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

Percentage Accurate: 77.8% → 99.6%

Time: 13.4s

Alternatives: 10

Speedup: 12.3×

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: 77.8% 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: 99.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+67} \lor \neg \left(x \leq 1\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5e+67) (not (<= x 1.0)))
   (/ (exp (- y)) x)
   (/ (pow (exp x) (log (/ x (+ x y)))) x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5e+67) || !(x <= 1.0)) {
		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 <= (-5d+67)) .or. (.not. (x <= 1.0d0))) 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 <= -5e+67) || !(x <= 1.0)) {
		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 <= -5e+67) or not (x <= 1.0):
		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 <= -5e+67) || !(x <= 1.0))
		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 <= -5e+67) || ~((x <= 1.0)))
		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, -5e+67], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision], N[(N[Power[N[Exp[x], $MachinePrecision], N[Log[N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.99999999999999976e67 or 1 < x

   1. Initial program 74.8%

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

      1. *-commutative 74.8%

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

      2. exp-to-pow 74.8%

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

   3. Simplified 74.8%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   if -4.99999999999999976e67 < x < 1

   1. Initial program 87.7%

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

      1. exp-prod 99.7%

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

   3. Simplified 99.7%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+67} \lor \neg \left(x \leq 1\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \lor \neg \left(x \leq 0.05\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -7.0) (not (<= x 0.05))) (/ (exp (- y)) x) (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -7.0) || !(x <= 0.05)) {
		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 <= (-7.0d0)) .or. (.not. (x <= 0.05d0))) 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 <= -7.0) || !(x <= 0.05)) {
		tmp = Math.exp(-y) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -7.0) or not (x <= 0.05):
		tmp = math.exp(-y) / x
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -7.0) || !(x <= 0.05))
		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 <= -7.0) || ~((x <= 0.05)))
		tmp = exp(-y) / x;
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -7.0], N[Not[LessEqual[x, 0.05]], $MachinePrecision]], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7 or 0.050000000000000003 < x

   1. Initial program 76.7%

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

      1. *-commutative 76.7%

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

      2. exp-to-pow 76.7%

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

   3. Simplified 76.7%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   if -7 < x < 0.050000000000000003

   1. Initial program 86.5%

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

      1. exp-prod 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 98.0%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \lor \neg \left(x \leq 0.05\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.7% accurate, 7.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4:\\ \;\;\;\;\frac{1}{x} + \frac{y \cdot \left(y \cdot \left(0.5 + y \cdot -0.16666666666666666\right) + -1\right)}{x}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + y \cdot \left(x + y \cdot \left(0.16666666666666666 \cdot \left(x \cdot y\right) + x \cdot 0.5\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.4)
   (+ (/ 1.0 x) (/ (* y (+ (* y (+ 0.5 (* y -0.16666666666666666))) -1.0)) x))
   (if (<= x 1.0)
     (/ 1.0 x)
     (/
      1.0
      (+ x (* y (+ x (* y (+ (* 0.16666666666666666 (* x y)) (* x 0.5))))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.4) {
		tmp = (1.0 / x) + ((y * ((y * (0.5 + (y * -0.16666666666666666))) + -1.0)) / x);
	} else if (x <= 1.0) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (y * (x + (y * ((0.16666666666666666 * (x * y)) + (x * 0.5))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-6.4d0)) then
        tmp = (1.0d0 / x) + ((y * ((y * (0.5d0 + (y * (-0.16666666666666666d0)))) + (-1.0d0))) / x)
    else if (x <= 1.0d0) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (x + (y * (x + (y * ((0.16666666666666666d0 * (x * y)) + (x * 0.5d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.4) {
		tmp = (1.0 / x) + ((y * ((y * (0.5 + (y * -0.16666666666666666))) + -1.0)) / x);
	} else if (x <= 1.0) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (y * (x + (y * ((0.16666666666666666 * (x * y)) + (x * 0.5))))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.4:
		tmp = (1.0 / x) + ((y * ((y * (0.5 + (y * -0.16666666666666666))) + -1.0)) / x)
	elif x <= 1.0:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (y * (x + (y * ((0.16666666666666666 * (x * y)) + (x * 0.5))))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.4)
		tmp = Float64(Float64(1.0 / x) + Float64(Float64(y * Float64(Float64(y * Float64(0.5 + Float64(y * -0.16666666666666666))) + -1.0)) / x));
	elseif (x <= 1.0)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(x + Float64(y * Float64(x + Float64(y * Float64(Float64(0.16666666666666666 * Float64(x * y)) + Float64(x * 0.5)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.4)
		tmp = (1.0 / x) + ((y * ((y * (0.5 + (y * -0.16666666666666666))) + -1.0)) / x);
	elseif (x <= 1.0)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (y * (x + (y * ((0.16666666666666666 * (x * y)) + (x * 0.5))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.4], N[(N[(1.0 / x), $MachinePrecision] + N[(N[(y * N[(N[(y * N[(0.5 + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x + N[(y * N[(x + N[(y * N[(N[(0.16666666666666666 * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.4000000000000004

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

      2. exp-to-pow 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 77.8%

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

   9. Taylor expanded in x around 0 81.5%

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

   if -6.4000000000000004 < x < 1

   1. Initial program 86.5%

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

      1. exp-prod 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 98.0%

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

   if 1 < x

   1. Initial program 72.0%

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

      1. *-commutative 72.0%

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

      2. exp-to-pow 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

      \[\leadsto \frac{\color{blue}{e^{-y}}}{x} \]
   8. 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. exp-neg 99.9%

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

      4. associate-/r/ 99.9%

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

      5. /-rgt-identity 99.9%

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

   9. Applied egg-rr 99.9%

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

   10. Taylor expanded in x around 0 99.9%

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

   11. Taylor expanded in y around 0 78.7%

       \[\leadsto \frac{1}{\color{blue}{x + y \cdot \left(x + y \cdot \left(0.16666666666666666 \cdot \left(x \cdot y\right) + 0.5 \cdot x\right)\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4:\\ \;\;\;\;\frac{1}{x} + \frac{y \cdot \left(y \cdot \left(0.5 + y \cdot -0.16666666666666666\right) + -1\right)}{x}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + y \cdot \left(x + y \cdot \left(0.16666666666666666 \cdot \left(x \cdot y\right) + x \cdot 0.5\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 9.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot 0.5 + -1\right)}{x}\\ \mathbf{elif}\;x \leq 0.36:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + y \cdot \left(x + y \cdot \left(x \cdot 0.5\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.4)
   (/ (+ 1.0 (* y (+ (* y 0.5) -1.0))) x)
   (if (<= x 0.36) (/ 1.0 x) (/ 1.0 (+ x (* y (+ x (* y (* x 0.5)))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.4) {
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	} else if (x <= 0.36) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (y * (x + (y * (x * 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-6.4d0)) then
        tmp = (1.0d0 + (y * ((y * 0.5d0) + (-1.0d0)))) / x
    else if (x <= 0.36d0) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (x + (y * (x + (y * (x * 0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.4) {
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	} else if (x <= 0.36) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (y * (x + (y * (x * 0.5)))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.4:
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x
	elif x <= 0.36:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (y * (x + (y * (x * 0.5)))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.4)
		tmp = Float64(Float64(1.0 + Float64(y * Float64(Float64(y * 0.5) + -1.0))) / x);
	elseif (x <= 0.36)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(x + Float64(y * Float64(x + Float64(y * Float64(x * 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.4)
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	elseif (x <= 0.36)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (y * (x + (y * (x * 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.4], N[(N[(1.0 + N[(y * N[(N[(y * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 0.36], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x + N[(y * N[(x + N[(y * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.4000000000000004

   1. Initial program 81.6%

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

      1. exp-prod 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in y around 0 78.9%

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

   6. Taylor expanded in x around inf 78.9%

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

      1. *-commutative 78.9%

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

   8. Simplified 78.9%

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

   if -6.4000000000000004 < x < 0.35999999999999999

   1. Initial program 86.5%

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

      1. exp-prod 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 98.0%

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

   if 0.35999999999999999 < x

   1. Initial program 72.0%

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

      1. *-commutative 72.0%

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

      2. exp-to-pow 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

      \[\leadsto \frac{\color{blue}{e^{-y}}}{x} \]
   8. 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. exp-neg 99.9%

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

      4. associate-/r/ 99.9%

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

      5. /-rgt-identity 99.9%

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

   9. Applied egg-rr 99.9%

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

   10. Taylor expanded in x around 0 99.9%

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

   11. Taylor expanded in y around 0 78.3%

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

       1. associate-*r* 78.3%

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

       2. *-commutative 78.3%

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

   13. Simplified 78.3%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot 0.5 + -1\right)}{x}\\ \mathbf{elif}\;x \leq 0.36:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + y \cdot \left(x + y \cdot \left(x \cdot 0.5\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.1% accurate, 9.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4:\\ \;\;\;\;\frac{1}{x} + \frac{y \cdot \left(y \cdot \left(0.5 + y \cdot -0.16666666666666666\right) + -1\right)}{x}\\ \mathbf{elif}\;x \leq 0.05:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + y \cdot \left(x + y \cdot \left(x \cdot 0.5\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.4)
   (+ (/ 1.0 x) (/ (* y (+ (* y (+ 0.5 (* y -0.16666666666666666))) -1.0)) x))
   (if (<= x 0.05) (/ 1.0 x) (/ 1.0 (+ x (* y (+ x (* y (* x 0.5)))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.4) {
		tmp = (1.0 / x) + ((y * ((y * (0.5 + (y * -0.16666666666666666))) + -1.0)) / x);
	} else if (x <= 0.05) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (y * (x + (y * (x * 0.5)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-6.4d0)) then
        tmp = (1.0d0 / x) + ((y * ((y * (0.5d0 + (y * (-0.16666666666666666d0)))) + (-1.0d0))) / x)
    else if (x <= 0.05d0) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (x + (y * (x + (y * (x * 0.5d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.4) {
		tmp = (1.0 / x) + ((y * ((y * (0.5 + (y * -0.16666666666666666))) + -1.0)) / x);
	} else if (x <= 0.05) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (y * (x + (y * (x * 0.5)))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.4:
		tmp = (1.0 / x) + ((y * ((y * (0.5 + (y * -0.16666666666666666))) + -1.0)) / x)
	elif x <= 0.05:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (y * (x + (y * (x * 0.5)))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.4)
		tmp = Float64(Float64(1.0 / x) + Float64(Float64(y * Float64(Float64(y * Float64(0.5 + Float64(y * -0.16666666666666666))) + -1.0)) / x));
	elseif (x <= 0.05)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(x + Float64(y * Float64(x + Float64(y * Float64(x * 0.5))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.4)
		tmp = (1.0 / x) + ((y * ((y * (0.5 + (y * -0.16666666666666666))) + -1.0)) / x);
	elseif (x <= 0.05)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (y * (x + (y * (x * 0.5)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.4], N[(N[(1.0 / x), $MachinePrecision] + N[(N[(y * N[(N[(y * N[(0.5 + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.05], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x + N[(y * N[(x + N[(y * N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.4000000000000004

   1. Initial program 81.6%

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

      1. *-commutative 81.6%

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

      2. exp-to-pow 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 77.8%

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

   9. Taylor expanded in x around 0 81.5%

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

   if -6.4000000000000004 < x < 0.050000000000000003

   1. Initial program 86.5%

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

      1. exp-prod 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 98.0%

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

   if 0.050000000000000003 < x

   1. Initial program 72.0%

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

      1. *-commutative 72.0%

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

      2. exp-to-pow 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

      \[\leadsto \frac{\color{blue}{e^{-y}}}{x} \]
   8. 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. exp-neg 99.9%

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

      4. associate-/r/ 99.9%

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

      5. /-rgt-identity 99.9%

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

   9. Applied egg-rr 99.9%

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

   10. Taylor expanded in x around 0 99.9%

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

   11. Taylor expanded in y around 0 78.3%

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

       1. associate-*r* 78.3%

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

       2. *-commutative 78.3%

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

   13. Simplified 78.3%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4:\\ \;\;\;\;\frac{1}{x} + \frac{y \cdot \left(y \cdot \left(0.5 + y \cdot -0.16666666666666666\right) + -1\right)}{x}\\ \mathbf{elif}\;x \leq 0.05:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + y \cdot \left(x + y \cdot \left(x \cdot 0.5\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.2% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+177} \lor \neg \left(x \leq 0.005\right):\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.25e+177) (not (<= x 0.005)))
   (/ 1.0 (+ x (* x y)))
   (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.25e+177) || !(x <= 0.005)) {
		tmp = 1.0 / (x + (x * y));
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.25d+177)) .or. (.not. (x <= 0.005d0))) then
        tmp = 1.0d0 / (x + (x * y))
    else
        tmp = 1.0d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.25e+177) || !(x <= 0.005)) {
		tmp = 1.0 / (x + (x * y));
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.25e+177) or not (x <= 0.005):
		tmp = 1.0 / (x + (x * y))
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.25e+177) || !(x <= 0.005))
		tmp = Float64(1.0 / Float64(x + Float64(x * y)));
	else
		tmp = Float64(1.0 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.25e+177) || ~((x <= 0.005)))
		tmp = 1.0 / (x + (x * y));
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.25e+177], N[Not[LessEqual[x, 0.005]], $MachinePrecision]], N[(1.0 / N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2500000000000001e177 or 0.0050000000000000001 < x

   1. Initial program 72.4%

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

      1. *-commutative 72.4%

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

      2. exp-to-pow 72.4%

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

   3. Simplified 72.4%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

      \[\leadsto \frac{\color{blue}{e^{-y}}}{x} \]
   8. 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. exp-neg 99.9%

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

      4. associate-/r/ 99.9%

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

      5. /-rgt-identity 99.9%

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

   9. Applied egg-rr 99.9%

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

   10. Taylor expanded in x around 0 99.9%

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

   11. Taylor expanded in y around 0 68.0%

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

   if -1.2500000000000001e177 < x < 0.0050000000000000001

   1. Initial program 87.3%

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

      1. exp-prod 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in x around 0 88.3%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+177} \lor \neg \left(x \leq 0.005\right):\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.6% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4:\\ \;\;\;\;\frac{\frac{x - x \cdot y}{x}}{x}\\ \mathbf{elif}\;x \leq 0.00035:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.4)
   (/ (/ (- x (* x y)) x) x)
   (if (<= x 0.00035) (/ 1.0 x) (/ 1.0 (+ x (* x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.4) {
		tmp = ((x - (x * y)) / x) / x;
	} else if (x <= 0.00035) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-6.4d0)) then
        tmp = ((x - (x * y)) / x) / x
    else if (x <= 0.00035d0) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (x + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.4) {
		tmp = ((x - (x * y)) / x) / x;
	} else if (x <= 0.00035) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (x * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.4:
		tmp = ((x - (x * y)) / x) / x
	elif x <= 0.00035:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (x * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.4)
		tmp = Float64(Float64(Float64(x - Float64(x * y)) / x) / x);
	elseif (x <= 0.00035)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(x + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.4)
		tmp = ((x - (x * y)) / x) / x;
	elseif (x <= 0.00035)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.4], N[(N[(N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 0.00035], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.4000000000000004

   1. Initial program 81.6%

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

      1. exp-prod 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in y around 0 60.2%

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

      1. +-commutative 60.2%

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

      2. mul-1-neg 60.2%

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

      3. unsub-neg 60.2%

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

   7. Simplified 60.2%

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

      1. frac-sub 31.7%

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

      2. associate-/r* 70.5%

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

      3. *-un-lft-identity 70.5%

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

      4. *-commutative 70.5%

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

   9. Applied egg-rr 70.5%

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

   if -6.4000000000000004 < x < 3.49999999999999996e-4

   1. Initial program 86.5%

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

      1. exp-prod 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 98.0%

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

   if 3.49999999999999996e-4 < x

   1. Initial program 72.0%

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

      1. *-commutative 72.0%

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

      2. exp-to-pow 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

      \[\leadsto \frac{\color{blue}{e^{-y}}}{x} \]
   8. 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. exp-neg 99.9%

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

      4. associate-/r/ 99.9%

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

      5. /-rgt-identity 99.9%

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

   9. Applied egg-rr 99.9%

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

   10. Taylor expanded in x around 0 99.9%

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

   11. Taylor expanded in y around 0 66.2%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4:\\ \;\;\;\;\frac{\frac{x - x \cdot y}{x}}{x}\\ \mathbf{elif}\;x \leq 0.00035:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.7% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot 0.5 + -1\right)}{x}\\ \mathbf{elif}\;x \leq 0.045:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.4)
   (/ (+ 1.0 (* y (+ (* y 0.5) -1.0))) x)
   (if (<= x 0.045) (/ 1.0 x) (/ 1.0 (+ x (* x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.4) {
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	} else if (x <= 0.045) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (x * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-6.4d0)) then
        tmp = (1.0d0 + (y * ((y * 0.5d0) + (-1.0d0)))) / x
    else if (x <= 0.045d0) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (x + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.4) {
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	} else if (x <= 0.045) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (x * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.4:
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x
	elif x <= 0.045:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (x * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.4)
		tmp = Float64(Float64(1.0 + Float64(y * Float64(Float64(y * 0.5) + -1.0))) / x);
	elseif (x <= 0.045)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(x + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.4)
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	elseif (x <= 0.045)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.4], N[(N[(1.0 + N[(y * N[(N[(y * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 0.045], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.4000000000000004

   1. Initial program 81.6%

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

      1. exp-prod 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in y around 0 78.9%

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

   6. Taylor expanded in x around inf 78.9%

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

      1. *-commutative 78.9%

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

   8. Simplified 78.9%

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

   if -6.4000000000000004 < x < 0.044999999999999998

   1. Initial program 86.5%

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

      1. exp-prod 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 98.0%

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

   if 0.044999999999999998 < x

   1. Initial program 72.0%

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

      1. *-commutative 72.0%

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

      2. exp-to-pow 72.0%

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

   3. Simplified 72.0%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   7. Simplified 100.0%

      \[\leadsto \frac{\color{blue}{e^{-y}}}{x} \]
   8. 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. exp-neg 99.9%

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

      4. associate-/r/ 99.9%

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

      5. /-rgt-identity 99.9%

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

   9. Applied egg-rr 99.9%

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

   10. Taylor expanded in x around 0 99.9%

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

   11. Taylor expanded in y around 0 66.2%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot 0.5 + -1\right)}{x}\\ \mathbf{elif}\;x \leq 0.045:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.5% accurate, 23.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -2.2e+128) (* x (- y)) (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.2e+128) {
		tmp = x * -y;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-2.2d+128)) then
        tmp = x * -y
    else
        tmp = 1.0d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.2e+128) {
		tmp = x * -y;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.2e+128:
		tmp = x * -y
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.2e+128)
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(1.0 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.2e+128)
		tmp = x * -y;
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.2e+128], N[(x * (-y)), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.20000000000000017e128

   1. Initial program 68.2%

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

      1. exp-prod 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in y around 0 4.3%

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

      1. +-commutative 4.3%

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

      2. mul-1-neg 4.3%

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

      3. unsub-neg 4.3%

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

   7. Simplified 4.3%

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

      1. clear-num 4.3%

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

      2. frac-sub 4.2%

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

      3. *-un-lft-identity 4.2%

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

      4. *-commutative 4.2%

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

      5. *-un-lft-identity 4.2%

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

   9. Applied egg-rr 4.2%

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

   10. Taylor expanded in y around inf 4.2%

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

       1. neg-mul-1 4.2%

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

   12. Simplified 4.2%

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

   14. Applied egg-rr 48.1%

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

   if -2.20000000000000017e128 < y

   1. Initial program 82.2%

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

      1. exp-prod 85.9%

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

   3. Simplified 85.9%

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

   5. Taylor expanded in x around 0 79.2%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+128}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.4% 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 80.7%

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

   1. exp-prod 86.2%

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

3. Simplified 86.2%

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

5. Taylor expanded in x around 0 73.4%

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

6. Final simplification 73.4%

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

Developer target: 77.9% 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 2024078 
(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))