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

Percentage Accurate: 77.6% → 99.5%

Time: 12.6s

Alternatives: 10

Speedup: 11.0×

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: 77.6% 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: 99.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1000000000 \lor \neg \left(x \leq 3.6 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1000000000.0) (not (<= x 3.6e-14)))
   (/ (exp (- y)) x)
   (/ (pow (exp x) (log (/ x (+ x y)))) x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1000000000.0) || !(x <= 3.6e-14)) {
		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 <= (-1000000000.0d0)) .or. (.not. (x <= 3.6d-14))) 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 <= -1000000000.0) || !(x <= 3.6e-14)) {
		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 <= -1000000000.0) or not (x <= 3.6e-14):
		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 <= -1000000000.0) || !(x <= 3.6e-14))
		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 <= -1000000000.0) || ~((x <= 3.6e-14)))
		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, -1000000000.0], N[Not[LessEqual[x, 3.6e-14]], $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 < -1e9 or 3.5999999999999998e-14 < x

   1. Initial program 71.9%

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

      1. *-commutative 71.9%

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

      2. exp-to-pow 71.9%

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

   3. Simplified 71.9%

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

   5. Taylor expanded in x around inf 99.8%

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

      1. mul-1-neg 99.8%

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

   7. Simplified 99.8%

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

   if -1e9 < x < 3.5999999999999998e-14

   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 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. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1000000000 \lor \neg \left(x \leq 3.6 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.76 \lor \neg \left(x \leq 3.6 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.76) (not (<= x 3.6e-14))) (/ (exp (- y)) x) (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.76) || !(x <= 3.6e-14)) {
		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 <= (-0.76d0)) .or. (.not. (x <= 3.6d-14))) 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 <= -0.76) || !(x <= 3.6e-14)) {
		tmp = Math.exp(-y) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.76) or not (x <= 3.6e-14):
		tmp = math.exp(-y) / x
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.76) || !(x <= 3.6e-14))
		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 <= -0.76) || ~((x <= 3.6e-14)))
		tmp = exp(-y) / x;
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.76], N[Not[LessEqual[x, 3.6e-14]], $MachinePrecision]], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.76000000000000001 or 3.5999999999999998e-14 < x

   1. Initial program 72.3%

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

      1. *-commutative 72.3%

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

      2. exp-to-pow 72.3%

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

   3. Simplified 72.3%

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

   5. Taylor expanded in x around inf 99.8%

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

      1. mul-1-neg 99.8%

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

   7. Simplified 99.8%

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

   if -0.76000000000000001 < x < 3.5999999999999998e-14

   1. Initial program 77.0%

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

   5. Taylor expanded in x around 0 99.5%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.76 \lor \neg \left(x \leq 3.6 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.8% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -105000000:\\ \;\;\;\;\frac{\frac{x + y \cdot \left(y \cdot \left(0.5 + \left(x \cdot 0.5 + y \cdot \left(x \cdot -0.16666666666666666 - 0.5\right)\right)\right) - x\right)}{x}}{x}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+184}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x + y \cdot \left(y \cdot \left(0.5 + x \cdot 0.5\right) - x\right)}{x}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -105000000.0)
   (/
    (/
     (+
      x
      (*
       y
       (-
        (* y (+ 0.5 (+ (* x 0.5) (* y (- (* x -0.16666666666666666) 0.5)))))
        x)))
     x)
    x)
   (if (<= x 4.2e+184)
     (/ 1.0 x)
     (/ (/ (+ x (* y (- (* y (+ 0.5 (* x 0.5))) x))) x) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -105000000.0) {
		tmp = ((x + (y * ((y * (0.5 + ((x * 0.5) + (y * ((x * -0.16666666666666666) - 0.5))))) - x))) / x) / x;
	} else if (x <= 4.2e+184) {
		tmp = 1.0 / x;
	} else {
		tmp = ((x + (y * ((y * (0.5 + (x * 0.5))) - x))) / x) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-105000000.0d0)) then
        tmp = ((x + (y * ((y * (0.5d0 + ((x * 0.5d0) + (y * ((x * (-0.16666666666666666d0)) - 0.5d0))))) - x))) / x) / x
    else if (x <= 4.2d+184) then
        tmp = 1.0d0 / x
    else
        tmp = ((x + (y * ((y * (0.5d0 + (x * 0.5d0))) - x))) / x) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -105000000.0) {
		tmp = ((x + (y * ((y * (0.5 + ((x * 0.5) + (y * ((x * -0.16666666666666666) - 0.5))))) - x))) / x) / x;
	} else if (x <= 4.2e+184) {
		tmp = 1.0 / x;
	} else {
		tmp = ((x + (y * ((y * (0.5 + (x * 0.5))) - x))) / x) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -105000000.0:
		tmp = ((x + (y * ((y * (0.5 + ((x * 0.5) + (y * ((x * -0.16666666666666666) - 0.5))))) - x))) / x) / x
	elif x <= 4.2e+184:
		tmp = 1.0 / x
	else:
		tmp = ((x + (y * ((y * (0.5 + (x * 0.5))) - x))) / x) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -105000000.0)
		tmp = Float64(Float64(Float64(x + Float64(y * Float64(Float64(y * Float64(0.5 + Float64(Float64(x * 0.5) + Float64(y * Float64(Float64(x * -0.16666666666666666) - 0.5))))) - x))) / x) / x);
	elseif (x <= 4.2e+184)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(Float64(Float64(x + Float64(y * Float64(Float64(y * Float64(0.5 + Float64(x * 0.5))) - x))) / x) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -105000000.0)
		tmp = ((x + (y * ((y * (0.5 + ((x * 0.5) + (y * ((x * -0.16666666666666666) - 0.5))))) - x))) / x) / x;
	elseif (x <= 4.2e+184)
		tmp = 1.0 / x;
	else
		tmp = ((x + (y * ((y * (0.5 + (x * 0.5))) - x))) / x) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -105000000.0], N[(N[(N[(x + N[(y * N[(N[(y * N[(0.5 + N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(N[(x * -0.16666666666666666), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 4.2e+184], N[(1.0 / x), $MachinePrecision], N[(N[(N[(x + N[(y * N[(N[(y * N[(0.5 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.05e8

   1. Initial program 73.8%

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

      1. *-commutative 73.8%

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

      2. exp-to-pow 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in x around inf 63.1%

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

      1. mul-1-neg 63.1%

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

      2. associate-/l* 63.1%

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

      3. mul-1-neg 63.1%

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

      4. distribute-rgt-out 63.1%

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

      5. metadata-eval 63.1%

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

   7. Simplified 63.1%

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

   8. Taylor expanded in x around 0 63.0%

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

      1. associate-*r* 63.0%

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

      2. distribute-rgt-out 70.7%

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

      3. *-commutative 70.7%

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

   10. Simplified 70.7%

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

   11. Taylor expanded in y around 0 77.2%

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

   if -1.05e8 < x < 4.2e184

   1. Initial program 82.3%

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

      1. exp-prod 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around 0 88.3%

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

   if 4.2e184 < x

   1. Initial program 42.8%

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

      1. *-commutative 42.8%

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

      2. exp-to-pow 42.8%

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

   3. Simplified 42.8%

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

   5. Taylor expanded in x around inf 78.9%

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

      1. mul-1-neg 78.9%

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

      2. associate-/l* 78.9%

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

      3. mul-1-neg 78.9%

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

      4. distribute-rgt-out 84.2%

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

      5. metadata-eval 84.2%

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

   7. Simplified 84.2%

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

   8. Taylor expanded in x around 0 84.2%

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

      1. associate-*r* 84.2%

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

      2. distribute-rgt-out 84.2%

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

      3. *-commutative 84.2%

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

   10. Simplified 84.2%

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

   11. Taylor expanded in y around 0 56.9%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -105000000:\\ \;\;\;\;\frac{\frac{x + y \cdot \left(y \cdot \left(0.5 + \left(x \cdot 0.5 + y \cdot \left(x \cdot -0.16666666666666666 - 0.5\right)\right)\right) - x\right)}{x}}{x}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+184}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x + y \cdot \left(y \cdot \left(0.5 + x \cdot 0.5\right) - x\right)}{x}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.5% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.98 \lor \neg \left(x \leq 2.2 \cdot 10^{+185}\right):\\ \;\;\;\;\frac{\frac{x + y \cdot \left(y \cdot \left(0.5 + x \cdot 0.5\right) - x\right)}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.98) (not (<= x 2.2e+185)))
   (/ (/ (+ x (* y (- (* y (+ 0.5 (* x 0.5))) x))) x) x)
   (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.98) || !(x <= 2.2e+185)) {
		tmp = ((x + (y * ((y * (0.5 + (x * 0.5))) - x))) / x) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-0.98d0)) .or. (.not. (x <= 2.2d+185))) then
        tmp = ((x + (y * ((y * (0.5d0 + (x * 0.5d0))) - x))) / x) / x
    else
        tmp = 1.0d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -0.98) || !(x <= 2.2e+185)) {
		tmp = ((x + (y * ((y * (0.5 + (x * 0.5))) - x))) / x) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.98) or not (x <= 2.2e+185):
		tmp = ((x + (y * ((y * (0.5 + (x * 0.5))) - x))) / x) / x
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.98) || !(x <= 2.2e+185))
		tmp = Float64(Float64(Float64(x + Float64(y * Float64(Float64(y * Float64(0.5 + Float64(x * 0.5))) - x))) / x) / x);
	else
		tmp = Float64(1.0 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -0.98) || ~((x <= 2.2e+185)))
		tmp = ((x + (y * ((y * (0.5 + (x * 0.5))) - x))) / x) / x;
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.98], N[Not[LessEqual[x, 2.2e+185]], $MachinePrecision]], N[(N[(N[(x + N[(y * N[(N[(y * N[(0.5 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.97999999999999998 or 2.2000000000000001e185 < x

   1. Initial program 63.1%

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

      1. *-commutative 63.1%

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

      2. exp-to-pow 63.1%

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

   3. Simplified 63.1%

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

   5. Taylor expanded in x around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. associate-/l* 68.5%

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

      3. mul-1-neg 68.5%

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

      4. distribute-rgt-out 70.4%

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

      5. metadata-eval 70.4%

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

   7. Simplified 70.4%

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

   8. Taylor expanded in x around 0 70.4%

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

      1. associate-*r* 70.4%

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

      2. distribute-rgt-out 75.2%

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

      3. *-commutative 75.2%

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

   10. Simplified 75.2%

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

   11. Taylor expanded in y around 0 69.2%

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

   if -0.97999999999999998 < x < 2.2000000000000001e185

   1. Initial program 82.1%

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

      1. exp-prod 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around 0 88.8%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.98 \lor \neg \left(x \leq 2.2 \cdot 10^{+185}\right):\\ \;\;\;\;\frac{\frac{x + y \cdot \left(y \cdot \left(0.5 + x \cdot 0.5\right) - x\right)}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.4% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;y \cdot \left(\frac{y}{x} \cdot \left(0.5 + y \cdot -0.16666666666666666\right)\right) + \frac{1 - y}{x}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+185}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + y \cdot \left(-1 + \frac{0.5 \cdot \left(y + x \cdot y\right)}{x}\right)}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.35)
   (+ (* y (* (/ y x) (+ 0.5 (* y -0.16666666666666666)))) (/ (- 1.0 y) x))
   (if (<= x 8.5e+185)
     (/ 1.0 x)
     (/ (+ 1.0 (* y (+ -1.0 (/ (* 0.5 (+ y (* x y))) x)))) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.35) {
		tmp = (y * ((y / x) * (0.5 + (y * -0.16666666666666666)))) + ((1.0 - y) / x);
	} else if (x <= 8.5e+185) {
		tmp = 1.0 / x;
	} else {
		tmp = (1.0 + (y * (-1.0 + ((0.5 * (y + (x * y))) / x)))) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.35d0)) then
        tmp = (y * ((y / x) * (0.5d0 + (y * (-0.16666666666666666d0))))) + ((1.0d0 - y) / x)
    else if (x <= 8.5d+185) then
        tmp = 1.0d0 / x
    else
        tmp = (1.0d0 + (y * ((-1.0d0) + ((0.5d0 * (y + (x * y))) / x)))) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.35) {
		tmp = (y * ((y / x) * (0.5 + (y * -0.16666666666666666)))) + ((1.0 - y) / x);
	} else if (x <= 8.5e+185) {
		tmp = 1.0 / x;
	} else {
		tmp = (1.0 + (y * (-1.0 + ((0.5 * (y + (x * y))) / x)))) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.35:
		tmp = (y * ((y / x) * (0.5 + (y * -0.16666666666666666)))) + ((1.0 - y) / x)
	elif x <= 8.5e+185:
		tmp = 1.0 / x
	else:
		tmp = (1.0 + (y * (-1.0 + ((0.5 * (y + (x * y))) / x)))) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.35)
		tmp = Float64(Float64(y * Float64(Float64(y / x) * Float64(0.5 + Float64(y * -0.16666666666666666)))) + Float64(Float64(1.0 - y) / x));
	elseif (x <= 8.5e+185)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(Float64(1.0 + Float64(y * Float64(-1.0 + Float64(Float64(0.5 * Float64(y + Float64(x * y))) / x)))) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.35)
		tmp = (y * ((y / x) * (0.5 + (y * -0.16666666666666666)))) + ((1.0 - y) / x);
	elseif (x <= 8.5e+185)
		tmp = 1.0 / x;
	else
		tmp = (1.0 + (y * (-1.0 + ((0.5 * (y + (x * y))) / x)))) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.35], N[(N[(y * N[(N[(y / x), $MachinePrecision] * N[(0.5 + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e+185], N[(1.0 / x), $MachinePrecision], N[(N[(1.0 + N[(y * N[(-1.0 + N[(N[(0.5 * N[(y + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3500000000000001

   1. Initial program 74.6%

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

      1. *-commutative 74.6%

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

      2. exp-to-pow 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in x around inf 99.6%

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

      1. mul-1-neg 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around 0 75.1%

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

   10. Simplified 75.1%

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

   if -1.3500000000000001 < x < 8.50000000000000013e185

   1. Initial program 82.1%

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

      1. exp-prod 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around 0 88.8%

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

   if 8.50000000000000013e185 < x

   1. Initial program 42.8%

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

      1. exp-prod 42.8%

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

   3. Simplified 42.8%

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

   5. Taylor expanded in y around 0 39.4%

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

   6. Taylor expanded in x around 0 49.2%

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

      1. distribute-lft-out 49.2%

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

   8. Simplified 49.2%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35:\\ \;\;\;\;y \cdot \left(\frac{y}{x} \cdot \left(0.5 + y \cdot -0.16666666666666666\right)\right) + \frac{1 - y}{x}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+185}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + y \cdot \left(-1 + \frac{0.5 \cdot \left(y + x \cdot y\right)}{x}\right)}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.4% accurate, 9.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.85:\\ \;\;\;\;y \cdot \left(\frac{y}{x} \cdot \left(0.5 + y \cdot -0.16666666666666666\right)\right) + \frac{1 - y}{x}\\ \mathbf{elif}\;x \leq 10^{+186}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - y\right)}{x}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.85)
   (+ (* y (* (/ y x) (+ 0.5 (* y -0.16666666666666666)))) (/ (- 1.0 y) x))
   (if (<= x 1e+186) (/ 1.0 x) (/ (/ (* x (- 1.0 y)) x) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.85) {
		tmp = (y * ((y / x) * (0.5 + (y * -0.16666666666666666)))) + ((1.0 - y) / x);
	} else if (x <= 1e+186) {
		tmp = 1.0 / x;
	} else {
		tmp = ((x * (1.0 - y)) / x) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.85d0)) then
        tmp = (y * ((y / x) * (0.5d0 + (y * (-0.16666666666666666d0))))) + ((1.0d0 - y) / x)
    else if (x <= 1d+186) then
        tmp = 1.0d0 / x
    else
        tmp = ((x * (1.0d0 - y)) / x) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.85) {
		tmp = (y * ((y / x) * (0.5 + (y * -0.16666666666666666)))) + ((1.0 - y) / x);
	} else if (x <= 1e+186) {
		tmp = 1.0 / x;
	} else {
		tmp = ((x * (1.0 - y)) / x) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.85:
		tmp = (y * ((y / x) * (0.5 + (y * -0.16666666666666666)))) + ((1.0 - y) / x)
	elif x <= 1e+186:
		tmp = 1.0 / x
	else:
		tmp = ((x * (1.0 - y)) / x) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.85)
		tmp = Float64(Float64(y * Float64(Float64(y / x) * Float64(0.5 + Float64(y * -0.16666666666666666)))) + Float64(Float64(1.0 - y) / x));
	elseif (x <= 1e+186)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(Float64(Float64(x * Float64(1.0 - y)) / x) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.85)
		tmp = (y * ((y / x) * (0.5 + (y * -0.16666666666666666)))) + ((1.0 - y) / x);
	elseif (x <= 1e+186)
		tmp = 1.0 / x;
	else
		tmp = ((x * (1.0 - y)) / x) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.85], N[(N[(y * N[(N[(y / x), $MachinePrecision] * N[(0.5 + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e+186], N[(1.0 / x), $MachinePrecision], N[(N[(N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.849999999999999978

   1. Initial program 74.6%

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

      1. *-commutative 74.6%

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

      2. exp-to-pow 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in x around inf 99.6%

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

      1. mul-1-neg 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around 0 75.1%

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

   10. Simplified 75.1%

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

   if -0.849999999999999978 < x < 9.9999999999999998e185

   1. Initial program 82.1%

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

      1. exp-prod 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around 0 88.8%

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

   if 9.9999999999999998e185 < x

   1. Initial program 42.8%

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

      1. *-commutative 42.8%

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

      2. exp-to-pow 42.8%

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

   3. Simplified 42.8%

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

   5. Taylor expanded in x around inf 78.9%

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

      1. mul-1-neg 78.9%

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

      2. associate-/l* 78.9%

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

      3. mul-1-neg 78.9%

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

      4. distribute-rgt-out 84.2%

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

      5. metadata-eval 84.2%

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

   7. Simplified 84.2%

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

   8. Taylor expanded in x around 0 84.2%

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

      1. associate-*r* 84.2%

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

      2. distribute-rgt-out 84.2%

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

      3. *-commutative 84.2%

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

   10. Simplified 84.2%

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

   11. Taylor expanded in y around 0 49.2%

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

       1. mul-1-neg 49.2%

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

       2. *-commutative 49.2%

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

       3. distribute-lft-neg-in 49.2%

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

       4. distribute-rgt1-in 49.2%

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

       5. +-commutative 49.2%

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

       6. sub-neg 49.2%

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

   13. Simplified 49.2%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.85:\\ \;\;\;\;y \cdot \left(\frac{y}{x} \cdot \left(0.5 + y \cdot -0.16666666666666666\right)\right) + \frac{1 - y}{x}\\ \mathbf{elif}\;x \leq 10^{+186}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - y\right)}{x}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 81.0% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.44 \lor \neg \left(x \leq 1.95 \cdot 10^{+185}\right):\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - y\right)}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.44) (not (<= x 1.95e+185)))
   (/ (/ (* x (- 1.0 y)) x) x)
   (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.44) || !(x <= 1.95e+185)) {
		tmp = ((x * (1.0 - y)) / x) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-0.44d0)) .or. (.not. (x <= 1.95d+185))) then
        tmp = ((x * (1.0d0 - y)) / x) / x
    else
        tmp = 1.0d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -0.44) || !(x <= 1.95e+185)) {
		tmp = ((x * (1.0 - y)) / x) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.44) or not (x <= 1.95e+185):
		tmp = ((x * (1.0 - y)) / x) / x
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.44) || !(x <= 1.95e+185))
		tmp = Float64(Float64(Float64(x * Float64(1.0 - y)) / x) / x);
	else
		tmp = Float64(1.0 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -0.44) || ~((x <= 1.95e+185)))
		tmp = ((x * (1.0 - y)) / x) / x;
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.44], N[Not[LessEqual[x, 1.95e+185]], $MachinePrecision]], N[(N[(N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.440000000000000002 or 1.9499999999999999e185 < x

   1. Initial program 63.1%

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

      1. *-commutative 63.1%

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

      2. exp-to-pow 63.1%

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

   3. Simplified 63.1%

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

   5. Taylor expanded in x around inf 68.5%

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

      1. mul-1-neg 68.5%

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

      2. associate-/l* 68.5%

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

      3. mul-1-neg 68.5%

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

      4. distribute-rgt-out 70.4%

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

      5. metadata-eval 70.4%

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

   7. Simplified 70.4%

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

   8. Taylor expanded in x around 0 70.4%

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

      1. associate-*r* 70.4%

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

      2. distribute-rgt-out 75.2%

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

      3. *-commutative 75.2%

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

   10. Simplified 75.2%

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

   11. Taylor expanded in y around 0 61.8%

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

       1. mul-1-neg 61.8%

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

       2. *-commutative 61.8%

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

       3. distribute-lft-neg-in 61.8%

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

       4. distribute-rgt1-in 61.8%

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

       5. +-commutative 61.8%

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

       6. sub-neg 61.8%

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

   13. Simplified 61.8%

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

   if -0.440000000000000002 < x < 1.9499999999999999e185

   1. Initial program 82.1%

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

      1. exp-prod 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around 0 88.8%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.44 \lor \neg \left(x \leq 1.95 \cdot 10^{+185}\right):\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - y\right)}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 81.0% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.44:\\ \;\;\;\;\frac{\frac{x - x \cdot y}{x}}{x}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+185}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - y\right)}{x}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.44)
   (/ (/ (- x (* x y)) x) x)
   (if (<= x 1.05e+185) (/ 1.0 x) (/ (/ (* x (- 1.0 y)) x) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.44) {
		tmp = ((x - (x * y)) / x) / x;
	} else if (x <= 1.05e+185) {
		tmp = 1.0 / x;
	} else {
		tmp = ((x * (1.0 - y)) / x) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.44d0)) then
        tmp = ((x - (x * y)) / x) / x
    else if (x <= 1.05d+185) then
        tmp = 1.0d0 / x
    else
        tmp = ((x * (1.0d0 - y)) / x) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.44) {
		tmp = ((x - (x * y)) / x) / x;
	} else if (x <= 1.05e+185) {
		tmp = 1.0 / x;
	} else {
		tmp = ((x * (1.0 - y)) / x) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.44:
		tmp = ((x - (x * y)) / x) / x
	elif x <= 1.05e+185:
		tmp = 1.0 / x
	else:
		tmp = ((x * (1.0 - y)) / x) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.44)
		tmp = Float64(Float64(Float64(x - Float64(x * y)) / x) / x);
	elseif (x <= 1.05e+185)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(Float64(Float64(x * Float64(1.0 - y)) / x) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.44)
		tmp = ((x - (x * y)) / x) / x;
	elseif (x <= 1.05e+185)
		tmp = 1.0 / x;
	else
		tmp = ((x * (1.0 - y)) / x) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.44], N[(N[(N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 1.05e+185], N[(1.0 / x), $MachinePrecision], N[(N[(N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.440000000000000002

   1. Initial program 74.6%

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

      1. *-commutative 74.6%

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

      2. exp-to-pow 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in x around inf 62.7%

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

      1. mul-1-neg 62.7%

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

      2. associate-/l* 62.7%

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

      3. mul-1-neg 62.7%

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

      4. distribute-rgt-out 62.7%

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

      5. metadata-eval 62.7%

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

   7. Simplified 62.7%

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

   8. Taylor expanded in x around 0 62.6%

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

      1. associate-*r* 62.6%

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

      2. distribute-rgt-out 70.1%

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

      3. *-commutative 70.1%

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

   10. Simplified 70.1%

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

   11. Taylor expanded in y around 0 69.0%

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

       1. mul-1-neg 69.0%

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

       2. sub-neg 69.0%

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

   13. Simplified 69.0%

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

   if -0.440000000000000002 < x < 1.05e185

   1. Initial program 82.1%

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

      1. exp-prod 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around 0 88.8%

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

   if 1.05e185 < x

   1. Initial program 42.8%

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

      1. *-commutative 42.8%

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

      2. exp-to-pow 42.8%

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

   3. Simplified 42.8%

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

   5. Taylor expanded in x around inf 78.9%

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

      1. mul-1-neg 78.9%

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

      2. associate-/l* 78.9%

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

      3. mul-1-neg 78.9%

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

      4. distribute-rgt-out 84.2%

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

      5. metadata-eval 84.2%

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

   7. Simplified 84.2%

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

   8. Taylor expanded in x around 0 84.2%

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

      1. associate-*r* 84.2%

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

      2. distribute-rgt-out 84.2%

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

      3. *-commutative 84.2%

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

   10. Simplified 84.2%

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

   11. Taylor expanded in y around 0 49.2%

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

       1. mul-1-neg 49.2%

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

       2. *-commutative 49.2%

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

       3. distribute-lft-neg-in 49.2%

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

       4. distribute-rgt1-in 49.2%

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

       5. +-commutative 49.2%

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

       6. sub-neg 49.2%

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

   13. Simplified 49.2%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.44:\\ \;\;\;\;\frac{\frac{x - x \cdot y}{x}}{x}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+185}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - y\right)}{x}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.4% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.7:\\ \;\;\;\;\frac{1 + y \cdot \left(-1 + y \cdot 0.5\right)}{x}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+185}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - y\right)}{x}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.7)
   (/ (+ 1.0 (* y (+ -1.0 (* y 0.5)))) x)
   (if (<= x 1.2e+185) (/ 1.0 x) (/ (/ (* x (- 1.0 y)) x) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.7) {
		tmp = (1.0 + (y * (-1.0 + (y * 0.5)))) / x;
	} else if (x <= 1.2e+185) {
		tmp = 1.0 / x;
	} else {
		tmp = ((x * (1.0 - y)) / x) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.7d0)) then
        tmp = (1.0d0 + (y * ((-1.0d0) + (y * 0.5d0)))) / x
    else if (x <= 1.2d+185) then
        tmp = 1.0d0 / x
    else
        tmp = ((x * (1.0d0 - y)) / x) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.7) {
		tmp = (1.0 + (y * (-1.0 + (y * 0.5)))) / x;
	} else if (x <= 1.2e+185) {
		tmp = 1.0 / x;
	} else {
		tmp = ((x * (1.0 - y)) / x) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.7:
		tmp = (1.0 + (y * (-1.0 + (y * 0.5)))) / x
	elif x <= 1.2e+185:
		tmp = 1.0 / x
	else:
		tmp = ((x * (1.0 - y)) / x) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.7)
		tmp = Float64(Float64(1.0 + Float64(y * Float64(-1.0 + Float64(y * 0.5)))) / x);
	elseif (x <= 1.2e+185)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(Float64(Float64(x * Float64(1.0 - y)) / x) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.7)
		tmp = (1.0 + (y * (-1.0 + (y * 0.5)))) / x;
	elseif (x <= 1.2e+185)
		tmp = 1.0 / x;
	else
		tmp = ((x * (1.0 - y)) / x) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.7], N[(N[(1.0 + N[(y * N[(-1.0 + N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 1.2e+185], N[(1.0 / x), $MachinePrecision], N[(N[(N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.69999999999999996

   1. Initial program 74.6%

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

      1. exp-prod 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in y around 0 74.9%

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

   6. Taylor expanded in x around inf 74.9%

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

      1. *-commutative 74.9%

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

   8. Simplified 74.9%

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

   if -0.69999999999999996 < x < 1.19999999999999995e185

   1. Initial program 82.1%

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

      1. exp-prod 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around 0 88.8%

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

   if 1.19999999999999995e185 < x

   1. Initial program 42.8%

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

      1. *-commutative 42.8%

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

      2. exp-to-pow 42.8%

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

   3. Simplified 42.8%

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

   5. Taylor expanded in x around inf 78.9%

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

      1. mul-1-neg 78.9%

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

      2. associate-/l* 78.9%

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

      3. mul-1-neg 78.9%

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

      4. distribute-rgt-out 84.2%

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

      5. metadata-eval 84.2%

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

   7. Simplified 84.2%

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

   8. Taylor expanded in x around 0 84.2%

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

      1. associate-*r* 84.2%

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

      2. distribute-rgt-out 84.2%

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

      3. *-commutative 84.2%

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

   10. Simplified 84.2%

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

   11. Taylor expanded in y around 0 49.2%

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

       1. mul-1-neg 49.2%

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

       2. *-commutative 49.2%

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

       3. distribute-lft-neg-in 49.2%

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

       4. distribute-rgt1-in 49.2%

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

       5. +-commutative 49.2%

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

       6. sub-neg 49.2%

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

   13. Simplified 49.2%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.7:\\ \;\;\;\;\frac{1 + y \cdot \left(-1 + y \cdot 0.5\right)}{x}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+185}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - y\right)}{x}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.1% 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 74.3%

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

   1. exp-prod 83.9%

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

3. Simplified 83.9%

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

5. Taylor expanded in x around 0 71.3%

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

6. Final simplification 71.3%

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

Developer target: 77.7% 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 2024115 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, F"
  :precision binary64

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

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