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

Percentage Accurate: 77.7% → 99.1%

Time: 9.0s

Alternatives: 7

Speedup: 23.1×

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: 77.7% 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: 99.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+61} \lor \neg \left(x \leq 6.5 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4e+61) (not (<= x 6.5e-15)))
   (/ (exp (- y)) x)
   (/ (pow (exp x) (log (/ x (+ x y)))) x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4e+61) || !(x <= 6.5e-15)) {
		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 <= (-4d+61)) .or. (.not. (x <= 6.5d-15))) 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 <= -4e+61) || !(x <= 6.5e-15)) {
		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 <= -4e+61) or not (x <= 6.5e-15):
		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 <= -4e+61) || !(x <= 6.5e-15))
		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 <= -4e+61) || ~((x <= 6.5e-15)))
		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, -4e+61], N[Not[LessEqual[x, 6.5e-15]], $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 < -3.9999999999999998e61 or 6.49999999999999991e-15 < x

   1. Initial program 77.0%

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

      1. *-commutative 77.0%

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

      2. exp-to-pow 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

   if -3.9999999999999998e61 < x < 6.49999999999999991e-15

   1. Initial program 86.1%

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

      1. exp-prod 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+61} \lor \neg \left(x \leq 6.5 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \end{array} \]

Alternative 2: 99.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.78 \lor \neg \left(x \leq 6.8 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.78) (not (<= x 6.8e-15))) (/ (exp (- y)) x) (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.78) || !(x <= 6.8e-15)) {
		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 <= (-0.78d0)) .or. (.not. (x <= 6.8d-15))) 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 <= -0.78) || !(x <= 6.8e-15)) {
		tmp = Math.exp(-y) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.78) or not (x <= 6.8e-15):
		tmp = math.exp(-y) / x
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.78) || !(x <= 6.8e-15))
		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 <= -0.78) || ~((x <= 6.8e-15)))
		tmp = exp(-y) / x;
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.78], N[Not[LessEqual[x, 6.8e-15]], $MachinePrecision]], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.78000000000000003 or 6.8000000000000001e-15 < x

   1. Initial program 79.3%

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

      1. *-commutative 79.3%

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

      2. exp-to-pow 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

   if -0.78000000000000003 < x < 6.8000000000000001e-15

   1. Initial program 84.4%

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

      1. exp-prod 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 99.5%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.78 \lor \neg \left(x \leq 6.8 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]

Alternative 3: 82.8% accurate, 16.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.8:\\ \;\;\;\;\frac{1 - y}{x} + \frac{y \cdot y}{x}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \left(y + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.8)
   (+ (/ (- 1.0 y) x) (/ (* y y) x))
   (if (<= x 6.8e-15) (/ 1.0 x) (/ 1.0 (* x (+ y 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.8) {
		tmp = ((1.0 - y) / x) + ((y * y) / x);
	} else if (x <= 6.8e-15) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x * (y + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.8d0)) then
        tmp = ((1.0d0 - y) / x) + ((y * y) / x)
    else if (x <= 6.8d-15) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (x * (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.8) {
		tmp = ((1.0 - y) / x) + ((y * y) / x);
	} else if (x <= 6.8e-15) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x * (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.8:
		tmp = ((1.0 - y) / x) + ((y * y) / x)
	elif x <= 6.8e-15:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x * (y + 1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.8)
		tmp = Float64(Float64(Float64(1.0 - y) / x) + Float64(Float64(y * y) / x));
	elseif (x <= 6.8e-15)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(x * Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.8)
		tmp = ((1.0 - y) / x) + ((y * y) / x);
	elseif (x <= 6.8e-15)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x * (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.8], N[(N[(N[(1.0 - y), $MachinePrecision] / x), $MachinePrecision] + N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e-15], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.80000000000000004

   1. Initial program 79.7%

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

      1. exp-prod 79.7%

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

   3. Simplified 79.7%

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

      1. clear-num 79.7%

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

      2. inv-pow 79.7%

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

      3. add-exp-log 79.7%

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

      4. log-pow 20.0%

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

      5. add-log-exp 79.7%

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

      6. pow-to-exp 79.7%

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

   5. Applied egg-rr 79.7%

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

      1. unpow-1 79.7%

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

      2. +-commutative 79.7%

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

   7. Simplified 79.7%

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

   8. Taylor expanded in y around 0 62.8%

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

   9. Taylor expanded in y around 0 74.1%

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

       1. +-commutative 74.1%

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

       2. neg-mul-1 74.1%

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

       3. sub-neg 74.1%

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

       4. div-sub 74.1%

          \[\leadsto \color{blue}{\frac{1 - y}{x}} + \frac{{y}^{2}}{x} \]

       5. unpow2 74.1%

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

   11. Simplified 74.1%

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

   if -0.80000000000000004 < x < 6.8000000000000001e-15

   1. Initial program 84.4%

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

      1. exp-prod 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 99.5%

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

   if 6.8000000000000001e-15 < x

   1. Initial program 79.0%

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

      1. exp-prod 79.0%

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

   3. Simplified 79.0%

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

      1. clear-num 79.0%

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

      2. inv-pow 79.0%

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

      3. add-exp-log 79.0%

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

      4. log-pow 20.3%

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

      5. add-log-exp 79.0%

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

      6. pow-to-exp 79.0%

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

   5. Applied egg-rr 79.0%

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

      1. unpow-1 79.0%

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

      2. +-commutative 79.0%

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

   7. Simplified 79.0%

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

   8. Taylor expanded in y around 0 74.4%

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

   9. Taylor expanded in x around 0 74.4%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.8:\\ \;\;\;\;\frac{1 - y}{x} + \frac{y \cdot y}{x}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \left(y + 1\right)}\\ \end{array} \]

Alternative 4: 82.8% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.65:\\ \;\;\;\;\frac{\frac{x - x \cdot y}{x}}{x}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \left(y + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.65)
   (/ (/ (- x (* x y)) x) x)
   (if (<= x 6.8e-15) (/ 1.0 x) (/ 1.0 (* x (+ y 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.65) {
		tmp = ((x - (x * y)) / x) / x;
	} else if (x <= 6.8e-15) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x * (y + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.65d0)) then
        tmp = ((x - (x * y)) / x) / x
    else if (x <= 6.8d-15) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (x * (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.65) {
		tmp = ((x - (x * y)) / x) / x;
	} else if (x <= 6.8e-15) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x * (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.65:
		tmp = ((x - (x * y)) / x) / x
	elif x <= 6.8e-15:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x * (y + 1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.65)
		tmp = Float64(Float64(Float64(x - Float64(x * y)) / x) / x);
	elseif (x <= 6.8e-15)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(x * Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.65)
		tmp = ((x - (x * y)) / x) / x;
	elseif (x <= 6.8e-15)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x * (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.65], N[(N[(N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 6.8e-15], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.650000000000000022

   1. Initial program 79.7%

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

      1. exp-prod 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in x around inf 60.5%

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

      1. mul-1-neg 60.5%

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

      2. unsub-neg 60.5%

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

   6. Simplified 60.5%

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

      1. frac-sub 34.7%

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

      2. associate-/r* 72.8%

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

      3. *-commutative 72.8%

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

      4. *-un-lft-identity 72.8%

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

   8. Applied egg-rr 72.8%

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

   if -0.650000000000000022 < x < 6.8000000000000001e-15

   1. Initial program 84.4%

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

      1. exp-prod 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 99.5%

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

   if 6.8000000000000001e-15 < x

   1. Initial program 79.0%

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

      1. exp-prod 79.0%

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

   3. Simplified 79.0%

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

      1. clear-num 79.0%

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

      2. inv-pow 79.0%

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

      3. add-exp-log 79.0%

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

      4. log-pow 20.3%

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

      5. add-log-exp 79.0%

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

      6. pow-to-exp 79.0%

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

   5. Applied egg-rr 79.0%

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

      1. unpow-1 79.0%

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

      2. +-commutative 79.0%

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

   7. Simplified 79.0%

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

   8. Taylor expanded in y around 0 74.4%

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

   9. Taylor expanded in x around 0 74.4%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.65:\\ \;\;\;\;\frac{\frac{x - x \cdot y}{x}}{x}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \left(y + 1\right)}\\ \end{array} \]

Alternative 5: 74.8% accurate, 20.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+195}:\\ \;\;\;\;\frac{\frac{-x \cdot y}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.75e+195) (/ (/ (- (* x y)) x) x) (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.75e+195) {
		tmp = (-(x * 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 (y <= (-1.75d+195)) then
        tmp = (-(x * 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 (y <= -1.75e+195) {
		tmp = (-(x * y) / x) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.75e+195:
		tmp = (-(x * y) / x) / x
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.75e+195)
		tmp = Float64(Float64(Float64(-Float64(x * y)) / x) / x);
	else
		tmp = Float64(1.0 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.75e+195)
		tmp = (-(x * y) / x) / x;
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.75e+195], N[(N[((-N[(x * y), $MachinePrecision]) / x), $MachinePrecision] / x), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7500000000000001e195

   1. Initial program 54.7%

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

      1. exp-prod 73.3%

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

   3. Simplified 73.3%

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

   4. Taylor expanded in x around inf 4.5%

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

      1. mul-1-neg 4.5%

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

      2. unsub-neg 4.5%

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

   6. Simplified 4.5%

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

      1. frac-sub 28.7%

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

      2. associate-/r* 68.7%

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

      3. *-commutative 68.7%

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

      4. *-un-lft-identity 68.7%

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

   8. Applied egg-rr 68.7%

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

   9. Taylor expanded in y around inf 68.7%

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

       1. associate-*r* 68.7%

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

       2. neg-mul-1 68.7%

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

   11. Simplified 68.7%

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

   if -1.7500000000000001e195 < y

   1. Initial program 83.3%

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

      1. exp-prod 89.7%

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

   3. Simplified 89.7%

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

   4. Taylor expanded in x around 0 82.5%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{+195}:\\ \;\;\;\;\frac{\frac{-x \cdot y}{x}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]

Alternative 6: 78.6% accurate, 23.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \left(y + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 6.8e-15) (/ 1.0 x) (/ 1.0 (* x (+ y 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 6.8e-15) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x * (y + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 6.8d-15) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (x * (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 6.8e-15) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x * (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 6.8e-15:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x * (y + 1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 6.8e-15)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(x * Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 6.8e-15)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x * (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 6.8e-15], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.8000000000000001e-15

   1. Initial program 82.6%

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

      1. exp-prod 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around 0 84.8%

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

   if 6.8000000000000001e-15 < x

   1. Initial program 79.0%

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

      1. exp-prod 79.0%

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

   3. Simplified 79.0%

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

      1. clear-num 79.0%

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

      2. inv-pow 79.0%

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

      3. add-exp-log 79.0%

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

      4. log-pow 20.3%

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

      5. add-log-exp 79.0%

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

      6. pow-to-exp 79.0%

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

   5. Applied egg-rr 79.0%

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

      1. unpow-1 79.0%

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

      2. +-commutative 79.0%

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

   7. Simplified 79.0%

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

   8. Taylor expanded in y around 0 74.4%

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

   9. Taylor expanded in x around 0 74.4%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.8 \cdot 10^{-15}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot \left(y + 1\right)}\\ \end{array} \]

Alternative 7: 74.3% accurate, 69.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.6%

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

   1. exp-prod 88.7%

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

3. Simplified 88.7%

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

4. Taylor expanded in x around 0 79.2%

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

5. Final simplification 79.2%

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

Developer target: 77.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{e^{\frac{-1}{y}}}{x}\\ t_1 := \frac{{\left(\frac{x}{y + x}\right)}^{x}}{x}\\ \mathbf{if}\;y < -3.7311844206647956 \cdot 10^{+94}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y < 2.817959242728288 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y < 2.347387415166998 \cdot 10^{+178}:\\ \;\;\;\;\log \left(e^{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (exp (/ -1.0 y)) x)) (t_1 (/ (pow (/ x (+ y x)) x) x)))
   (if (< y -3.7311844206647956e+94)
     t_0
     (if (< y 2.817959242728288e+37)
       t_1
       (if (< y 2.347387415166998e+178) (log (exp t_1)) t_0)))))

C

double code(double x, double y) {
	double t_0 = exp((-1.0 / y)) / x;
	double t_1 = pow((x / (y + x)), x) / x;
	double tmp;
	if (y < -3.7311844206647956e+94) {
		tmp = t_0;
	} else if (y < 2.817959242728288e+37) {
		tmp = t_1;
	} else if (y < 2.347387415166998e+178) {
		tmp = log(exp(t_1));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = exp(((-1.0d0) / y)) / x
    t_1 = ((x / (y + x)) ** x) / x
    if (y < (-3.7311844206647956d+94)) then
        tmp = t_0
    else if (y < 2.817959242728288d+37) then
        tmp = t_1
    else if (y < 2.347387415166998d+178) then
        tmp = log(exp(t_1))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.exp((-1.0 / y)) / x;
	double t_1 = Math.pow((x / (y + x)), x) / x;
	double tmp;
	if (y < -3.7311844206647956e+94) {
		tmp = t_0;
	} else if (y < 2.817959242728288e+37) {
		tmp = t_1;
	} else if (y < 2.347387415166998e+178) {
		tmp = Math.log(Math.exp(t_1));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.exp((-1.0 / y)) / x
	t_1 = math.pow((x / (y + x)), x) / x
	tmp = 0
	if y < -3.7311844206647956e+94:
		tmp = t_0
	elif y < 2.817959242728288e+37:
		tmp = t_1
	elif y < 2.347387415166998e+178:
		tmp = math.log(math.exp(t_1))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(exp(Float64(-1.0 / y)) / x)
	t_1 = Float64((Float64(x / Float64(y + x)) ^ x) / x)
	tmp = 0.0
	if (y < -3.7311844206647956e+94)
		tmp = t_0;
	elseif (y < 2.817959242728288e+37)
		tmp = t_1;
	elseif (y < 2.347387415166998e+178)
		tmp = log(exp(t_1));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = exp((-1.0 / y)) / x;
	t_1 = ((x / (y + x)) ^ x) / x;
	tmp = 0.0;
	if (y < -3.7311844206647956e+94)
		tmp = t_0;
	elseif (y < 2.817959242728288e+37)
		tmp = t_1;
	elseif (y < 2.347387415166998e+178)
		tmp = log(exp(t_1));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Exp[N[(-1.0 / y), $MachinePrecision]], $MachinePrecision] / x), $MachinePrecision]}, Block[{t$95$1 = N[(N[Power[N[(x / N[(y + x), $MachinePrecision]), $MachinePrecision], x], $MachinePrecision] / x), $MachinePrecision]}, If[Less[y, -3.7311844206647956e+94], t$95$0, If[Less[y, 2.817959242728288e+37], t$95$1, If[Less[y, 2.347387415166998e+178], N[Log[N[Exp[t$95$1], $MachinePrecision]], $MachinePrecision], t$95$0]]]]]

Reproduce

herbie shell --seed 2023196 
(FPCore (x y)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, F"
  :precision binary64

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

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