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

Percentage Accurate: 77.7% → 99.6%

Time: 11.7s

Alternatives: 9

Speedup: 17.4×

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: 99.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+58} \lor \neg \left(x \leq 0.0032\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2e+58) (not (<= x 0.0032)))
   (/ (exp (- y)) x)
   (/ (pow (exp x) (log (/ x (+ x y)))) x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2e+58) || !(x <= 0.0032)) {
		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 <= (-2d+58)) .or. (.not. (x <= 0.0032d0))) 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 <= -2e+58) || !(x <= 0.0032)) {
		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 <= -2e+58) or not (x <= 0.0032):
		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 <= -2e+58) || !(x <= 0.0032))
		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 <= -2e+58) || ~((x <= 0.0032)))
		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, -2e+58], N[Not[LessEqual[x, 0.0032]], $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 < -1.99999999999999989e58 or 0.00320000000000000015 < x

   1. Initial program 68.8%

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

      1. *-commutative 68.8%

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

      2. exp-to-pow 68.8%

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

   3. Simplified 68.8%

      \[\leadsto \color{blue}{\frac{{\left(\frac{x}{x + y}\right)}^{x}}{x}} \]
   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 -1.99999999999999989e58 < x < 0.00320000000000000015

   1. Initial program 82.8%

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

      1. exp-prod 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+58} \lor \neg \left(x \leq 0.0032\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+22} \lor \neg \left(x \leq 0.0026\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.85e+22) (not (<= x 0.0026))) (/ (exp (- y)) x) (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.85e+22) || !(x <= 0.0026)) {
		tmp = exp(-y) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.85d+22)) .or. (.not. (x <= 0.0026d0))) then
        tmp = exp(-y) / x
    else
        tmp = 1.0d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.85e+22) || !(x <= 0.0026)) {
		tmp = Math.exp(-y) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.85e+22) or not (x <= 0.0026):
		tmp = math.exp(-y) / x
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.85e+22) || !(x <= 0.0026))
		tmp = Float64(exp(Float64(-y)) / x);
	else
		tmp = Float64(1.0 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.85e+22) || ~((x <= 0.0026)))
		tmp = exp(-y) / x;
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.85e+22], N[Not[LessEqual[x, 0.0026]], $MachinePrecision]], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8499999999999999e22 or 0.0025999999999999999 < x

   1. Initial program 69.9%

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

      1. *-commutative 69.9%

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

      2. exp-to-pow 69.9%

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

   3. Simplified 69.9%

      \[\leadsto \color{blue}{\frac{{\left(\frac{x}{x + y}\right)}^{x}}{x}} \]
   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 -1.8499999999999999e22 < x < 0.0025999999999999999

   1. Initial program 82.1%

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

      1. exp-prod 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}} \]
   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 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+22} \lor \neg \left(x \leq 0.0026\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.6% accurate, 8.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+22}:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot 0.5 + -1\right)}{x}\\ \mathbf{elif}\;x \leq 0.0032:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + y \cdot \left(x + y \cdot \left(x \cdot \left(y + 1\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.85e+22)
   (/ (+ 1.0 (* y (+ (* y 0.5) -1.0))) x)
   (if (<= x 0.0032)
     (/ 1.0 x)
     (/ 1.0 (+ x (* y (+ x (* y (* x (+ y 1.0))))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.85e+22) {
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	} else if (x <= 0.0032) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (y * (x + (y * (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 <= (-1.85d+22)) then
        tmp = (1.0d0 + (y * ((y * 0.5d0) + (-1.0d0)))) / x
    else if (x <= 0.0032d0) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (x + (y * (x + (y * (x * (y + 1.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.85e+22) {
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	} else if (x <= 0.0032) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (y * (x + (y * (x * (y + 1.0))))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.85e+22:
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x
	elif x <= 0.0032:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (y * (x + (y * (x * (y + 1.0))))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.85e+22)
		tmp = Float64(Float64(1.0 + Float64(y * Float64(Float64(y * 0.5) + -1.0))) / x);
	elseif (x <= 0.0032)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(x + Float64(y * Float64(x + Float64(y * Float64(x * Float64(y + 1.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.85e+22)
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	elseif (x <= 0.0032)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (y * (x + (y * (x * (y + 1.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.85e+22], N[(N[(1.0 + N[(y * N[(N[(y * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 0.0032], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x + N[(y * N[(x + N[(y * N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.8499999999999999e22

   1. Initial program 67.3%

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

      1. exp-prod 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in y around 0 69.5%

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

   6. Taylor expanded in x around inf 69.5%

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

      1. *-commutative 69.5%

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

   8. Simplified 69.5%

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

   if -1.8499999999999999e22 < x < 0.00320000000000000015

   1. Initial program 82.1%

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

      1. exp-prod 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 98.0%

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

   if 0.00320000000000000015 < x

   1. Initial program 71.8%

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

      1. exp-prod 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in y around 0 54.3%

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

   6. Taylor expanded in y around 0 50.5%

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

      1. +-commutative 50.5%

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

      2. mul-1-neg 50.5%

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

      3. unsub-neg 50.5%

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

   8. Simplified 50.5%

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

      1. sub-div 50.5%

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

      2. clear-num 50.5%

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

   10. Applied egg-rr 50.5%

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

   11. Taylor expanded in y around 0 81.0%

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

       1. cancel-sign-sub-inv 81.0%

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

       2. *-commutative 81.0%

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

       3. metadata-eval 81.0%

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

       4. distribute-rgt-in 81.0%

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

       5. +-commutative 81.0%

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

       6. mul-1-neg 81.0%

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

   13. Simplified 81.0%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+22}:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot 0.5 + -1\right)}{x}\\ \mathbf{elif}\;x \leq 0.0032:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + y \cdot \left(x + y \cdot \left(x \cdot \left(y + 1\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.8% accurate, 8.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+22}:\\ \;\;\;\;\frac{1 - y \cdot \left(1 - \frac{y \cdot \left(0.5 + x \cdot 0.5\right)}{x}\right)}{x}\\ \mathbf{elif}\;x \leq 0.0032:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + y \cdot \left(x + y \cdot \left(x \cdot \left(y + 1\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.85e+22)
   (/ (- 1.0 (* y (- 1.0 (/ (* y (+ 0.5 (* x 0.5))) x)))) x)
   (if (<= x 0.0032)
     (/ 1.0 x)
     (/ 1.0 (+ x (* y (+ x (* y (* x (+ y 1.0))))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.85e+22) {
		tmp = (1.0 - (y * (1.0 - ((y * (0.5 + (x * 0.5))) / x)))) / x;
	} else if (x <= 0.0032) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (y * (x + (y * (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 <= (-1.85d+22)) then
        tmp = (1.0d0 - (y * (1.0d0 - ((y * (0.5d0 + (x * 0.5d0))) / x)))) / x
    else if (x <= 0.0032d0) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (x + (y * (x + (y * (x * (y + 1.0d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.85e+22) {
		tmp = (1.0 - (y * (1.0 - ((y * (0.5 + (x * 0.5))) / x)))) / x;
	} else if (x <= 0.0032) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (y * (x + (y * (x * (y + 1.0))))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.85e+22:
		tmp = (1.0 - (y * (1.0 - ((y * (0.5 + (x * 0.5))) / x)))) / x
	elif x <= 0.0032:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (y * (x + (y * (x * (y + 1.0))))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.85e+22)
		tmp = Float64(Float64(1.0 - Float64(y * Float64(1.0 - Float64(Float64(y * Float64(0.5 + Float64(x * 0.5))) / x)))) / x);
	elseif (x <= 0.0032)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(x + Float64(y * Float64(x + Float64(y * Float64(x * Float64(y + 1.0)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.85e+22)
		tmp = (1.0 - (y * (1.0 - ((y * (0.5 + (x * 0.5))) / x)))) / x;
	elseif (x <= 0.0032)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (y * (x + (y * (x * (y + 1.0))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.85e+22], N[(N[(1.0 - N[(y * N[(1.0 - N[(N[(y * N[(0.5 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 0.0032], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x + N[(y * N[(x + N[(y * N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.8499999999999999e22

   1. Initial program 67.3%

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

      1. exp-prod 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in y around 0 69.5%

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

   6. Taylor expanded in x around 0 72.8%

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

      1. associate-*r* 72.8%

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

      2. distribute-rgt-out 72.8%

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

      3. *-commutative 72.8%

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

   8. Simplified 72.8%

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

   if -1.8499999999999999e22 < x < 0.00320000000000000015

   1. Initial program 82.1%

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

      1. exp-prod 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 98.0%

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

   if 0.00320000000000000015 < x

   1. Initial program 71.8%

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

      1. exp-prod 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in y around 0 54.3%

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

   6. Taylor expanded in y around 0 50.5%

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

      1. +-commutative 50.5%

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

      2. mul-1-neg 50.5%

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

      3. unsub-neg 50.5%

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

   8. Simplified 50.5%

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

      1. sub-div 50.5%

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

      2. clear-num 50.5%

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

   10. Applied egg-rr 50.5%

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

   11. Taylor expanded in y around 0 81.0%

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

       1. cancel-sign-sub-inv 81.0%

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

       2. *-commutative 81.0%

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

       3. metadata-eval 81.0%

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

       4. distribute-rgt-in 81.0%

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

       5. +-commutative 81.0%

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

       6. mul-1-neg 81.0%

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

   13. Simplified 81.0%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+22}:\\ \;\;\;\;\frac{1 - y \cdot \left(1 - \frac{y \cdot \left(0.5 + x \cdot 0.5\right)}{x}\right)}{x}\\ \mathbf{elif}\;x \leq 0.0032:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + y \cdot \left(x + y \cdot \left(x \cdot \left(y + 1\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 85.5% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x - x \cdot y}{x}}{x}\\ \mathbf{elif}\;x \leq 0.0032:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + y \cdot \left(x \cdot \left(y + 1\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.85e+22)
   (/ (/ (- x (* x y)) x) x)
   (if (<= x 0.0032) (/ 1.0 x) (/ 1.0 (+ x (* y (* x (+ y 1.0))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.85e+22) {
		tmp = ((x - (x * y)) / x) / x;
	} else if (x <= 0.0032) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (y * (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 <= (-1.85d+22)) then
        tmp = ((x - (x * y)) / x) / x
    else if (x <= 0.0032d0) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (x + (y * (x * (y + 1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.85e+22) {
		tmp = ((x - (x * y)) / x) / x;
	} else if (x <= 0.0032) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (y * (x * (y + 1.0))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.85e+22:
		tmp = ((x - (x * y)) / x) / x
	elif x <= 0.0032:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (y * (x * (y + 1.0))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.85e+22)
		tmp = Float64(Float64(Float64(x - Float64(x * y)) / x) / x);
	elseif (x <= 0.0032)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(x + Float64(y * Float64(x * Float64(y + 1.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.85e+22)
		tmp = ((x - (x * y)) / x) / x;
	elseif (x <= 0.0032)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (y * (x * (y + 1.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.85e+22], N[(N[(N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 0.0032], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x + N[(y * N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.8499999999999999e22

   1. Initial program 67.3%

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

      1. exp-prod 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in y around 0 69.5%

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

   6. Taylor expanded in y around 0 51.5%

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

      1. +-commutative 51.5%

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

      2. mul-1-neg 51.5%

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

      3. unsub-neg 51.5%

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

   8. Simplified 51.5%

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

      1. frac-sub 36.1%

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

      2. associate-/r* 64.5%

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

      3. *-un-lft-identity 64.5%

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

   10. Applied egg-rr 64.5%

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

   if -1.8499999999999999e22 < x < 0.00320000000000000015

   1. Initial program 82.1%

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

      1. exp-prod 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 98.0%

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

   if 0.00320000000000000015 < x

   1. Initial program 71.8%

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

      1. exp-prod 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in y around 0 54.3%

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

   6. Taylor expanded in y around 0 50.5%

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

      1. +-commutative 50.5%

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

      2. mul-1-neg 50.5%

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

      3. unsub-neg 50.5%

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

   8. Simplified 50.5%

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

      1. sub-div 50.5%

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

      2. clear-num 50.5%

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

   10. Applied egg-rr 50.5%

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

   11. Taylor expanded in y around 0 78.7%

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

       1. cancel-sign-sub-inv 78.7%

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

       2. *-commutative 78.7%

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

       3. metadata-eval 78.7%

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

       4. distribute-rgt-in 78.7%

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

       5. +-commutative 78.7%

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

   13. Simplified 78.7%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x - x \cdot y}{x}}{x}\\ \mathbf{elif}\;x \leq 0.0032:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + y \cdot \left(x \cdot \left(y + 1\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.0% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+22}:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot 0.5 + -1\right)}{x}\\ \mathbf{elif}\;x \leq 0.0032:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + y \cdot \left(x \cdot \left(y + 1\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.85e+22)
   (/ (+ 1.0 (* y (+ (* y 0.5) -1.0))) x)
   (if (<= x 0.0032) (/ 1.0 x) (/ 1.0 (+ x (* y (* x (+ y 1.0))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.85e+22) {
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	} else if (x <= 0.0032) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (y * (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 <= (-1.85d+22)) then
        tmp = (1.0d0 + (y * ((y * 0.5d0) + (-1.0d0)))) / x
    else if (x <= 0.0032d0) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (x + (y * (x * (y + 1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.85e+22) {
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	} else if (x <= 0.0032) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (y * (x * (y + 1.0))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.85e+22:
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x
	elif x <= 0.0032:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (y * (x * (y + 1.0))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.85e+22)
		tmp = Float64(Float64(1.0 + Float64(y * Float64(Float64(y * 0.5) + -1.0))) / x);
	elseif (x <= 0.0032)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(x + Float64(y * Float64(x * Float64(y + 1.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.85e+22)
		tmp = (1.0 + (y * ((y * 0.5) + -1.0))) / x;
	elseif (x <= 0.0032)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (y * (x * (y + 1.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.85e+22], N[(N[(1.0 + N[(y * N[(N[(y * 0.5), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 0.0032], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x + N[(y * N[(x * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.8499999999999999e22

   1. Initial program 67.3%

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

      1. exp-prod 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in y around 0 69.5%

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

   6. Taylor expanded in x around inf 69.5%

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

      1. *-commutative 69.5%

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

   8. Simplified 69.5%

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

   if -1.8499999999999999e22 < x < 0.00320000000000000015

   1. Initial program 82.1%

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

      1. exp-prod 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 98.0%

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

   if 0.00320000000000000015 < x

   1. Initial program 71.8%

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

      1. exp-prod 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in y around 0 54.3%

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

   6. Taylor expanded in y around 0 50.5%

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

      1. +-commutative 50.5%

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

      2. mul-1-neg 50.5%

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

      3. unsub-neg 50.5%

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

   8. Simplified 50.5%

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

      1. sub-div 50.5%

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

      2. clear-num 50.5%

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

   10. Applied egg-rr 50.5%

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

   11. Taylor expanded in y around 0 78.7%

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

       1. cancel-sign-sub-inv 78.7%

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

       2. *-commutative 78.7%

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

       3. metadata-eval 78.7%

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

       4. distribute-rgt-in 78.7%

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

       5. +-commutative 78.7%

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

   13. Simplified 78.7%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+22}:\\ \;\;\;\;\frac{1 + y \cdot \left(y \cdot 0.5 + -1\right)}{x}\\ \mathbf{elif}\;x \leq 0.0032:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + y \cdot \left(x \cdot \left(y + 1\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.5% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x - x \cdot y}{x}}{x}\\ \mathbf{elif}\;x \leq 0.0032:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.85e+22)
   (/ (/ (- x (* x y)) x) x)
   (if (<= x 0.0032) (/ 1.0 x) (/ 1.0 (+ x (* x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.85e+22) {
		tmp = ((x - (x * y)) / x) / x;
	} else if (x <= 0.0032) {
		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 <= (-1.85d+22)) then
        tmp = ((x - (x * y)) / x) / x
    else if (x <= 0.0032d0) 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 <= -1.85e+22) {
		tmp = ((x - (x * y)) / x) / x;
	} else if (x <= 0.0032) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (x * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.85e+22:
		tmp = ((x - (x * y)) / x) / x
	elif x <= 0.0032:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (x * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.85e+22)
		tmp = Float64(Float64(Float64(x - Float64(x * y)) / x) / x);
	elseif (x <= 0.0032)
		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 <= -1.85e+22)
		tmp = ((x - (x * y)) / x) / x;
	elseif (x <= 0.0032)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.85e+22], N[(N[(N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 0.0032], 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 < -1.8499999999999999e22

   1. Initial program 67.3%

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

      1. exp-prod 67.3%

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

   3. Simplified 67.3%

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

   5. Taylor expanded in y around 0 69.5%

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

   6. Taylor expanded in y around 0 51.5%

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

      1. +-commutative 51.5%

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

      2. mul-1-neg 51.5%

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

      3. unsub-neg 51.5%

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

   8. Simplified 51.5%

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

      1. frac-sub 36.1%

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

      2. associate-/r* 64.5%

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

      3. *-un-lft-identity 64.5%

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

   10. Applied egg-rr 64.5%

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

   if -1.8499999999999999e22 < x < 0.00320000000000000015

   1. Initial program 82.1%

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

      1. exp-prod 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 98.0%

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

   if 0.00320000000000000015 < x

   1. Initial program 71.8%

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

      1. exp-prod 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in y around 0 54.3%

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

   6. Taylor expanded in y around 0 50.5%

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

      1. +-commutative 50.5%

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

      2. mul-1-neg 50.5%

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

      3. unsub-neg 50.5%

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

   8. Simplified 50.5%

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

      1. sub-div 50.5%

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

      2. clear-num 50.5%

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

   10. Applied egg-rr 50.5%

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

   11. Taylor expanded in y around 0 66.7%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+22}:\\ \;\;\;\;\frac{\frac{x - x \cdot y}{x}}{x}\\ \mathbf{elif}\;x \leq 0.0032:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 79.3% accurate, 17.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.0032:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.0032) (/ 1.0 x) (/ 1.0 (+ x (* x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.0032) {
		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 <= 0.0032d0) 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 <= 0.0032) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (x * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.0032:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (x * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.0032)
		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 <= 0.0032)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.0032], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.00320000000000000015

   1. Initial program 77.2%

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

      1. exp-prod 89.0%

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

   3. Simplified 89.0%

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

   5. Taylor expanded in x around 0 82.3%

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

   if 0.00320000000000000015 < x

   1. Initial program 71.8%

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

      1. exp-prod 71.1%

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

   3. Simplified 71.1%

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

   5. Taylor expanded in y around 0 54.3%

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

   6. Taylor expanded in y around 0 50.5%

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

      1. +-commutative 50.5%

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

      2. mul-1-neg 50.5%

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

      3. unsub-neg 50.5%

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

   8. Simplified 50.5%

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

      1. sub-div 50.5%

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

      2. clear-num 50.5%

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

   10. Applied egg-rr 50.5%

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

   11. Taylor expanded in y around 0 66.7%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.0032:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.0% 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 75.5%

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

   1. exp-prod 83.5%

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

3. Simplified 83.5%

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

5. Taylor expanded in x around 0 72.3%

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

6. Final simplification 72.3%

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

Developer target: 78.3% 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 2024096 
(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))