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

Percentage Accurate: 77.6% → 98.9%

Time: 11.4s

Alternatives: 9

Speedup: 26.1×

• Could not converge on a ground truth

  1. x = -3.2481296436577424e+292
  2. y = -1.38456534481287e-104

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: 77.6% 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: 98.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+91} \lor \neg \left(x \leq 7.2 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.8e+91) (not (<= x 7.2e-13)))
   (/ (exp (- y)) x)
   (/ (pow (exp x) (log (/ x (+ x y)))) x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.8e+91) || !(x <= 7.2e-13)) {
		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 <= (-4.8d+91)) .or. (.not. (x <= 7.2d-13))) 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 <= -4.8e+91) || !(x <= 7.2e-13)) {
		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 <= -4.8e+91) or not (x <= 7.2e-13):
		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 <= -4.8e+91) || !(x <= 7.2e-13))
		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 <= -4.8e+91) || ~((x <= 7.2e-13)))
		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, -4.8e+91], N[Not[LessEqual[x, 7.2e-13]], $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 < -4.79999999999999966e91 or 7.1999999999999996e-13 < x

   1. Initial program 75.6%

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

      1. *-commutative 75.6%

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

      2. exp-to-pow 75.6%

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

   3. Simplified 75.6%

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

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

   if -4.79999999999999966e91 < x < 7.1999999999999996e-13

   1. Initial program 86.7%

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

      1. exp-prod 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+91} \lor \neg \left(x \leq 7.2 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -24500 \lor \neg \left(x \leq 7.2 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -24500.0) (not (<= x 7.2e-13))) (/ (exp (- y)) x) (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -24500.0) || !(x <= 7.2e-13)) {
		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 <= (-24500.0d0)) .or. (.not. (x <= 7.2d-13))) 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 <= -24500.0) || !(x <= 7.2e-13)) {
		tmp = Math.exp(-y) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -24500.0) or not (x <= 7.2e-13):
		tmp = math.exp(-y) / x
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -24500.0) || !(x <= 7.2e-13))
		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 <= -24500.0) || ~((x <= 7.2e-13)))
		tmp = exp(-y) / x;
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -24500.0], N[Not[LessEqual[x, 7.2e-13]], $MachinePrecision]], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -24500 or 7.1999999999999996e-13 < x

   1. Initial program 78.2%

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

      1. *-commutative 78.2%

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

      2. exp-to-pow 78.2%

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

   3. Simplified 78.2%

      \[\leadsto \color{blue}{\frac{{\left(\frac{x}{x + y}\right)}^{x}}{x}} \]
   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 -24500 < x < 7.1999999999999996e-13

   1. Initial program 84.7%

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

      1. exp-prod 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 99.2%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -24500 \lor \neg \left(x \leq 7.2 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.3% accurate, 10.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -24500:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot \left(0.5 + y \cdot -0.16666666666666666\right) + -1\right)}{x}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+33}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1 - y}{x \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -24500.0)
   (/ (+ 1.0 (* y (+ (* y (+ 0.5 (* y -0.16666666666666666))) -1.0))) x)
   (if (<= x 1.25e+33) (/ 1.0 x) (* y (/ (- 1.0 y) (* x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -24500.0) {
		tmp = (1.0 + (y * ((y * (0.5 + (y * -0.16666666666666666))) + -1.0))) / x;
	} else if (x <= 1.25e+33) {
		tmp = 1.0 / x;
	} else {
		tmp = y * ((1.0 - y) / (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-24500.0d0)) then
        tmp = (1.0d0 + (y * ((y * (0.5d0 + (y * (-0.16666666666666666d0)))) + (-1.0d0)))) / x
    else if (x <= 1.25d+33) then
        tmp = 1.0d0 / x
    else
        tmp = y * ((1.0d0 - y) / (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -24500.0) {
		tmp = (1.0 + (y * ((y * (0.5 + (y * -0.16666666666666666))) + -1.0))) / x;
	} else if (x <= 1.25e+33) {
		tmp = 1.0 / x;
	} else {
		tmp = y * ((1.0 - y) / (x * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -24500.0:
		tmp = (1.0 + (y * ((y * (0.5 + (y * -0.16666666666666666))) + -1.0))) / x
	elif x <= 1.25e+33:
		tmp = 1.0 / x
	else:
		tmp = y * ((1.0 - y) / (x * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -24500.0)
		tmp = Float64(Float64(1.0 + Float64(y * Float64(Float64(y * Float64(0.5 + Float64(y * -0.16666666666666666))) + -1.0))) / x);
	elseif (x <= 1.25e+33)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(y * Float64(Float64(1.0 - y) / Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -24500.0)
		tmp = (1.0 + (y * ((y * (0.5 + (y * -0.16666666666666666))) + -1.0))) / x;
	elseif (x <= 1.25e+33)
		tmp = 1.0 / x;
	else
		tmp = y * ((1.0 - y) / (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -24500.0], N[(N[(1.0 + N[(y * N[(N[(y * N[(0.5 + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 1.25e+33], N[(1.0 / x), $MachinePrecision], N[(y * N[(N[(1.0 - y), $MachinePrecision] / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -24500

   1. Initial program 75.9%

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

      1. *-commutative 75.9%

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

      2. exp-to-pow 75.9%

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

   3. Simplified 75.9%

      \[\leadsto \color{blue}{\frac{{\left(\frac{x}{x + y}\right)}^{x}}{x}} \]
   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 78.0%

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

   if -24500 < x < 1.24999999999999993e33

   1. Initial program 85.0%

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

      1. exp-prod 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around 0 96.8%

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

   if 1.24999999999999993e33 < x

   1. Initial program 79.5%

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

      1. exp-prod 79.5%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in x around inf 66.0%

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

      1. mul-1-neg 66.0%

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

      2. unsub-neg 66.0%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in y around inf 65.7%

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

   9. Taylor expanded in y around 0 65.8%

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

       1. neg-mul-1 65.8%

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

       2. +-commutative 65.8%

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

       3. sub-neg 65.8%

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

       4. div-sub 65.9%

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

       5. associate-/r* 81.2%

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

       6. *-commutative 81.2%

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

   11. Simplified 81.2%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -24500:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot \left(0.5 + y \cdot -0.16666666666666666\right) + -1\right)}{x}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+33}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1 - y}{x \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.2% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -24500:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot \left(y \cdot -0.16666666666666666\right) + -1\right)}{x}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1 - y}{x \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -24500.0)
   (/ (+ 1.0 (* y (+ (* y (* y -0.16666666666666666)) -1.0))) x)
   (if (<= x 4.8e+33) (/ 1.0 x) (* y (/ (- 1.0 y) (* x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -24500.0) {
		tmp = (1.0 + (y * ((y * (y * -0.16666666666666666)) + -1.0))) / x;
	} else if (x <= 4.8e+33) {
		tmp = 1.0 / x;
	} else {
		tmp = y * ((1.0 - y) / (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-24500.0d0)) then
        tmp = (1.0d0 + (y * ((y * (y * (-0.16666666666666666d0))) + (-1.0d0)))) / x
    else if (x <= 4.8d+33) then
        tmp = 1.0d0 / x
    else
        tmp = y * ((1.0d0 - y) / (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -24500.0) {
		tmp = (1.0 + (y * ((y * (y * -0.16666666666666666)) + -1.0))) / x;
	} else if (x <= 4.8e+33) {
		tmp = 1.0 / x;
	} else {
		tmp = y * ((1.0 - y) / (x * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -24500.0:
		tmp = (1.0 + (y * ((y * (y * -0.16666666666666666)) + -1.0))) / x
	elif x <= 4.8e+33:
		tmp = 1.0 / x
	else:
		tmp = y * ((1.0 - y) / (x * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -24500.0)
		tmp = Float64(Float64(1.0 + Float64(y * Float64(Float64(y * Float64(y * -0.16666666666666666)) + -1.0))) / x);
	elseif (x <= 4.8e+33)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(y * Float64(Float64(1.0 - y) / Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -24500.0)
		tmp = (1.0 + (y * ((y * (y * -0.16666666666666666)) + -1.0))) / x;
	elseif (x <= 4.8e+33)
		tmp = 1.0 / x;
	else
		tmp = y * ((1.0 - y) / (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -24500.0], N[(N[(1.0 + N[(y * N[(N[(y * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 4.8e+33], N[(1.0 / x), $MachinePrecision], N[(y * N[(N[(1.0 - y), $MachinePrecision] / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -24500

   1. Initial program 75.9%

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

      1. *-commutative 75.9%

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

      2. exp-to-pow 75.9%

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

   3. Simplified 75.9%

      \[\leadsto \color{blue}{\frac{{\left(\frac{x}{x + y}\right)}^{x}}{x}} \]
   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 78.0%

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

   9. Taylor expanded in y around inf 77.8%

      \[\leadsto \frac{1 + y \cdot \left(y \cdot \color{blue}{\left(-0.16666666666666666 \cdot y\right)} - 1\right)}{x} \]
   10. Step-by-step derivation

       1. *-commutative 77.8%

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

   11. Simplified 77.8%

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

   if -24500 < x < 4.8e33

   1. Initial program 85.0%

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

      1. exp-prod 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around 0 96.8%

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

   if 4.8e33 < x

   1. Initial program 79.5%

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

      1. exp-prod 79.5%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in x around inf 66.0%

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

      1. mul-1-neg 66.0%

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

      2. unsub-neg 66.0%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in y around inf 65.7%

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

   9. Taylor expanded in y around 0 65.8%

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

       1. neg-mul-1 65.8%

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

       2. +-commutative 65.8%

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

       3. sub-neg 65.8%

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

       4. div-sub 65.9%

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

       5. associate-/r* 81.2%

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

       6. *-commutative 81.2%

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

   11. Simplified 81.2%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -24500:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot \left(y \cdot -0.16666666666666666\right) + -1\right)}{x}\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+33}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1 - y}{x \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.9% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -24500:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot 0.5 + -1\right)}{x}\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+33}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1 - y}{x \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -24500.0)
   (/ (+ 1.0 (* y (+ (* y 0.5) -1.0))) x)
   (if (<= x 3.4e+33) (/ 1.0 x) (* y (/ (- 1.0 y) (* x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -24500.0) {
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	} else if (x <= 3.4e+33) {
		tmp = 1.0 / x;
	} else {
		tmp = y * ((1.0 - y) / (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-24500.0d0)) then
        tmp = (1.0d0 + (y * ((y * 0.5d0) + (-1.0d0)))) / x
    else if (x <= 3.4d+33) then
        tmp = 1.0d0 / x
    else
        tmp = y * ((1.0d0 - y) / (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -24500.0) {
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	} else if (x <= 3.4e+33) {
		tmp = 1.0 / x;
	} else {
		tmp = y * ((1.0 - y) / (x * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -24500.0:
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x
	elif x <= 3.4e+33:
		tmp = 1.0 / x
	else:
		tmp = y * ((1.0 - y) / (x * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -24500.0)
		tmp = Float64(Float64(1.0 + Float64(y * Float64(Float64(y * 0.5) + -1.0))) / x);
	elseif (x <= 3.4e+33)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(y * Float64(Float64(1.0 - y) / Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -24500.0)
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	elseif (x <= 3.4e+33)
		tmp = 1.0 / x;
	else
		tmp = y * ((1.0 - y) / (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -24500.0], N[(N[(1.0 + N[(y * N[(N[(y * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 3.4e+33], N[(1.0 / x), $MachinePrecision], N[(y * N[(N[(1.0 - y), $MachinePrecision] / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -24500

   1. Initial program 75.9%

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

      1. exp-prod 75.9%

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

   3. Simplified 75.9%

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

   5. Taylor expanded in y around 0 73.2%

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

   6. Taylor expanded in x around inf 73.2%

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

      1. *-commutative 73.2%

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

   8. Simplified 73.2%

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

   if -24500 < x < 3.3999999999999999e33

   1. Initial program 85.0%

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

      1. exp-prod 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around 0 96.8%

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

   if 3.3999999999999999e33 < x

   1. Initial program 79.5%

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

      1. exp-prod 79.5%

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

   3. Simplified 79.5%

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

   5. Taylor expanded in x around inf 66.0%

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

      1. mul-1-neg 66.0%

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

      2. unsub-neg 66.0%

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

   7. Simplified 66.0%

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

   8. Taylor expanded in y around inf 65.7%

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

   9. Taylor expanded in y around 0 65.8%

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

       1. neg-mul-1 65.8%

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

       2. +-commutative 65.8%

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

       3. sub-neg 65.8%

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

       4. div-sub 65.9%

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

       5. associate-/r* 81.2%

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

       6. *-commutative 81.2%

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

   11. Simplified 81.2%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -24500:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot 0.5 + -1\right)}{x}\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+33}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1 - y}{x \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.9% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1}{x \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.6e+102)
   (* y (* y y))
   (if (<= y 5.2e-31) (/ 1.0 x) (* y (/ 1.0 (* x y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.6e+102) {
		tmp = y * (y * y);
	} else if (y <= 5.2e-31) {
		tmp = 1.0 / x;
	} else {
		tmp = y * (1.0 / (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-5.6d+102)) then
        tmp = y * (y * y)
    else if (y <= 5.2d-31) then
        tmp = 1.0d0 / x
    else
        tmp = y * (1.0d0 / (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5.6e+102) {
		tmp = y * (y * y);
	} else if (y <= 5.2e-31) {
		tmp = 1.0 / x;
	} else {
		tmp = y * (1.0 / (x * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.6e+102:
		tmp = y * (y * y)
	elif y <= 5.2e-31:
		tmp = 1.0 / x
	else:
		tmp = y * (1.0 / (x * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.6e+102)
		tmp = Float64(y * Float64(y * y));
	elseif (y <= 5.2e-31)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(y * Float64(1.0 / Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.6e+102)
		tmp = y * (y * y);
	elseif (y <= 5.2e-31)
		tmp = 1.0 / x;
	else
		tmp = y * (1.0 / (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.6e+102], N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e-31], N[(1.0 / x), $MachinePrecision], N[(y * N[(1.0 / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.60000000000000037e102

   1. Initial program 66.7%

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

      1. exp-prod 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in x around inf 4.6%

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

      1. mul-1-neg 4.6%

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

      2. unsub-neg 4.6%

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

   7. Simplified 4.6%

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

   8. Taylor expanded in y around inf 4.6%

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

   9. Taylor expanded in y around 0 39.4%

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

       1. *-commutative 39.4%

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

   11. Simplified 39.4%

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

   13. Applied egg-rr 56.4%

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

   if -5.60000000000000037e102 < y < 5.19999999999999991e-31

   1. Initial program 96.8%

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

      1. exp-prod 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in x around 0 96.1%

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

   if 5.19999999999999991e-31 < y

   1. Initial program 48.4%

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

      1. exp-prod 61.2%

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

   3. Simplified 61.2%

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

   5. Taylor expanded in x around inf 8.9%

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

      1. mul-1-neg 8.9%

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

      2. unsub-neg 8.9%

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

   7. Simplified 8.9%

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

   8. Taylor expanded in y around inf 8.9%

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

   9. Taylor expanded in y around 0 74.2%

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

       1. *-commutative 74.2%

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

   11. Simplified 74.2%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{1}{x \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.3% accurate, 16.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+102}:\\ \;\;\;\;y \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 250:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.8e+102) (* y (* y y)) (if (<= y 250.0) (/ 1.0 x) 0.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.8e+102) {
		tmp = y * (y * y);
	} else if (y <= 250.0) {
		tmp = 1.0 / x;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-4.8d+102)) then
        tmp = y * (y * y)
    else if (y <= 250.0d0) then
        tmp = 1.0d0 / x
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.8e+102) {
		tmp = y * (y * y);
	} else if (y <= 250.0) {
		tmp = 1.0 / x;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.8e+102:
		tmp = y * (y * y)
	elif y <= 250.0:
		tmp = 1.0 / x
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.8e+102)
		tmp = Float64(y * Float64(y * y));
	elseif (y <= 250.0)
		tmp = Float64(1.0 / x);
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.8e+102)
		tmp = y * (y * y);
	elseif (y <= 250.0)
		tmp = 1.0 / x;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.8e+102], N[(y * N[(y * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 250.0], N[(1.0 / x), $MachinePrecision], 0.0]]

Derivation

1. Split input into 3 regimes

2. if y < -4.79999999999999989e102

   1. Initial program 66.7%

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

      1. exp-prod 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in x around inf 4.6%

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

      1. mul-1-neg 4.6%

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

      2. unsub-neg 4.6%

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

   7. Simplified 4.6%

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

   8. Taylor expanded in y around inf 4.6%

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

   9. Taylor expanded in y around 0 39.4%

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

       1. *-commutative 39.4%

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

   11. Simplified 39.4%

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

   13. Applied egg-rr 56.4%

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

   if -4.79999999999999989e102 < y < 250

   1. Initial program 96.1%

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

      1. exp-prod 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in x around 0 95.5%

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

   if 250 < y

   1. Initial program 46.1%

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

      1. exp-prod 60.0%

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

   3. Simplified 60.0%

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

   5. Taylor expanded in x around inf 2.5%

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

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

   8. Taylor expanded in y around inf 2.5%

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

      1. *-un-lft-identity 2.5%

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

      2. cancel-sign-sub-inv 2.5%

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

      3. add-sqr-sqrt 1.3%

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

      4. sqrt-unprod 31.6%

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

      5. sqr-neg 31.6%

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

      6. sqrt-unprod 1.2%

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

      7. add-sqr-sqrt 5.0%

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

      8. div-inv 5.0%

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

      9. frac-2neg 5.0%

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

      10. *-commutative 5.0%

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

      11. frac-add 15.5%

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

      12. *-un-lft-identity 15.5%

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

      13. *-rgt-identity 15.5%

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

   10. Applied egg-rr 15.5%

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

   12. Applied egg-rr 61.6%

       \[\leadsto \color{blue}{y - y} \]
   13. Step-by-step derivation

       1. +-inverses 61.6%

          \[\leadsto \color{blue}{0} \]

   14. Simplified 61.6%

       \[\leadsto \color{blue}{0} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 79.1% accurate, 26.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 280:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 280.0) (/ 1.0 x) 0.0))

C

double code(double x, double y) {
	double tmp;
	if (y <= 280.0) {
		tmp = 1.0 / x;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 280.0d0) then
        tmp = 1.0d0 / x
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 280.0) {
		tmp = 1.0 / x;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 280.0:
		tmp = 1.0 / x
	else:
		tmp = 0.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 280.0)
		tmp = Float64(1.0 / x);
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 280.0)
		tmp = 1.0 / x;
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 280.0], N[(1.0 / x), $MachinePrecision], 0.0]

Derivation

1. Split input into 2 regimes

2. if y < 280

   1. Initial program 90.6%

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

      1. exp-prod 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in x around 0 85.1%

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

   if 280 < y

   1. Initial program 46.1%

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

      1. exp-prod 60.0%

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

   3. Simplified 60.0%

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

   5. Taylor expanded in x around inf 2.5%

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

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

   8. Taylor expanded in y around inf 2.5%

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

      1. *-un-lft-identity 2.5%

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

      2. cancel-sign-sub-inv 2.5%

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

      3. add-sqr-sqrt 1.3%

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

      4. sqrt-unprod 31.6%

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

      5. sqr-neg 31.6%

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

      6. sqrt-unprod 1.2%

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

      7. add-sqr-sqrt 5.0%

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

      8. div-inv 5.0%

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

      9. frac-2neg 5.0%

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

      10. *-commutative 5.0%

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

      11. frac-add 15.5%

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

      12. *-un-lft-identity 15.5%

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

      13. *-rgt-identity 15.5%

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

   10. Applied egg-rr 15.5%

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

   12. Applied egg-rr 61.6%

       \[\leadsto \color{blue}{y - y} \]
   13. Step-by-step derivation

       1. +-inverses 61.6%

          \[\leadsto \color{blue}{0} \]

   14. Simplified 61.6%

       \[\leadsto \color{blue}{0} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 15.3% accurate, 209.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.0)

C

double code(double x, double y) {
	return 0.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.0d0
end function

Java

public static double code(double x, double y) {
	return 0.0;
}

Python

def code(x, y):
	return 0.0

Julia

function code(x, y)
	return 0.0
end

MATLAB

function tmp = code(x, y)
	tmp = 0.0;
end

Wolfram

code[x_, y_] := 0.0

Derivation

1. Initial program 80.9%

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

   1. exp-prod 87.2%

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

3. Simplified 87.2%

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

5. Taylor expanded in x around inf 61.1%

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

   1. mul-1-neg 61.1%

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

   2. unsub-neg 61.1%

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

7. Simplified 61.1%

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

8. Taylor expanded in y around inf 48.0%

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

   1. *-un-lft-identity 48.0%

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

   2. cancel-sign-sub-inv 48.0%

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

   3. add-sqr-sqrt 25.0%

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

   4. sqrt-unprod 51.4%

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

   5. sqr-neg 51.4%

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

   6. sqrt-unprod 22.2%

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

   7. add-sqr-sqrt 47.5%

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

   8. div-inv 47.5%

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

   9. frac-2neg 47.5%

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

   10. *-commutative 47.5%

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

   11. frac-add 35.5%

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

   12. *-un-lft-identity 35.5%

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

   13. *-rgt-identity 35.5%

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

10. Applied egg-rr 35.5%

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

12. Applied egg-rr 16.3%

    \[\leadsto \color{blue}{y - y} \]
13. Step-by-step derivation

    1. +-inverses 16.3%

       \[\leadsto \color{blue}{0} \]

14. Simplified 16.3%

    \[\leadsto \color{blue}{0} \]
15. Add Preprocessing

Developer Target 1: 78.3% 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 2024170 
(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))