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

Percentage Accurate: 77.7% → 99.6%

Time: 12.3s

Alternatives: 7

Speedup: 20.9×

• Could not converge on a ground truth

  1. reg0 = (bf "4.265731139129554358996650757354153368771e272")
  2. reg1 = (bf #e2.17017447770188148996765157603697009232e-24)

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = exp((x * log((x / (x + y))))) / x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = exp((x * log((x / (x + y))))) / x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+34} \lor \neg \left(x \leq 1.22 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2e+34) (not (<= x 1.22e-11)))
   (/ (exp (- y)) x)
   (/ (pow (exp x) (log (/ x (+ x y)))) x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2e+34) || !(x <= 1.22e-11)) {
		tmp = exp(-y) / x;
	} else {
		tmp = pow(exp(x), log((x / (x + y)))) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-2d+34)) .or. (.not. (x <= 1.22d-11))) then
        tmp = exp(-y) / x
    else
        tmp = (exp(x) ** log((x / (x + y)))) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2e+34) || !(x <= 1.22e-11)) {
		tmp = Math.exp(-y) / x;
	} else {
		tmp = Math.pow(Math.exp(x), Math.log((x / (x + y)))) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2e+34) or not (x <= 1.22e-11):
		tmp = math.exp(-y) / x
	else:
		tmp = math.pow(math.exp(x), math.log((x / (x + y)))) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2e+34) || !(x <= 1.22e-11))
		tmp = Float64(exp(Float64(-y)) / x);
	else
		tmp = Float64((exp(x) ^ log(Float64(x / Float64(x + y)))) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2e+34) || ~((x <= 1.22e-11)))
		tmp = exp(-y) / x;
	else
		tmp = (exp(x) ^ log((x / (x + y)))) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2e+34], N[Not[LessEqual[x, 1.22e-11]], $MachinePrecision]], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision], N[(N[Power[N[Exp[x], $MachinePrecision], N[Log[N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.99999999999999989e34 or 1.2200000000000001e-11 < x

   1. Initial program 73.3%

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

      1. *-commutative 73.3%

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

      2. exp-to-pow 73.3%

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

   3. Simplified 73.3%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   if -1.99999999999999989e34 < x < 1.2200000000000001e-11

   1. Initial program 86.4%

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

      1. exp-prod 99.7%

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

   3. Simplified 99.7%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+34} \lor \neg \left(x \leq 1.22 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+14} \lor \neg \left(x \leq 1.22 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.2e+14) (not (<= x 1.22e-11))) (/ (exp (- y)) x) (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.2e+14) || !(x <= 1.22e-11)) {
		tmp = exp(-y) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.2d+14)) .or. (.not. (x <= 1.22d-11))) then
        tmp = exp(-y) / x
    else
        tmp = 1.0d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.2e+14) || !(x <= 1.22e-11)) {
		tmp = Math.exp(-y) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.2e+14) or not (x <= 1.22e-11):
		tmp = math.exp(-y) / x
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.2e+14) || !(x <= 1.22e-11))
		tmp = Float64(exp(Float64(-y)) / x);
	else
		tmp = Float64(1.0 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.2e+14) || ~((x <= 1.22e-11)))
		tmp = exp(-y) / x;
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.2e+14], N[Not[LessEqual[x, 1.22e-11]], $MachinePrecision]], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2e14 or 1.2200000000000001e-11 < x

   1. Initial program 73.8%

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

      1. *-commutative 73.8%

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

      2. exp-to-pow 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   if -1.2e14 < x < 1.2200000000000001e-11

   1. Initial program 86.0%

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

      1. exp-prod 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 99.4%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+14} \lor \neg \left(x \leq 1.22 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.8% accurate, 10.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{1 - y \cdot \left(1 - y \cdot \left(0.5 + y \cdot -0.16666666666666666\right)\right)}{x}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+105}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - y\right)}{x}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.2e+14)
   (/ (- 1.0 (* y (- 1.0 (* y (+ 0.5 (* y -0.16666666666666666)))))) x)
   (if (<= x 1.8e+105) (/ 1.0 x) (/ (/ (* x (- 1.0 y)) x) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.2e+14) {
		tmp = (1.0 - (y * (1.0 - (y * (0.5 + (y * -0.16666666666666666)))))) / x;
	} else if (x <= 1.8e+105) {
		tmp = 1.0 / x;
	} else {
		tmp = ((x * (1.0 - y)) / x) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.2d+14)) then
        tmp = (1.0d0 - (y * (1.0d0 - (y * (0.5d0 + (y * (-0.16666666666666666d0))))))) / x
    else if (x <= 1.8d+105) then
        tmp = 1.0d0 / x
    else
        tmp = ((x * (1.0d0 - y)) / x) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.2e+14) {
		tmp = (1.0 - (y * (1.0 - (y * (0.5 + (y * -0.16666666666666666)))))) / x;
	} else if (x <= 1.8e+105) {
		tmp = 1.0 / x;
	} else {
		tmp = ((x * (1.0 - y)) / x) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.2e+14:
		tmp = (1.0 - (y * (1.0 - (y * (0.5 + (y * -0.16666666666666666)))))) / x
	elif x <= 1.8e+105:
		tmp = 1.0 / x
	else:
		tmp = ((x * (1.0 - y)) / x) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.2e+14)
		tmp = Float64(Float64(1.0 - Float64(y * Float64(1.0 - Float64(y * Float64(0.5 + Float64(y * -0.16666666666666666)))))) / x);
	elseif (x <= 1.8e+105)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(Float64(Float64(x * Float64(1.0 - y)) / x) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.2e+14)
		tmp = (1.0 - (y * (1.0 - (y * (0.5 + (y * -0.16666666666666666)))))) / x;
	elseif (x <= 1.8e+105)
		tmp = 1.0 / x;
	else
		tmp = ((x * (1.0 - y)) / x) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.2e+14], N[(N[(1.0 - N[(y * N[(1.0 - N[(y * N[(0.5 + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 1.8e+105], N[(1.0 / x), $MachinePrecision], N[(N[(N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.2e14

   1. Initial program 78.6%

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

      1. *-commutative 78.6%

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

      2. exp-to-pow 78.6%

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

   3. Simplified 78.6%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 86.5%

      \[\leadsto \frac{\color{blue}{1 + y \cdot \left(y \cdot \left(0.5 + -0.16666666666666666 \cdot y\right) - 1\right)}}{x} \]

   if -1.2e14 < x < 1.7999999999999999e105

   1. Initial program 87.8%

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

      1. exp-prod 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in x around 0 92.6%

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

   if 1.7999999999999999e105 < x

   1. Initial program 59.2%

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

      1. exp-prod 59.2%

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

   3. Simplified 59.2%

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

   5. Taylor expanded in y around 0 52.8%

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

      1. +-commutative 52.8%

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

      2. mul-1-neg 52.8%

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

      3. unsub-neg 52.8%

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

   7. Simplified 52.8%

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

      1. frac-sub 28.0%

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

      2. associate-/r* 70.8%

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

      3. *-un-lft-identity 70.8%

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

      4. *-commutative 70.8%

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

   9. Applied egg-rr 70.8%

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

   10. Taylor expanded in x around 0 70.8%

       \[\leadsto \frac{\frac{\color{blue}{x \cdot \left(1 - y\right)}}{x}}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{1 - y \cdot \left(1 - y \cdot \left(0.5 + y \cdot -0.16666666666666666\right)\right)}{x}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+105}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - y\right)}{x}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.8% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+14} \lor \neg \left(x \leq 9.5 \cdot 10^{+105}\right):\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - y\right)}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.2e+14) (not (<= x 9.5e+105)))
   (/ (/ (* x (- 1.0 y)) x) x)
   (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.2e+14) || !(x <= 9.5e+105)) {
		tmp = ((x * (1.0 - y)) / x) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.2d+14)) .or. (.not. (x <= 9.5d+105))) then
        tmp = ((x * (1.0d0 - y)) / x) / x
    else
        tmp = 1.0d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.2e+14) || !(x <= 9.5e+105)) {
		tmp = ((x * (1.0 - y)) / x) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.2e+14) or not (x <= 9.5e+105):
		tmp = ((x * (1.0 - y)) / x) / x
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.2e+14) || !(x <= 9.5e+105))
		tmp = Float64(Float64(Float64(x * Float64(1.0 - y)) / x) / x);
	else
		tmp = Float64(1.0 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.2e+14) || ~((x <= 9.5e+105)))
		tmp = ((x * (1.0 - y)) / x) / x;
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.2e+14], N[Not[LessEqual[x, 9.5e+105]], $MachinePrecision]], N[(N[(N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2e14 or 9.4999999999999995e105 < x

   1. Initial program 70.0%

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

      1. exp-prod 70.0%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in y around 0 63.6%

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

      1. +-commutative 63.6%

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

      2. mul-1-neg 63.6%

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

      3. unsub-neg 63.6%

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

   7. Simplified 63.6%

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

      1. frac-sub 33.8%

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

      2. associate-/r* 78.3%

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

      3. *-un-lft-identity 78.3%

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

      4. *-commutative 78.3%

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

   9. Applied egg-rr 78.3%

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

   10. Taylor expanded in x around 0 78.3%

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

   if -1.2e14 < x < 9.4999999999999995e105

   1. Initial program 87.8%

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

      1. exp-prod 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in x around 0 92.6%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+14} \lor \neg \left(x \leq 9.5 \cdot 10^{+105}\right):\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - y\right)}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.3% accurate, 13.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+119}:\\ \;\;\;\;\frac{\frac{x \cdot \left(-y\right)}{x}}{x}\\ \mathbf{elif}\;y \leq 0.000102:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x \cdot x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.3e+119)
   (/ (/ (* x (- y)) x) x)
   (if (<= y 0.000102) (/ 1.0 x) (/ x (* x x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.3e+119) {
		tmp = ((x * -y) / x) / x;
	} else if (y <= 0.000102) {
		tmp = 1.0 / x;
	} else {
		tmp = x / (x * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-2.3d+119)) then
        tmp = ((x * -y) / x) / x
    else if (y <= 0.000102d0) then
        tmp = 1.0d0 / x
    else
        tmp = x / (x * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.3e+119) {
		tmp = ((x * -y) / x) / x;
	} else if (y <= 0.000102) {
		tmp = 1.0 / x;
	} else {
		tmp = x / (x * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.3e+119:
		tmp = ((x * -y) / x) / x
	elif y <= 0.000102:
		tmp = 1.0 / x
	else:
		tmp = x / (x * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.3e+119)
		tmp = Float64(Float64(Float64(x * Float64(-y)) / x) / x);
	elseif (y <= 0.000102)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(x / Float64(x * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.3e+119)
		tmp = ((x * -y) / x) / x;
	elseif (y <= 0.000102)
		tmp = 1.0 / x;
	else
		tmp = x / (x * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.3e+119], N[(N[(N[(x * (-y)), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[y, 0.000102], N[(1.0 / x), $MachinePrecision], N[(x / N[(x * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3000000000000001e119

   1. Initial program 36.4%

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

      1. exp-prod 59.8%

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

   3. Simplified 59.8%

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

   5. Taylor expanded in y around 0 4.0%

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

      1. +-commutative 4.0%

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

      2. mul-1-neg 4.0%

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

      3. unsub-neg 4.0%

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

   7. Simplified 4.0%

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

      1. frac-sub 11.6%

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

      2. associate-/r* 58.5%

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

      3. *-un-lft-identity 58.5%

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

      4. *-commutative 58.5%

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

   9. Applied egg-rr 58.5%

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

   10. Taylor expanded in y around inf 58.5%

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

       1. neg-mul-1 58.5%

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

       2. *-commutative 58.5%

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

       3. distribute-rgt-neg-in 58.5%

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

   12. Simplified 58.5%

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

   if -2.3000000000000001e119 < y < 1.01999999999999999e-4

   1. Initial program 91.3%

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

      1. exp-prod 91.8%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in x around 0 91.3%

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

   if 1.01999999999999999e-4 < y

   1. Initial program 58.0%

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

      1. exp-prod 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in y around 0 3.9%

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

      1. +-commutative 3.9%

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

      2. mul-1-neg 3.9%

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

      3. unsub-neg 3.9%

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

   7. Simplified 3.9%

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

      1. frac-2neg 3.9%

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

      2. frac-sub 18.0%

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

      3. *-un-lft-identity 18.0%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 19.7%

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

      6. sqr-neg 19.7%

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

      7. sqrt-unprod 19.7%

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

      8. add-sqr-sqrt 19.7%

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

      9. *-commutative 19.7%

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

   9. Applied egg-rr 19.7%

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

   10. Taylor expanded in y around 0 67.3%

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

       1. mul-1-neg 67.3%

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

   12. Simplified 67.3%

       \[\leadsto \frac{\color{blue}{-x}}{x \cdot \left(-x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{+119}:\\ \;\;\;\;\frac{\frac{x \cdot \left(-y\right)}{x}}{x}\\ \mathbf{elif}\;y \leq 0.000102:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x \cdot x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.4% accurate, 20.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.000102:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x \cdot x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 0.000102) (/ 1.0 x) (/ x (* x x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 0.000102) {
		tmp = 1.0 / x;
	} else {
		tmp = x / (x * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 0.000102d0) then
        tmp = 1.0d0 / x
    else
        tmp = x / (x * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 0.000102) {
		tmp = 1.0 / x;
	} else {
		tmp = x / (x * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 0.000102:
		tmp = 1.0 / x
	else:
		tmp = x / (x * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 0.000102)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(x / Float64(x * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 0.000102)
		tmp = 1.0 / x;
	else
		tmp = x / (x * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 0.000102], N[(1.0 / x), $MachinePrecision], N[(x / N[(x * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.01999999999999999e-4

   1. Initial program 83.0%

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

      1. exp-prod 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in x around 0 83.8%

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

   if 1.01999999999999999e-4 < y

   1. Initial program 58.0%

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

      1. exp-prod 71.0%

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

   3. Simplified 71.0%

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

   5. Taylor expanded in y around 0 3.9%

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

      1. +-commutative 3.9%

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

      2. mul-1-neg 3.9%

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

      3. unsub-neg 3.9%

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

   7. Simplified 3.9%

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

      1. frac-2neg 3.9%

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

      2. frac-sub 18.0%

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

      3. *-un-lft-identity 18.0%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 19.7%

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

      6. sqr-neg 19.7%

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

      7. sqrt-unprod 19.7%

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

      8. add-sqr-sqrt 19.7%

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

      9. *-commutative 19.7%

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

   9. Applied egg-rr 19.7%

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

   10. Taylor expanded in y around 0 67.3%

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

       1. mul-1-neg 67.3%

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

   12. Simplified 67.3%

       \[\leadsto \frac{\color{blue}{-x}}{x \cdot \left(-x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 0.000102:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x \cdot x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.2% accurate, 69.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.7%

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

   1. exp-prod 84.2%

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

3. Simplified 84.2%

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

5. Taylor expanded in x around 0 77.3%

   \[\leadsto \color{blue}{\frac{1}{x}} \]
6. Add Preprocessing

Developer Target 1: 78.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{e^{\frac{-1}{y}}}{x}\\ t_1 := \frac{{\left(\frac{x}{y + x}\right)}^{x}}{x}\\ \mathbf{if}\;y < -3.7311844206647956 \cdot 10^{+94}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y < 2.817959242728288 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y < 2.347387415166998 \cdot 10^{+178}:\\ \;\;\;\;\log \left(e^{t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (exp (/ -1.0 y)) x)) (t_1 (/ (pow (/ x (+ y x)) x) x)))
   (if (< y -3.7311844206647956e+94)
     t_0
     (if (< y 2.817959242728288e+37)
       t_1
       (if (< y 2.347387415166998e+178) (log (exp t_1)) t_0)))))

C

double code(double x, double y) {
	double t_0 = exp((-1.0 / y)) / x;
	double t_1 = pow((x / (y + x)), x) / x;
	double tmp;
	if (y < -3.7311844206647956e+94) {
		tmp = t_0;
	} else if (y < 2.817959242728288e+37) {
		tmp = t_1;
	} else if (y < 2.347387415166998e+178) {
		tmp = log(exp(t_1));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = exp(((-1.0d0) / y)) / x
    t_1 = ((x / (y + x)) ** x) / x
    if (y < (-3.7311844206647956d+94)) then
        tmp = t_0
    else if (y < 2.817959242728288d+37) then
        tmp = t_1
    else if (y < 2.347387415166998d+178) then
        tmp = log(exp(t_1))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.exp((-1.0 / y)) / x;
	double t_1 = Math.pow((x / (y + x)), x) / x;
	double tmp;
	if (y < -3.7311844206647956e+94) {
		tmp = t_0;
	} else if (y < 2.817959242728288e+37) {
		tmp = t_1;
	} else if (y < 2.347387415166998e+178) {
		tmp = Math.log(Math.exp(t_1));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.exp((-1.0 / y)) / x
	t_1 = math.pow((x / (y + x)), x) / x
	tmp = 0
	if y < -3.7311844206647956e+94:
		tmp = t_0
	elif y < 2.817959242728288e+37:
		tmp = t_1
	elif y < 2.347387415166998e+178:
		tmp = math.log(math.exp(t_1))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(exp(Float64(-1.0 / y)) / x)
	t_1 = Float64((Float64(x / Float64(y + x)) ^ x) / x)
	tmp = 0.0
	if (y < -3.7311844206647956e+94)
		tmp = t_0;
	elseif (y < 2.817959242728288e+37)
		tmp = t_1;
	elseif (y < 2.347387415166998e+178)
		tmp = log(exp(t_1));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = exp((-1.0 / y)) / x;
	t_1 = ((x / (y + x)) ^ x) / x;
	tmp = 0.0;
	if (y < -3.7311844206647956e+94)
		tmp = t_0;
	elseif (y < 2.817959242728288e+37)
		tmp = t_1;
	elseif (y < 2.347387415166998e+178)
		tmp = log(exp(t_1));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Exp[N[(-1.0 / y), $MachinePrecision]], $MachinePrecision] / x), $MachinePrecision]}, Block[{t$95$1 = N[(N[Power[N[(x / N[(y + x), $MachinePrecision]), $MachinePrecision], x], $MachinePrecision] / x), $MachinePrecision]}, If[Less[y, -3.7311844206647956e+94], t$95$0, If[Less[y, 2.817959242728288e+37], t$95$1, If[Less[y, 2.347387415166998e+178], N[Log[N[Exp[t$95$1], $MachinePrecision]], $MachinePrecision], t$95$0]]]]]

Reproduce

herbie shell --seed 2024141 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, F"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -37311844206647956000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (exp (/ -1 y)) x) (if (< y 28179592427282880000000000000000000000) (/ (pow (/ x (+ y x)) x) x) (if (< y 23473874151669980000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (log (exp (/ (pow (/ x (+ y x)) x) x))) (/ (exp (/ -1 y)) x)))))

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