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

Percentage Accurate: 77.5% → 99.9%

Time: 7.8s

Alternatives: 6

Speedup: 16.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -20000000000000:\\ \;\;\;\;{\left(x \cdot e^{y}\right)}^{-1}\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-y}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -20000000000000.0)
   (pow (* x (exp y)) -1.0)
   (if (<= x 5.0) (/ (pow (exp x) (log (/ x (+ x y)))) x) (/ (exp (- y)) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -20000000000000.0) {
		tmp = pow((x * exp(y)), -1.0);
	} else if (x <= 5.0) {
		tmp = pow(exp(x), log((x / (x + y)))) / x;
	} else {
		tmp = exp(-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 <= (-20000000000000.0d0)) then
        tmp = (x * exp(y)) ** (-1.0d0)
    else if (x <= 5.0d0) then
        tmp = (exp(x) ** log((x / (x + y)))) / x
    else
        tmp = exp(-y) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -20000000000000.0) {
		tmp = Math.pow((x * Math.exp(y)), -1.0);
	} else if (x <= 5.0) {
		tmp = Math.pow(Math.exp(x), Math.log((x / (x + y)))) / x;
	} else {
		tmp = Math.exp(-y) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -20000000000000.0:
		tmp = math.pow((x * math.exp(y)), -1.0)
	elif x <= 5.0:
		tmp = math.pow(math.exp(x), math.log((x / (x + y)))) / x
	else:
		tmp = math.exp(-y) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -20000000000000.0)
		tmp = Float64(x * exp(y)) ^ -1.0;
	elseif (x <= 5.0)
		tmp = Float64((exp(x) ^ log(Float64(x / Float64(x + y)))) / x);
	else
		tmp = Float64(exp(Float64(-y)) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -20000000000000.0)
		tmp = (x * exp(y)) ^ -1.0;
	elseif (x <= 5.0)
		tmp = (exp(x) ^ log((x / (x + y)))) / x;
	else
		tmp = exp(-y) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -20000000000000.0], N[Power[N[(x * N[Exp[y], $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision], If[LessEqual[x, 5.0], N[(N[Power[N[Exp[x], $MachinePrecision], N[Log[N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / x), $MachinePrecision], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2e13

   1. Initial program 79.8%

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

      1. *-commutative 79.8%

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

      2. exp-to-pow 79.8%

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

   3. Simplified 79.8%

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

   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%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. div-inv 100.0%

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

      4. add-sqr-sqrt 68.4%

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

      5. sqrt-unprod 90.7%

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

      6. sqr-neg 90.7%

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

      7. sqrt-prod 22.3%

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

      8. add-sqr-sqrt 63.7%

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

      9. exp-neg 63.7%

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

      10. add-sqr-sqrt 41.4%

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

      11. sqrt-unprod 73.0%

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

      12. sqr-neg 73.0%

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

      13. sqrt-prod 31.6%

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

      14. add-sqr-sqrt 100.0%

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

   8. Applied egg-rr 100.0%

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

   if -2e13 < x < 5

   1. Initial program 78.6%

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

      1. exp-prod 99.6%

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

   3. Simplified 99.6%

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

   if 5 < x

   1. Initial program 86.3%

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

      1. *-commutative 86.3%

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

      2. exp-to-pow 86.3%

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

   3. Simplified 86.3%

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

   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%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -20000000000000:\\ \;\;\;\;{\left(x \cdot e^{y}\right)}^{-1}\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-y}}{x}\\ \end{array} \]

Alternative 2: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.45:\\ \;\;\;\;{\left(x \cdot e^{y}\right)}^{-1}\\ \mathbf{elif}\;x \leq 0.76:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-y}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.45)
   (pow (* x (exp y)) -1.0)
   (if (<= x 0.76) (/ 1.0 x) (/ (exp (- y)) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.45) {
		tmp = pow((x * exp(y)), -1.0);
	} else if (x <= 0.76) {
		tmp = 1.0 / x;
	} else {
		tmp = exp(-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 <= (-0.45d0)) then
        tmp = (x * exp(y)) ** (-1.0d0)
    else if (x <= 0.76d0) then
        tmp = 1.0d0 / x
    else
        tmp = exp(-y) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.45) {
		tmp = Math.pow((x * Math.exp(y)), -1.0);
	} else if (x <= 0.76) {
		tmp = 1.0 / x;
	} else {
		tmp = Math.exp(-y) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.45:
		tmp = math.pow((x * math.exp(y)), -1.0)
	elif x <= 0.76:
		tmp = 1.0 / x
	else:
		tmp = math.exp(-y) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.45)
		tmp = Float64(x * exp(y)) ^ -1.0;
	elseif (x <= 0.76)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(exp(Float64(-y)) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.45)
		tmp = (x * exp(y)) ^ -1.0;
	elseif (x <= 0.76)
		tmp = 1.0 / x;
	else
		tmp = exp(-y) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.45], N[Power[N[(x * N[Exp[y], $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision], If[LessEqual[x, 0.76], N[(1.0 / x), $MachinePrecision], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.450000000000000011

   1. Initial program 80.8%

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

      1. *-commutative 80.8%

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

      2. exp-to-pow 80.8%

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

   3. Simplified 80.8%

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

   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%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. div-inv 100.0%

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

      4. add-sqr-sqrt 68.8%

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

      5. sqrt-unprod 91.2%

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

      6. sqr-neg 91.2%

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

      7. sqrt-prod 22.5%

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

      8. add-sqr-sqrt 63.1%

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

      9. exp-neg 63.1%

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

      10. add-sqr-sqrt 40.6%

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

      11. sqrt-unprod 71.9%

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

      12. sqr-neg 71.9%

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

      13. sqrt-prod 31.2%

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

      14. add-sqr-sqrt 100.0%

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

   8. Applied egg-rr 100.0%

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

   if -0.450000000000000011 < x < 0.76000000000000001

   1. Initial program 77.8%

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

      1. exp-prod 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 97.6%

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

   if 0.76000000000000001 < x

   1. Initial program 86.3%

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

      1. *-commutative 86.3%

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

      2. exp-to-pow 86.3%

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

   3. Simplified 86.3%

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

   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%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.45:\\ \;\;\;\;{\left(x \cdot e^{y}\right)}^{-1}\\ \mathbf{elif}\;x \leq 0.76:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{e^{-y}}{x}\\ \end{array} \]

Alternative 3: 99.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.195 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.195) (not (<= x 1.0))) (/ (exp (- y)) x) (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.195) || !(x <= 1.0)) {
		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 <= (-0.195d0)) .or. (.not. (x <= 1.0d0))) 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 <= -0.195) || !(x <= 1.0)) {
		tmp = Math.exp(-y) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.195) or not (x <= 1.0):
		tmp = math.exp(-y) / x
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.195) || !(x <= 1.0))
		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 <= -0.195) || ~((x <= 1.0)))
		tmp = exp(-y) / x;
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.195], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.19500000000000001 or 1 < x

   1. Initial program 83.3%

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

      1. *-commutative 83.3%

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

      2. exp-to-pow 83.3%

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

   3. Simplified 83.3%

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

   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 -0.19500000000000001 < x < 1

   1. Initial program 77.8%

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

      1. exp-prod 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 97.6%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.195 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]

Alternative 4: 79.1% accurate, 12.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.39:\\ \;\;\;\;\left(\frac{1}{x} - \frac{y}{x}\right) + \frac{y \cdot y}{x \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.39) (+ (- (/ 1.0 x) (/ y x)) (/ (* y y) (* x 2.0))) (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.39) {
		tmp = ((1.0 / x) - (y / x)) + ((y * y) / (x * 2.0));
	} 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 <= (-0.39d0)) then
        tmp = ((1.0d0 / x) - (y / x)) + ((y * y) / (x * 2.0d0))
    else
        tmp = 1.0d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.39) {
		tmp = ((1.0 / x) - (y / x)) + ((y * y) / (x * 2.0));
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.39:
		tmp = ((1.0 / x) - (y / x)) + ((y * y) / (x * 2.0))
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.39)
		tmp = Float64(Float64(Float64(1.0 / x) - Float64(y / x)) + Float64(Float64(y * y) / Float64(x * 2.0)));
	else
		tmp = Float64(1.0 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.39)
		tmp = ((1.0 / x) - (y / x)) + ((y * y) / (x * 2.0));
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.39], N[(N[(N[(1.0 / x), $MachinePrecision] - N[(y / x), $MachinePrecision]), $MachinePrecision] + N[(N[(y * y), $MachinePrecision] / N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.39000000000000001

   1. Initial program 80.8%

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

      1. exp-prod 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in x around inf 65.4%

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

      1. associate-+r+ 65.4%

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

      2. +-commutative 65.4%

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

      3. associate-*r/ 65.4%

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

      4. distribute-rgt-out 65.4%

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

      5. metadata-eval 65.4%

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

      6. *-rgt-identity 65.4%

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

      7. associate-*l/ 65.4%

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

      8. metadata-eval 65.4%

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

      9. associate-*r/ 65.4%

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

      10. distribute-rgt-in 80.4%

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

      11. mul-1-neg 80.4%

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

      12. unsub-neg 80.4%

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

      13. unpow2 80.4%

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

      14. associate-*r/ 80.4%

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

      15. metadata-eval 80.4%

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

   6. Simplified 80.4%

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

   7. Taylor expanded in y around inf 80.5%

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

      1. associate-+r+ 80.5%

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

      2. +-commutative 80.5%

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

      3. neg-mul-1 80.5%

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

      4. sub-neg 80.5%

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

      5. unpow2 80.5%

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

      6. associate-/l* 80.5%

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

      7. associate-*r/ 80.5%

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

      8. metadata-eval 80.5%

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

   9. Simplified 80.5%

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

   10. Taylor expanded in x around inf 80.5%

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

       1. *-commutative 80.5%

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

   12. Simplified 80.5%

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

   if -0.39000000000000001 < x

   1. Initial program 81.1%

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

      1. exp-prod 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in x around 0 84.0%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.39:\\ \;\;\;\;\left(\frac{1}{x} - \frac{y}{x}\right) + \frac{y \cdot y}{x \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]

Alternative 5: 79.1% accurate, 16.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.47:\\ \;\;\;\;\frac{\left(1 - y\right) + y \cdot \left(y \cdot 0.5\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.47) (/ (+ (- 1.0 y) (* y (* y 0.5))) x) (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.47) {
		tmp = ((1.0 - y) + (y * (y * 0.5))) / 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 <= (-0.47d0)) then
        tmp = ((1.0d0 - y) + (y * (y * 0.5d0))) / 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 <= -0.47) {
		tmp = ((1.0 - y) + (y * (y * 0.5))) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.47:
		tmp = ((1.0 - y) + (y * (y * 0.5))) / x
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.47)
		tmp = Float64(Float64(Float64(1.0 - y) + Float64(y * Float64(y * 0.5))) / x);
	else
		tmp = Float64(1.0 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.47)
		tmp = ((1.0 - y) + (y * (y * 0.5))) / x;
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.47], N[(N[(N[(1.0 - y), $MachinePrecision] + N[(y * N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.46999999999999997

   1. Initial program 80.8%

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

      1. exp-prod 80.8%

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

   3. Simplified 80.8%

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

   4. Taylor expanded in x around inf 65.4%

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

      1. associate-+r+ 65.4%

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

      2. +-commutative 65.4%

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

      3. associate-*r/ 65.4%

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

      4. distribute-rgt-out 65.4%

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

      5. metadata-eval 65.4%

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

      6. *-rgt-identity 65.4%

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

      7. associate-*l/ 65.4%

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

      8. metadata-eval 65.4%

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

      9. associate-*r/ 65.4%

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

      10. distribute-rgt-in 80.4%

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

      11. mul-1-neg 80.4%

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

      12. unsub-neg 80.4%

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

      13. unpow2 80.4%

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

      14. associate-*r/ 80.4%

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

      15. metadata-eval 80.4%

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

   6. Simplified 80.4%

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

   7. Taylor expanded in x around inf 80.4%

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

      1. unpow2 80.4%

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

      2. *-commutative 80.4%

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

      3. associate-*r* 80.4%

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

   9. Simplified 80.4%

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

   if -0.46999999999999997 < x

   1. Initial program 81.1%

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

      1. exp-prod 94.5%

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

   3. Simplified 94.5%

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

   4. Taylor expanded in x around 0 84.0%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.47:\\ \;\;\;\;\frac{\left(1 - y\right) + y \cdot \left(y \cdot 0.5\right)}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]

Alternative 6: 74.7% accurate, 69.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.0%

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

   1. exp-prod 90.2%

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

3. Simplified 90.2%

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

4. Taylor expanded in x around 0 77.6%

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

5. Final simplification 77.6%

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

Developer target: 77.4% 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 2023290 
(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))