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

Percentage Accurate: 77.2% → 97.7%

Time: 12.1s

Alternatives: 8

Speedup: 15.9×

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: 77.2% 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: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+80} \lor \neg \left(x \leq 6 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.5e+80) (not (<= x 6e-57)))
   (/ (exp (- y)) x)
   (/ (pow (exp x) (log (/ x (+ x y)))) x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.5e+80) || !(x <= 6e-57)) {
		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 <= (-2.5d+80)) .or. (.not. (x <= 6d-57))) 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 <= -2.5e+80) || !(x <= 6e-57)) {
		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 <= -2.5e+80) or not (x <= 6e-57):
		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 <= -2.5e+80) || !(x <= 6e-57))
		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 <= -2.5e+80) || ~((x <= 6e-57)))
		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, -2.5e+80], N[Not[LessEqual[x, 6e-57]], $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 < -2.4999999999999998e80 or 6.00000000000000001e-57 < x

   1. Initial program 75.5%

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

      1. *-commutative 75.5%

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

      2. exp-to-pow 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

   if -2.4999999999999998e80 < x < 6.00000000000000001e-57

   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 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+80} \lor \neg \left(x \leq 6 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \end{array} \]

Alternative 2: 97.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \lor \neg \left(x \leq 6 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.05) (not (<= x 6e-57))) (/ (exp (- y)) x) (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.05) || !(x <= 6e-57)) {
		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 <= (-1.05d0)) .or. (.not. (x <= 6d-57))) 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 <= -1.05) || !(x <= 6e-57)) {
		tmp = Math.exp(-y) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.05) or not (x <= 6e-57):
		tmp = math.exp(-y) / x
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.05) || !(x <= 6e-57))
		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 <= -1.05) || ~((x <= 6e-57)))
		tmp = exp(-y) / x;
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.05], N[Not[LessEqual[x, 6e-57]], $MachinePrecision]], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05000000000000004 or 6.00000000000000001e-57 < x

   1. Initial program 78.4%

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

      1. *-commutative 78.4%

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

      2. exp-to-pow 78.4%

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

   3. Simplified 78.4%

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

   4. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

   if -1.05000000000000004 < x < 6.00000000000000001e-57

   1. Initial program 76.0%

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

      1. exp-prod 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 99.3%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \lor \neg \left(x \leq 6 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]

Alternative 3: 80.3% accurate, 6.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(y \cdot y\right)\\ t_1 := y - t_0\\ \mathbf{if}\;x \leq -3200000000:\\ \;\;\;\;\frac{\frac{1 + t_1 \cdot \left(t_0 - y\right)}{1 + t_1}}{x}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-57}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot \left(y + y \cdot y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 0.5 (* y y))) (t_1 (- y t_0)))
   (if (<= x -3200000000.0)
     (/ (/ (+ 1.0 (* t_1 (- t_0 y))) (+ 1.0 t_1)) x)
     (if (<= x 6e-57) (/ 1.0 x) (/ 1.0 (+ x (* x (+ y (* y y)))))))))

C

double code(double x, double y) {
	double t_0 = 0.5 * (y * y);
	double t_1 = y - t_0;
	double tmp;
	if (x <= -3200000000.0) {
		tmp = ((1.0 + (t_1 * (t_0 - y))) / (1.0 + t_1)) / x;
	} else if (x <= 6e-57) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (x * (y + (y * y))));
	}
	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 = 0.5d0 * (y * y)
    t_1 = y - t_0
    if (x <= (-3200000000.0d0)) then
        tmp = ((1.0d0 + (t_1 * (t_0 - y))) / (1.0d0 + t_1)) / x
    else if (x <= 6d-57) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (x + (x * (y + (y * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 0.5 * (y * y);
	double t_1 = y - t_0;
	double tmp;
	if (x <= -3200000000.0) {
		tmp = ((1.0 + (t_1 * (t_0 - y))) / (1.0 + t_1)) / x;
	} else if (x <= 6e-57) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (x * (y + (y * y))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 0.5 * (y * y)
	t_1 = y - t_0
	tmp = 0
	if x <= -3200000000.0:
		tmp = ((1.0 + (t_1 * (t_0 - y))) / (1.0 + t_1)) / x
	elif x <= 6e-57:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (x * (y + (y * y))))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(0.5 * Float64(y * y))
	t_1 = Float64(y - t_0)
	tmp = 0.0
	if (x <= -3200000000.0)
		tmp = Float64(Float64(Float64(1.0 + Float64(t_1 * Float64(t_0 - y))) / Float64(1.0 + t_1)) / x);
	elseif (x <= 6e-57)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(x + Float64(x * Float64(y + Float64(y * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 0.5 * (y * y);
	t_1 = y - t_0;
	tmp = 0.0;
	if (x <= -3200000000.0)
		tmp = ((1.0 + (t_1 * (t_0 - y))) / (1.0 + t_1)) / x;
	elseif (x <= 6e-57)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (x * (y + (y * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y - t$95$0), $MachinePrecision]}, If[LessEqual[x, -3200000000.0], N[(N[(N[(1.0 + N[(t$95$1 * N[(t$95$0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 6e-57], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x + N[(x * N[(y + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.2e9

   1. Initial program 75.8%

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

      1. exp-prod 75.8%

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

   3. Simplified 75.8%

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

   4. Taylor expanded in x around inf 61.5%

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

      1. associate-+r+ 61.5%

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

      2. +-commutative 61.5%

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

      3. associate-+r+ 61.5%

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

      4. associate-*r/ 61.5%

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

      5. distribute-rgt-out 61.5%

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

      6. metadata-eval 61.5%

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

      7. *-rgt-identity 61.5%

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

      8. associate-*l/ 61.5%

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

      9. metadata-eval 61.5%

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

      10. associate-*r/ 61.5%

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

      11. associate-+r+ 61.5%

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

      12. distribute-rgt-in 72.7%

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

   6. Simplified 72.7%

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

   7. Taylor expanded in x around inf 72.7%

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

      1. *-commutative 72.7%

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

      2. unpow2 72.7%

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

      3. associate-*r* 72.7%

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

   9. Simplified 72.7%

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

       1. associate-+l- 72.7%

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

       2. flip-- 75.0%

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

       3. metadata-eval 75.0%

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

       4. div-sub 75.0%

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

       5. associate-*r* 75.0%

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

       6. *-commutative 75.0%

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

       7. associate-*r* 75.0%

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

       8. *-commutative 75.0%

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

       9. associate-*r* 75.0%

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

       10. *-commutative 75.0%

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

       11. associate-*r* 75.0%

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

       12. *-commutative 75.0%

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

   11. Applied egg-rr 75.0%

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

       1. div-sub 75.0%

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

   13. Simplified 75.0%

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

   if -3.2e9 < x < 6.00000000000000001e-57

   1. Initial program 76.9%

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

      1. exp-prod 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 98.4%

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

   if 6.00000000000000001e-57 < x

   1. Initial program 79.3%

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

      1. exp-prod 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in x around inf 63.5%

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

      1. mul-1-neg 63.5%

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

      2. unsub-neg 63.5%

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

   6. Simplified 63.5%

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

      1. clear-num 63.4%

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

      2. frac-2neg 63.4%

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

      3. div-inv 63.4%

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

      4. metadata-eval 63.4%

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

   8. Applied egg-rr 63.4%

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

      1. associate-*r/ 63.4%

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

      2. metadata-eval 63.4%

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

      3. neg-mul-1 63.4%

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

      4. associate-/r* 63.4%

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

      5. metadata-eval 63.4%

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

   10. Simplified 63.4%

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

   11. Taylor expanded in y around 0 80.4%

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

       1. unpow2 80.4%

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

       2. distribute-lft-out 80.5%

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

   13. Simplified 80.5%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3200000000:\\ \;\;\;\;\frac{\frac{1 + \left(y - 0.5 \cdot \left(y \cdot y\right)\right) \cdot \left(0.5 \cdot \left(y \cdot y\right) - y\right)}{1 + \left(y - 0.5 \cdot \left(y \cdot y\right)\right)}}{x}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-57}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot \left(y + y \cdot y\right)}\\ \end{array} \]

Alternative 4: 81.0% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+84} \lor \neg \left(x \leq 6 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{1}{x + x \cdot \left(y + y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -6.2e+84) (not (<= x 6e-57)))
   (/ 1.0 (+ x (* x (+ y (* y y)))))
   (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -6.2e+84) || !(x <= 6e-57)) {
		tmp = 1.0 / (x + (x * (y + (y * y))));
	} 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 <= (-6.2d+84)) .or. (.not. (x <= 6d-57))) then
        tmp = 1.0d0 / (x + (x * (y + (y * y))))
    else
        tmp = 1.0d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -6.2e+84) || !(x <= 6e-57)) {
		tmp = 1.0 / (x + (x * (y + (y * y))));
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -6.2e+84) or not (x <= 6e-57):
		tmp = 1.0 / (x + (x * (y + (y * y))))
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -6.2e+84) || !(x <= 6e-57))
		tmp = Float64(1.0 / Float64(x + Float64(x * Float64(y + Float64(y * y)))));
	else
		tmp = Float64(1.0 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -6.2e+84) || ~((x <= 6e-57)))
		tmp = 1.0 / (x + (x * (y + (y * y))));
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -6.2e+84], N[Not[LessEqual[x, 6e-57]], $MachinePrecision]], N[(1.0 / N[(x + N[(x * N[(y + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.20000000000000006e84 or 6.00000000000000001e-57 < x

   1. Initial program 75.5%

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

      1. exp-prod 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in x around inf 62.4%

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

      1. mul-1-neg 62.4%

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

      2. unsub-neg 62.4%

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

   6. Simplified 62.4%

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

      1. clear-num 62.4%

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

      2. frac-2neg 62.4%

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

      3. div-inv 62.4%

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

      4. metadata-eval 62.4%

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

   8. Applied egg-rr 62.4%

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

      1. associate-*r/ 62.4%

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

      2. metadata-eval 62.4%

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

      3. neg-mul-1 62.4%

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

      4. associate-/r* 62.4%

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

      5. metadata-eval 62.4%

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

   10. Simplified 62.4%

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

   11. Taylor expanded in y around 0 76.6%

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

       1. unpow2 76.6%

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

       2. distribute-lft-out 76.7%

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

   13. Simplified 76.7%

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

   if -6.20000000000000006e84 < x < 6.00000000000000001e-57

   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 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 94.6%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+84} \lor \neg \left(x \leq 6 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{1}{x + x \cdot \left(y + y \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]

Alternative 5: 82.8% accurate, 13.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.78:\\ \;\;\;\;\frac{\left(1 - y\right) + y \cdot \left(y \cdot 0.5\right)}{x}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-57}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot \left(y + y \cdot y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.78)
   (/ (+ (- 1.0 y) (* y (* y 0.5))) x)
   (if (<= x 6e-57) (/ 1.0 x) (/ 1.0 (+ x (* x (+ y (* y y))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.78) {
		tmp = ((1.0 - y) + (y * (y * 0.5))) / x;
	} else if (x <= 6e-57) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (x * (y + (y * 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 <= (-0.78d0)) then
        tmp = ((1.0d0 - y) + (y * (y * 0.5d0))) / x
    else if (x <= 6d-57) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (x + (x * (y + (y * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.78) {
		tmp = ((1.0 - y) + (y * (y * 0.5))) / x;
	} else if (x <= 6e-57) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (x * (y + (y * y))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.78:
		tmp = ((1.0 - y) + (y * (y * 0.5))) / x
	elif x <= 6e-57:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (x * (y + (y * y))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.78)
		tmp = Float64(Float64(Float64(1.0 - y) + Float64(y * Float64(y * 0.5))) / x);
	elseif (x <= 6e-57)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(x + Float64(x * Float64(y + Float64(y * y)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.78)
		tmp = ((1.0 - y) + (y * (y * 0.5))) / x;
	elseif (x <= 6e-57)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (x * (y + (y * y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.78], N[(N[(N[(1.0 - y), $MachinePrecision] + N[(y * N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 6e-57], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x + N[(x * N[(y + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.78000000000000003

   1. Initial program 77.2%

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

      1. exp-prod 77.2%

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

   3. Simplified 77.2%

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

   4. Taylor expanded in x around inf 62.3%

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

      1. associate-+r+ 62.3%

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

      2. +-commutative 62.3%

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

      3. associate-+r+ 62.3%

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

      4. associate-*r/ 62.3%

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

      5. distribute-rgt-out 62.3%

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

      6. metadata-eval 62.3%

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

      7. *-rgt-identity 62.3%

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

      8. associate-*l/ 62.3%

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

      9. metadata-eval 62.3%

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

      10. associate-*r/ 62.3%

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

      11. associate-+r+ 62.3%

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

      12. distribute-rgt-in 74.3%

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

   6. Simplified 74.3%

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

   7. Taylor expanded in x around inf 74.3%

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

      1. *-commutative 74.3%

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

      2. unpow2 74.3%

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

      3. associate-*r* 74.3%

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

   9. Simplified 74.3%

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

   if -0.78000000000000003 < x < 6.00000000000000001e-57

   1. Initial program 76.0%

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

      1. exp-prod 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 99.3%

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

   if 6.00000000000000001e-57 < x

   1. Initial program 79.3%

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

      1. exp-prod 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in x around inf 63.5%

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

      1. mul-1-neg 63.5%

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

      2. unsub-neg 63.5%

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

   6. Simplified 63.5%

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

      1. clear-num 63.4%

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

      2. frac-2neg 63.4%

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

      3. div-inv 63.4%

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

      4. metadata-eval 63.4%

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

   8. Applied egg-rr 63.4%

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

      1. associate-*r/ 63.4%

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

      2. metadata-eval 63.4%

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

      3. neg-mul-1 63.4%

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

      4. associate-/r* 63.4%

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

      5. metadata-eval 63.4%

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

   10. Simplified 63.4%

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

   11. Taylor expanded in y around 0 80.4%

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

       1. unpow2 80.4%

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

       2. distribute-lft-out 80.5%

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

   13. Simplified 80.5%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.78:\\ \;\;\;\;\frac{\left(1 - y\right) + y \cdot \left(y \cdot 0.5\right)}{x}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-57}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot \left(y + y \cdot y\right)}\\ \end{array} \]

Alternative 6: 80.6% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+84} \lor \neg \left(x \leq 6 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{1}{x + y \cdot \left(x \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -9e+84) (not (<= x 6e-57)))
   (/ 1.0 (+ x (* y (* x y))))
   (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -9e+84) || !(x <= 6e-57)) {
		tmp = 1.0 / (x + (y * (x * y)));
	} 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 <= (-9d+84)) .or. (.not. (x <= 6d-57))) then
        tmp = 1.0d0 / (x + (y * (x * y)))
    else
        tmp = 1.0d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -9e+84) || !(x <= 6e-57)) {
		tmp = 1.0 / (x + (y * (x * y)));
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -9e+84) or not (x <= 6e-57):
		tmp = 1.0 / (x + (y * (x * y)))
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -9e+84) || !(x <= 6e-57))
		tmp = Float64(1.0 / Float64(x + Float64(y * Float64(x * y))));
	else
		tmp = Float64(1.0 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -9e+84) || ~((x <= 6e-57)))
		tmp = 1.0 / (x + (y * (x * y)));
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -9e+84], N[Not[LessEqual[x, 6e-57]], $MachinePrecision]], N[(1.0 / N[(x + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.9999999999999994e84 or 6.00000000000000001e-57 < x

   1. Initial program 75.5%

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

      1. exp-prod 75.5%

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

   3. Simplified 75.5%

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

   4. Taylor expanded in x around inf 62.4%

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

      1. mul-1-neg 62.4%

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

      2. unsub-neg 62.4%

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

   6. Simplified 62.4%

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

      1. clear-num 62.4%

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

      2. frac-2neg 62.4%

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

      3. div-inv 62.4%

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

      4. metadata-eval 62.4%

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

   8. Applied egg-rr 62.4%

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

      1. associate-*r/ 62.4%

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

      2. metadata-eval 62.4%

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

      3. neg-mul-1 62.4%

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

      4. associate-/r* 62.4%

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

      5. metadata-eval 62.4%

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

   10. Simplified 62.4%

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

   11. Taylor expanded in y around 0 76.6%

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

       1. unpow2 76.6%

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

       2. distribute-lft-out 76.7%

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

   13. Simplified 76.7%

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

   14. Taylor expanded in y around inf 76.5%

       \[\leadsto \frac{1}{x + \color{blue}{x \cdot {y}^{2}}} \]
   15. Step-by-step derivation

       1. unpow2 76.5%

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

       2. associate-*r* 76.5%

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

   16. Simplified 76.5%

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

   if -8.9999999999999994e84 < x < 6.00000000000000001e-57

   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 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 94.6%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+84} \lor \neg \left(x \leq 6 \cdot 10^{-57}\right):\\ \;\;\;\;\frac{1}{x + y \cdot \left(x \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]

Alternative 7: 76.2% accurate, 23.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6 \cdot 10^{-57}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 6e-57) (/ 1.0 x) (/ 1.0 (+ x (* x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 6e-57) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (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 <= 6d-57) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (x + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 6e-57) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (x * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 6e-57:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (x * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 6e-57)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(x + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 6e-57)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 6e-57], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.00000000000000001e-57

   1. Initial program 76.5%

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

      1. exp-prod 91.1%

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

   3. Simplified 91.1%

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

   4. Taylor expanded in x around 0 84.9%

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

   if 6.00000000000000001e-57 < x

   1. Initial program 79.3%

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

      1. exp-prod 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in x around inf 63.5%

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

      1. mul-1-neg 63.5%

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

      2. unsub-neg 63.5%

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

   6. Simplified 63.5%

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

      1. clear-num 63.4%

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

      2. frac-2neg 63.4%

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

      3. div-inv 63.4%

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

      4. metadata-eval 63.4%

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

   8. Applied egg-rr 63.4%

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

      1. associate-*r/ 63.4%

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

      2. metadata-eval 63.4%

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

      3. neg-mul-1 63.4%

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

      4. associate-/r* 63.4%

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

      5. metadata-eval 63.4%

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

   10. Simplified 63.4%

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

   11. Taylor expanded in y around 0 73.1%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6 \cdot 10^{-57}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \end{array} \]

Alternative 8: 73.8% 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 77.4%

   \[\frac{e^{x \cdot \log \left(\frac{x}{x + y}\right)}}{x} \]
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. Taylor expanded in x around 0 77.8%

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

5. Final simplification 77.8%

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

Developer target: 76.8% accurate, 0.7× 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 2023297 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, F"
  :precision binary64

  :herbie-target
  (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))