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

Percentage Accurate: 85.4% → 99.8%

Time: 13.7s

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: 85.4% 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: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -20000000 \lor \neg \left(y \leq 2 \cdot 10^{-14}\right):\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -20000000.0) (not (<= y 2e-14)))
   (+ 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 <= -20000000.0) || !(y <= 2e-14)) {
		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 <= (-20000000.0d0)) .or. (.not. (y <= 2d-14))) 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 <= -20000000.0) || !(y <= 2e-14)) {
		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 <= -20000000.0) or not (y <= 2e-14):
		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 <= -20000000.0) || !(y <= 2e-14))
		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 <= -20000000.0) || ~((y <= 2e-14)))
		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, -20000000.0], N[Not[LessEqual[y, 2e-14]], $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 < -2e7 or 2e-14 < y

   1. Initial program 87.7%

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

      1. *-commutative 87.7%

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

      2. exp-to-pow 87.7%

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

      3. +-commutative 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   if -2e7 < y < 2e-14

   1. Initial program 81.4%

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

      1. exp-prod 99.8%

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

      2. +-commutative 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -20000000 \lor \neg \left(y \leq 2 \cdot 10^{-14}\right):\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{{\left(e^{y}\right)}^{\log \left(\frac{y}{y + z}\right)}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -900000 \lor \neg \left(y \leq 5 \cdot 10^{-11}\right):\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + {y}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -900000.0) (not (<= y 5e-11)))
   (+ x (/ (exp (- z)) y))
   (+ x (pow y -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -900000.0) || !(y <= 5e-11)) {
		tmp = x + (exp(-z) / y);
	} else {
		tmp = x + pow(y, -1.0);
	}
	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) :: tmp
    if ((y <= (-900000.0d0)) .or. (.not. (y <= 5d-11))) then
        tmp = x + (exp(-z) / y)
    else
        tmp = x + (y ** (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -900000.0) || !(y <= 5e-11)) {
		tmp = x + (Math.exp(-z) / y);
	} else {
		tmp = x + Math.pow(y, -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -900000.0) or not (y <= 5e-11):
		tmp = x + (math.exp(-z) / y)
	else:
		tmp = x + math.pow(y, -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -900000.0) || !(y <= 5e-11))
		tmp = Float64(x + Float64(exp(Float64(-z)) / y));
	else
		tmp = Float64(x + (y ^ -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -900000.0) || ~((y <= 5e-11)))
		tmp = x + (exp(-z) / y);
	else
		tmp = x + (y ^ -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -900000.0], N[Not[LessEqual[y, 5e-11]], $MachinePrecision]], N[(x + N[(N[Exp[(-z)], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[Power[y, -1.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9e5 or 5.00000000000000018e-11 < y

   1. Initial program 87.7%

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

      1. *-commutative 87.7%

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

      2. exp-to-pow 87.7%

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

      3. +-commutative 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   if -9e5 < y < 5.00000000000000018e-11

   1. Initial program 81.4%

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

      1. exp-prod 99.8%

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

      2. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. +-commutative 99.8%

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

   7. Simplified 99.8%

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

      1. add-cube-cbrt 97.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{1}{y} + x} \cdot \sqrt[3]{\frac{1}{y} + x}\right) \cdot \sqrt[3]{\frac{1}{y} + x}} \]

      2. pow2 97.8%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{1}{y} + x}\right)}^{2}} \cdot \sqrt[3]{\frac{1}{y} + x} \]

   9. Applied egg-rr 97.8%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{1}{y} + x}\right)}^{2} \cdot \sqrt[3]{\frac{1}{y} + x}} \]
   10. Step-by-step derivation

       1. unpow2 97.8%

          \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{1}{y} + x} \cdot \sqrt[3]{\frac{1}{y} + x}\right)} \cdot \sqrt[3]{\frac{1}{y} + x} \]

       2. add-cube-cbrt 99.8%

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

       3. add-sqr-sqrt 57.0%

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

       4. fma-define 57.0%

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

       5. inv-pow 57.0%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{{y}^{-1}}}, \sqrt{\frac{1}{y}}, x\right) \]

       6. sqrt-pow1 57.0%

          \[\leadsto \mathsf{fma}\left(\color{blue}{{y}^{\left(\frac{-1}{2}\right)}}, \sqrt{\frac{1}{y}}, x\right) \]

       7. metadata-eval 57.0%

          \[\leadsto \mathsf{fma}\left({y}^{\color{blue}{-0.5}}, \sqrt{\frac{1}{y}}, x\right) \]

       8. inv-pow 57.0%

          \[\leadsto \mathsf{fma}\left({y}^{-0.5}, \sqrt{\color{blue}{{y}^{-1}}}, x\right) \]

       9. sqrt-pow1 57.0%

          \[\leadsto \mathsf{fma}\left({y}^{-0.5}, \color{blue}{{y}^{\left(\frac{-1}{2}\right)}}, x\right) \]

       10. metadata-eval 57.0%

           \[\leadsto \mathsf{fma}\left({y}^{-0.5}, {y}^{\color{blue}{-0.5}}, x\right) \]

   11. Applied egg-rr 57.0%

       \[\leadsto \color{blue}{\mathsf{fma}\left({y}^{-0.5}, {y}^{-0.5}, x\right)} \]
   12. Step-by-step derivation

       1. fma-undefine 57.0%

          \[\leadsto \color{blue}{{y}^{-0.5} \cdot {y}^{-0.5} + x} \]

       2. pow-sqr 99.8%

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

       3. metadata-eval 99.8%

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

   13. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -900000 \lor \neg \left(y \leq 5 \cdot 10^{-11}\right):\\ \;\;\;\;x + \frac{e^{-z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + {y}^{-1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -900000:\\ \;\;\;\;x + \frac{1 + z \cdot \left(-1 + \frac{0.5 \cdot \left(z + y \cdot z\right)}{y}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + {y}^{-1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -900000.0)
   (+ x (/ (+ 1.0 (* z (+ -1.0 (/ (* 0.5 (+ z (* y z))) y)))) y))
   (+ x (pow y -1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -900000.0) {
		tmp = x + ((1.0 + (z * (-1.0 + ((0.5 * (z + (y * z))) / y)))) / y);
	} else {
		tmp = x + pow(y, -1.0);
	}
	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) :: tmp
    if (y <= (-900000.0d0)) then
        tmp = x + ((1.0d0 + (z * ((-1.0d0) + ((0.5d0 * (z + (y * z))) / y)))) / y)
    else
        tmp = x + (y ** (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -900000.0) {
		tmp = x + ((1.0 + (z * (-1.0 + ((0.5 * (z + (y * z))) / y)))) / y);
	} else {
		tmp = x + Math.pow(y, -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -900000.0:
		tmp = x + ((1.0 + (z * (-1.0 + ((0.5 * (z + (y * z))) / y)))) / y)
	else:
		tmp = x + math.pow(y, -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -900000.0)
		tmp = Float64(x + Float64(Float64(1.0 + Float64(z * Float64(-1.0 + Float64(Float64(0.5 * Float64(z + Float64(y * z))) / y)))) / y));
	else
		tmp = Float64(x + (y ^ -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -900000.0)
		tmp = x + ((1.0 + (z * (-1.0 + ((0.5 * (z + (y * z))) / y)))) / y);
	else
		tmp = x + (y ^ -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -900000.0], N[(x + N[(N[(1.0 + N[(z * N[(-1.0 + N[(N[(0.5 * N[(z + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[Power[y, -1.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9e5

   1. Initial program 83.1%

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

      1. exp-prod 83.1%

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

      2. +-commutative 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in z around 0 76.0%

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

   6. Taylor expanded in y around 0 79.1%

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

      1. distribute-lft-out 79.1%

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

   8. Simplified 79.1%

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

   if -9e5 < 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 96.9%

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

      2. +-commutative 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in y around inf 95.8%

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

      1. +-commutative 95.8%

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

   7. Simplified 95.8%

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

      1. add-cube-cbrt 93.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{1}{y} + x} \cdot \sqrt[3]{\frac{1}{y} + x}\right) \cdot \sqrt[3]{\frac{1}{y} + x}} \]

      2. pow2 93.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{1}{y} + x}\right)}^{2}} \cdot \sqrt[3]{\frac{1}{y} + x} \]

   9. Applied egg-rr 93.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{1}{y} + x}\right)}^{2} \cdot \sqrt[3]{\frac{1}{y} + x}} \]
   10. Step-by-step derivation

       1. unpow2 93.9%

          \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{1}{y} + x} \cdot \sqrt[3]{\frac{1}{y} + x}\right)} \cdot \sqrt[3]{\frac{1}{y} + x} \]

       2. add-cube-cbrt 95.8%

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

       3. add-sqr-sqrt 68.9%

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

       4. fma-define 68.9%

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

       5. inv-pow 68.9%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{{y}^{-1}}}, \sqrt{\frac{1}{y}}, x\right) \]

       6. sqrt-pow1 68.9%

          \[\leadsto \mathsf{fma}\left(\color{blue}{{y}^{\left(\frac{-1}{2}\right)}}, \sqrt{\frac{1}{y}}, x\right) \]

       7. metadata-eval 68.9%

          \[\leadsto \mathsf{fma}\left({y}^{\color{blue}{-0.5}}, \sqrt{\frac{1}{y}}, x\right) \]

       8. inv-pow 68.9%

          \[\leadsto \mathsf{fma}\left({y}^{-0.5}, \sqrt{\color{blue}{{y}^{-1}}}, x\right) \]

       9. sqrt-pow1 68.9%

          \[\leadsto \mathsf{fma}\left({y}^{-0.5}, \color{blue}{{y}^{\left(\frac{-1}{2}\right)}}, x\right) \]

       10. metadata-eval 68.9%

           \[\leadsto \mathsf{fma}\left({y}^{-0.5}, {y}^{\color{blue}{-0.5}}, x\right) \]

   11. Applied egg-rr 68.9%

       \[\leadsto \color{blue}{\mathsf{fma}\left({y}^{-0.5}, {y}^{-0.5}, x\right)} \]
   12. Step-by-step derivation

       1. fma-undefine 68.9%

          \[\leadsto \color{blue}{{y}^{-0.5} \cdot {y}^{-0.5} + x} \]

       2. pow-sqr 95.8%

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

       3. metadata-eval 95.8%

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

   13. Simplified 95.8%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -900000:\\ \;\;\;\;x + \frac{1 + z \cdot \left(-1 + \frac{0.5 \cdot \left(z + y \cdot z\right)}{y}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + {y}^{-1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.1% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -900000:\\ \;\;\;\;x + \frac{1 + z \cdot \left(-1 + \frac{0.5 \cdot \left(z + y \cdot z\right)}{y}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -900000.0)
   (+ x (/ (+ 1.0 (* z (+ -1.0 (/ (* 0.5 (+ z (* y z))) y)))) y))
   (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -900000.0) {
		tmp = x + ((1.0 + (z * (-1.0 + ((0.5 * (z + (y * z))) / y)))) / 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 <= (-900000.0d0)) then
        tmp = x + ((1.0d0 + (z * ((-1.0d0) + ((0.5d0 * (z + (y * z))) / y)))) / 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 <= -900000.0) {
		tmp = x + ((1.0 + (z * (-1.0 + ((0.5 * (z + (y * z))) / y)))) / y);
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -900000.0:
		tmp = x + ((1.0 + (z * (-1.0 + ((0.5 * (z + (y * z))) / y)))) / y)
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -900000.0)
		tmp = Float64(x + Float64(Float64(1.0 + Float64(z * Float64(-1.0 + Float64(Float64(0.5 * Float64(z + Float64(y * z))) / y)))) / 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 <= -900000.0)
		tmp = x + ((1.0 + (z * (-1.0 + ((0.5 * (z + (y * z))) / y)))) / y);
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -900000.0], N[(x + N[(N[(1.0 + N[(z * N[(-1.0 + N[(N[(0.5 * N[(z + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9e5

   1. Initial program 83.1%

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

      1. exp-prod 83.1%

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

      2. +-commutative 83.1%

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

   3. Simplified 83.1%

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

   5. Taylor expanded in z around 0 76.0%

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

   6. Taylor expanded in y around 0 79.1%

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

      1. distribute-lft-out 79.1%

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

   8. Simplified 79.1%

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

   if -9e5 < 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 96.9%

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

      2. +-commutative 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in y around inf 95.8%

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

      1. +-commutative 95.8%

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

   7. Simplified 95.8%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -900000:\\ \;\;\;\;x + \frac{1 + z \cdot \left(-1 + \frac{0.5 \cdot \left(z + y \cdot z\right)}{y}\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.6% accurate, 16.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0138:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-111}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -0.0138) x (if (<= x 1.8e-111) (/ 1.0 y) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -0.0138) {
		tmp = x;
	} else if (x <= 1.8e-111) {
		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 (x <= (-0.0138d0)) then
        tmp = x
    else if (x <= 1.8d-111) 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 (x <= -0.0138) {
		tmp = x;
	} else if (x <= 1.8e-111) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -0.0138:
		tmp = x
	elif x <= 1.8e-111:
		tmp = 1.0 / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -0.0138)
		tmp = x;
	elseif (x <= 1.8e-111)
		tmp = Float64(1.0 / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -0.0138)
		tmp = x;
	elseif (x <= 1.8e-111)
		tmp = 1.0 / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -0.0138], x, If[LessEqual[x, 1.8e-111], N[(1.0 / y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0138 or 1.80000000000000005e-111 < x

   1. Initial program 85.2%

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

      1. exp-prod 93.5%

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

      2. +-commutative 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in x around inf 66.3%

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

   if -0.0138 < x < 1.80000000000000005e-111

   1. Initial program 84.1%

      \[x + \frac{e^{y \cdot \log \left(\frac{y}{z + y}\right)}}{y} \]
   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. Add Preprocessing

   5. Taylor expanded in y around 0 73.1%

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

Alternative 6: 86.8% accurate, 17.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+36}:\\ \;\;\;\;\frac{1 + y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.15e+36) (/ (+ 1.0 (* y x)) y) (+ x (/ 1.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.15e+36) {
		tmp = (1.0 + (y * x)) / 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 <= (-1.15d+36)) then
        tmp = (1.0d0 + (y * x)) / 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 <= -1.15e+36) {
		tmp = (1.0 + (y * x)) / y;
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.15e+36:
		tmp = (1.0 + (y * x)) / y
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.15e+36)
		tmp = Float64(Float64(1.0 + Float64(y * x)) / 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 <= -1.15e+36)
		tmp = (1.0 + (y * x)) / y;
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.15e+36], N[(N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14999999999999998e36

   1. Initial program 50.2%

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

      1. exp-prod 68.2%

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

      2. +-commutative 68.2%

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

   3. Simplified 68.2%

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

   5. Taylor expanded in y around inf 44.9%

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

      1. +-commutative 44.9%

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

   7. Simplified 44.9%

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

   8. Taylor expanded in y around 0 59.9%

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

      1. *-commutative 59.9%

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

   10. Simplified 59.9%

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

   if -1.14999999999999998e36 < z

   1. Initial program 90.6%

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

      1. exp-prod 97.6%

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

      2. +-commutative 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in y around inf 96.3%

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

      1. +-commutative 96.3%

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

   7. Simplified 96.3%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+36}:\\ \;\;\;\;\frac{1 + y \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.5% 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 84.7%

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

   1. exp-prod 93.4%

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

   2. +-commutative 93.4%

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

3. Simplified 93.4%

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

5. Taylor expanded in y around inf 88.8%

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

   1. +-commutative 88.8%

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

7. Simplified 88.8%

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

8. Final simplification 88.8%

   \[\leadsto x + \frac{1}{y} \]
9. Add Preprocessing

Alternative 8: 49.9% 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 84.7%

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

   1. exp-prod 93.4%

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

   2. +-commutative 93.4%

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

3. Simplified 93.4%

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

5. Taylor expanded in x around inf 47.8%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer target: 91.6% 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 2024087 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, G"
  :precision binary64

  :alt
  (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)))