\left(e^{y}\right)}^{\log \left(\frac{y}{z + y}\right)}}}{y} \]

   2. +-commutative 89.9%

      \[\leadsto x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{\color{blue}{y + z}}\right)}}{y} \]

3. Simplified 89.9%

   \[\leadsto \color{blue}{x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}} \]

4. Taylor expanded in y around inf 83.1%

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

5. Final simplification 83.1%

   \[\leadsto x + \frac{1}{y} \]

Alternative 8: 49.2% accurate, 211.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return x;
}

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
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 82.4%

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

   1. exp-prod 89.9%

      \[\leadsto x + \frac{\color{blue}{{\left(e^{y}\right)}^{\log \left(\frac{y}{z + y}\right)}}}{y} \]

   2. +-commutative 89.9%

      \[\leadsto x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{\color{blue}{y + z}}\right)}}{y} \]

3. Simplified 89.9%

   \[\leadsto \color{blue}{x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}} \]

4. Taylor expanded in x around inf 49.7%

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

5. Final simplification 49.7%

   \[\leadsto x \]

Developer target: 91.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y}{z + y} < 7.11541576 \cdot 10^{-315}:\\ \;\;\;\;x + \frac{e^{\frac{-1}{z}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{e^{\log \left({\left(\frac{y}{y + z}\right)}^{y}\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< (/ y (+ z y)) 7.11541576e-315)
   (+ x (/ (exp (/ -1.0 z)) y))
   (+ x (/ (exp (log (pow (/ y (+ y z)) y))) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y / (z + y)) < 7.11541576e-315) {
		tmp = x + (exp((-1.0 / z)) / y);
	} else {
		tmp = x + (exp(log(pow((y / (y + z)), y))) / 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) :: tmp
    if ((y / (z + y)) < 7.11541576d-315) then
        tmp = x + (exp(((-1.0d0) / z)) / y)
    else
        tmp = x + (exp(log(((y / (y + z)) ** y))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y / (z + y)) < 7.11541576e-315) {
		tmp = x + (Math.exp((-1.0 / z)) / y);
	} else {
		tmp = x + (Math.exp(Math.log(Math.pow((y / (y + z)), y))) / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y / (z + y)) < 7.11541576e-315:
		tmp = x + (math.exp((-1.0 / z)) / y)
	else:
		tmp = x + (math.exp(math.log(math.pow((y / (y + z)), y))) / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y / Float64(z + y)) < 7.11541576e-315)
		tmp = Float64(x + Float64(exp(Float64(-1.0 / z)) / y));
	else
		tmp = Float64(x + Float64(exp(log((Float64(y / Float64(y + z)) ^ y))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y / (z + y)) < 7.11541576e-315)
		tmp = x + (exp((-1.0 / z)) / y);
	else
		tmp = x + (exp(log(((y / (y + z)) ^ y))) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[N[(y / N[(z + y), $MachinePrecision]), $MachinePrecision], 7.11541576e-315], N[(x + N[(N[Exp[N[(-1.0 / z), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Exp[N[Log[N[Power[N[(y / N[(y + z), $MachinePrecision]), $MachinePrecision], y], $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, G"
  :precision binary64

  :herbie-target
  (if (< (/ y (+ z y)) 7.11541576e-315) (+ x (/ (exp (/ -1.0 z)) y)) (+ x (/ (exp (log (pow (/ y (+ y z)) y))) y)))

  (+ x (/ (exp (* y (log (/ y (+ z y))))) y)))