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

Percentage Accurate: 77.5% → 99.4%

Time: 11.3s

Alternatives: 7

Speedup: 20.9×

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: 77.5% 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: 99.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -720 \lor \neg \left(x \leq 2.2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(e^{-x}\right)}^{\left(\mathsf{log1p}\left(\frac{y}{x}\right)\right)}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -720.0) (not (<= x 2.2e-15)))
   (/ (exp (- y)) x)
   (/ (pow (exp (- x)) (log1p (/ y x))) x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -720.0) || !(x <= 2.2e-15)) {
		tmp = exp(-y) / x;
	} else {
		tmp = pow(exp(-x), log1p((y / x))) / x;
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -720.0) || !(x <= 2.2e-15)) {
		tmp = Math.exp(-y) / x;
	} else {
		tmp = Math.pow(Math.exp(-x), Math.log1p((y / x))) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -720.0) or not (x <= 2.2e-15):
		tmp = math.exp(-y) / x
	else:
		tmp = math.pow(math.exp(-x), math.log1p((y / x))) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -720.0) || !(x <= 2.2e-15))
		tmp = Float64(exp(Float64(-y)) / x);
	else
		tmp = Float64((exp(Float64(-x)) ^ log1p(Float64(y / x))) / x);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -720.0], N[Not[LessEqual[x, 2.2e-15]], $MachinePrecision]], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision], N[(N[Power[N[Exp[(-x)], $MachinePrecision], N[Log[1 + N[(y / x), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -720 or 2.19999999999999986e-15 < x

   1. Initial program 73.3%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   if -720 < x < 2.19999999999999986e-15

   1. Initial program 72.4%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{{\left(e^{-x}\right)}^{\left(\mathsf{log1p}\left(\frac{y}{x}\right)\right)}}{x}} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -720 \lor \neg \left(x \leq 2.2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(e^{-x}\right)}^{\left(\mathsf{log1p}\left(\frac{y}{x}\right)\right)}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+25} \lor \neg \left(x \leq 2.2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.4e+25) (not (<= x 2.2e-15))) (/ (exp (- y)) x) (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.4e+25) || !(x <= 2.2e-15)) {
		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 <= (-1.4d+25)) .or. (.not. (x <= 2.2d-15))) 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 <= -1.4e+25) || !(x <= 2.2e-15)) {
		tmp = Math.exp(-y) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.4e+25) or not (x <= 2.2e-15):
		tmp = math.exp(-y) / x
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.4e+25) || !(x <= 2.2e-15))
		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 <= -1.4e+25) || ~((x <= 2.2e-15)))
		tmp = exp(-y) / x;
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.4e+25], N[Not[LessEqual[x, 2.2e-15]], $MachinePrecision]], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4000000000000001e25 or 2.19999999999999986e-15 < x

   1. Initial program 72.4%

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

   3. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   if -1.4000000000000001e25 < x < 2.19999999999999986e-15

   1. Initial program 73.7%

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

   3. Taylor expanded in x around inf 53.4%

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

      1. mul-1-neg 53.4%

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

   5. Simplified 53.4%

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

   6. Taylor expanded in y around 0 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+25} \lor \neg \left(x \leq 2.2 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.0% accurate, 8.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+25}:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot 0.5 + -1\right)}{x}\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+185}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - y \cdot \left(1 - \frac{y \cdot \left(x \cdot 0.5\right)}{x}\right)}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.4e+25)
   (/ (+ 1.0 (* y (+ (* y 0.5) -1.0))) x)
   (if (<= x 1.16e+185)
     (/ 1.0 x)
     (/ (- 1.0 (* y (- 1.0 (/ (* y (* x 0.5)) x)))) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.4e+25) {
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	} else if (x <= 1.16e+185) {
		tmp = 1.0 / x;
	} else {
		tmp = (1.0 - (y * (1.0 - ((y * (x * 0.5)) / 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 <= (-1.4d+25)) then
        tmp = (1.0d0 + (y * ((y * 0.5d0) + (-1.0d0)))) / x
    else if (x <= 1.16d+185) then
        tmp = 1.0d0 / x
    else
        tmp = (1.0d0 - (y * (1.0d0 - ((y * (x * 0.5d0)) / x)))) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.4e+25) {
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	} else if (x <= 1.16e+185) {
		tmp = 1.0 / x;
	} else {
		tmp = (1.0 - (y * (1.0 - ((y * (x * 0.5)) / x)))) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.4e+25:
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x
	elif x <= 1.16e+185:
		tmp = 1.0 / x
	else:
		tmp = (1.0 - (y * (1.0 - ((y * (x * 0.5)) / x)))) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.4e+25)
		tmp = Float64(Float64(1.0 + Float64(y * Float64(Float64(y * 0.5) + -1.0))) / x);
	elseif (x <= 1.16e+185)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(Float64(1.0 - Float64(y * Float64(1.0 - Float64(Float64(y * Float64(x * 0.5)) / x)))) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.4e+25)
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	elseif (x <= 1.16e+185)
		tmp = 1.0 / x;
	else
		tmp = (1.0 - (y * (1.0 - ((y * (x * 0.5)) / x)))) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.4e+25], N[(N[(1.0 + N[(y * N[(N[(y * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 1.16e+185], N[(1.0 / x), $MachinePrecision], N[(N[(1.0 - N[(y * N[(1.0 - N[(N[(y * N[(x * 0.5), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4000000000000001e25

   1. Initial program 73.9%

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

   3. Simplified 67.8%

      \[\leadsto \color{blue}{\frac{{\left(e^{-x}\right)}^{\left(\mathsf{log1p}\left(\frac{y}{x}\right)\right)}}{x}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 74.3%

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

   6. Taylor expanded in x around inf 74.3%

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

      1. *-commutative 74.3%

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

   8. Simplified 74.3%

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

   if -1.4000000000000001e25 < x < 1.16e185

   1. Initial program 76.4%

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

   3. Taylor expanded in x around inf 68.0%

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

      1. mul-1-neg 68.0%

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

   5. Simplified 68.0%

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

   6. Taylor expanded in y around 0 86.3%

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

   if 1.16e185 < x

   1. Initial program 58.8%

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

   3. Simplified 88.7%

      \[\leadsto \color{blue}{\frac{{\left(e^{-x}\right)}^{\left(\mathsf{log1p}\left(\frac{y}{x}\right)\right)}}{x}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 53.9%

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

   6. Taylor expanded in x around 0 60.5%

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

   7. Taylor expanded in x around inf 60.5%

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

      1. associate-*r* 60.5%

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

      2. *-commutative 60.5%

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

      3. *-commutative 60.5%

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

   9. Simplified 60.5%

      \[\leadsto \frac{1 + y \cdot \left(\frac{\color{blue}{y \cdot \left(x \cdot 0.5\right)}}{x} - 1\right)}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+25}:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot 0.5 + -1\right)}{x}\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+185}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - y \cdot \left(1 - \frac{y \cdot \left(x \cdot 0.5\right)}{x}\right)}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.3% accurate, 10.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+198}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{+155}:\\ \;\;\;\;\frac{\frac{\left(-x\right) - x \cdot y}{x}}{x}\\ \mathbf{elif}\;y \leq 40000:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x \cdot x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -8.5e+198)
   (/ 1.0 x)
   (if (<= y -8.4e+155)
     (/ (/ (- (- x) (* x y)) x) x)
     (if (<= y 40000.0) (/ 1.0 x) (/ x (* x x))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -8.5e+198) {
		tmp = 1.0 / x;
	} else if (y <= -8.4e+155) {
		tmp = ((-x - (x * y)) / x) / x;
	} else if (y <= 40000.0) {
		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 <= (-8.5d+198)) then
        tmp = 1.0d0 / x
    else if (y <= (-8.4d+155)) then
        tmp = ((-x - (x * y)) / x) / x
    else if (y <= 40000.0d0) 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 <= -8.5e+198) {
		tmp = 1.0 / x;
	} else if (y <= -8.4e+155) {
		tmp = ((-x - (x * y)) / x) / x;
	} else if (y <= 40000.0) {
		tmp = 1.0 / x;
	} else {
		tmp = x / (x * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -8.5e+198:
		tmp = 1.0 / x
	elif y <= -8.4e+155:
		tmp = ((-x - (x * y)) / x) / x
	elif y <= 40000.0:
		tmp = 1.0 / x
	else:
		tmp = x / (x * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -8.5e+198)
		tmp = Float64(1.0 / x);
	elseif (y <= -8.4e+155)
		tmp = Float64(Float64(Float64(Float64(-x) - Float64(x * y)) / x) / x);
	elseif (y <= 40000.0)
		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 <= -8.5e+198)
		tmp = 1.0 / x;
	elseif (y <= -8.4e+155)
		tmp = ((-x - (x * y)) / x) / x;
	elseif (y <= 40000.0)
		tmp = 1.0 / x;
	else
		tmp = x / (x * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -8.5e+198], N[(1.0 / x), $MachinePrecision], If[LessEqual[y, -8.4e+155], N[(N[(N[((-x) - N[(x * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[y, 40000.0], N[(1.0 / x), $MachinePrecision], N[(x / N[(x * x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.5000000000000001e198 or -8.4e155 < y < 4e4

   1. Initial program 85.6%

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

   3. Taylor expanded in x around inf 86.3%

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

      1. mul-1-neg 86.3%

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

   5. Simplified 86.3%

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

   6. Taylor expanded in y around 0 86.4%

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

   if -8.5000000000000001e198 < y < -8.4e155

   1. Initial program 29.5%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{{\left(e^{-x}\right)}^{\left(\mathsf{log1p}\left(\frac{y}{x}\right)\right)}}{x}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 3.8%

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

      1. mul-1-neg 3.8%

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

      2. unsub-neg 3.8%

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

   7. Simplified 3.8%

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

      1. div-sub 3.8%

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

      2. frac-2neg 3.8%

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

      3. frac-sub 2.1%

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

      4. *-un-lft-identity 2.1%

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

      5. add-sqr-sqrt 2.1%

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

      6. sqrt-unprod 10.7%

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

      7. sqr-neg 10.7%

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

      8. sqrt-unprod 0.0%

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

      9. add-sqr-sqrt 0.1%

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

   9. Applied egg-rr 0.1%

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

       1. associate-/r* 0.1%

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

       2. frac-2neg 0.1%

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

       3. cancel-sign-sub-inv 0.1%

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

       4. add-sqr-sqrt 0.1%

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

       5. sqrt-unprod 0.1%

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

       6. sqr-neg 0.1%

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

       7. sqrt-unprod 0.0%

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

       8. add-sqr-sqrt 0.1%

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

       9. add-sqr-sqrt 0.1%

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

       10. sqrt-unprod 18.3%

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

       11. sqr-neg 18.3%

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

       12. sqrt-unprod 18.2%

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

       13. add-sqr-sqrt 65.7%

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

       14. *-commutative 65.7%

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

       15. add-sqr-sqrt 47.5%

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

       16. sqrt-unprod 2.1%

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

       17. sqr-neg 2.1%

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

       18. sqrt-unprod 0.0%

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

       19. add-sqr-sqrt 0.1%

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

   11. Applied egg-rr 65.7%

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

   if 4e4 < y

   1. Initial program 44.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{{\left(e^{-x}\right)}^{\left(\mathsf{log1p}\left(\frac{y}{x}\right)\right)}}{x}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 2.5%

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

      1. mul-1-neg 2.5%

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

      2. unsub-neg 2.5%

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

   7. Simplified 2.5%

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

      1. div-sub 2.5%

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

      2. frac-2neg 2.5%

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

      3. frac-sub 10.5%

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

      4. *-un-lft-identity 10.5%

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

      5. add-sqr-sqrt 0.0%

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

      6. sqrt-unprod 12.4%

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

      7. sqr-neg 12.4%

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

      8. sqrt-unprod 12.5%

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

      9. add-sqr-sqrt 12.5%

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

   9. Applied egg-rr 12.5%

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

   10. Taylor expanded in y around 0 51.8%

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

       1. mul-1-neg 51.8%

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

   12. Simplified 51.8%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+198}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{+155}:\\ \;\;\;\;\frac{\frac{\left(-x\right) - x \cdot y}{x}}{x}\\ \mathbf{elif}\;y \leq 40000:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x \cdot x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.2% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+25}:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot 0.5 + -1\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.4e+25) (/ (+ 1.0 (* y (+ (* y 0.5) -1.0))) x) (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.4e+25) {
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / 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 <= (-1.4d+25)) then
        tmp = (1.0d0 + (y * ((y * 0.5d0) + (-1.0d0)))) / 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 <= -1.4e+25) {
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.4e+25:
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.4e+25)
		tmp = Float64(Float64(1.0 + Float64(y * Float64(Float64(y * 0.5) + -1.0))) / x);
	else
		tmp = Float64(1.0 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.4e+25)
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.4e+25], N[(N[(1.0 + N[(y * N[(N[(y * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4000000000000001e25

   1. Initial program 73.9%

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

   3. Simplified 67.8%

      \[\leadsto \color{blue}{\frac{{\left(e^{-x}\right)}^{\left(\mathsf{log1p}\left(\frac{y}{x}\right)\right)}}{x}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 74.3%

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

   6. Taylor expanded in x around inf 74.3%

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

      1. *-commutative 74.3%

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

   8. Simplified 74.3%

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

   if -1.4000000000000001e25 < x

   1. Initial program 72.6%

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

   3. Taylor expanded in x around inf 74.8%

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

      1. mul-1-neg 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in y around 0 78.5%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+25}:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot 0.5 + -1\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.2% accurate, 20.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 40000:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x \cdot x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 40000.0) (/ 1.0 x) (/ x (* x x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 40000.0) {
		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 <= 40000.0d0) 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 <= 40000.0) {
		tmp = 1.0 / x;
	} else {
		tmp = x / (x * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 40000.0:
		tmp = 1.0 / x
	else:
		tmp = x / (x * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 40000.0)
		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 <= 40000.0)
		tmp = 1.0 / x;
	else
		tmp = x / (x * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 40000.0], N[(1.0 / x), $MachinePrecision], N[(x / N[(x * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4e4

   1. Initial program 82.4%

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

   3. Taylor expanded in x around inf 85.6%

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

      1. mul-1-neg 85.6%

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

   5. Simplified 85.6%

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

   6. Taylor expanded in y around 0 83.1%

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

   if 4e4 < y

   1. Initial program 44.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{{\left(e^{-x}\right)}^{\left(\mathsf{log1p}\left(\frac{y}{x}\right)\right)}}{x}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 2.5%

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

      1. mul-1-neg 2.5%

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

      2. unsub-neg 2.5%

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

   7. Simplified 2.5%

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

      1. div-sub 2.5%

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

      2. frac-2neg 2.5%

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

      3. frac-sub 10.5%

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

      4. *-un-lft-identity 10.5%

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

      5. add-sqr-sqrt 0.0%

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

      6. sqrt-unprod 12.4%

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

      7. sqr-neg 12.4%

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

      8. sqrt-unprod 12.5%

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

      9. add-sqr-sqrt 12.5%

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

   9. Applied egg-rr 12.5%

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

   10. Taylor expanded in y around 0 51.8%

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

       1. mul-1-neg 51.8%

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

   12. Simplified 51.8%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 40000:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x \cdot x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.7% 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 72.9%

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

3. Taylor expanded in x around inf 80.7%

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

   1. mul-1-neg 80.7%

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

5. Simplified 80.7%

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

6. Taylor expanded in y around 0 72.1%

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

Developer target: 78.2% 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 2024096 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, F"
  :precision binary64

  :alt
  (if (< y -3.7311844206647956e+94) (/ (exp (/ -1.0 y)) x) (if (< y 2.817959242728288e+37) (/ (pow (/ x (+ y x)) x) x) (if (< y 2.347387415166998e+178) (log (exp (/ (pow (/ x (+ y x)) x) x))) (/ (exp (/ -1.0 y)) x))))

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