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

Percentage Accurate: 77.5% → 99.4%

Time: 11.1s

Alternatives: 12

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: 77.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+60}:\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{e^{y}}{\frac{1}{x}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5e+60)
   (/ (exp (- y)) x)
   (if (<= x 7.6e-12)
     (/ (pow (exp x) (log (/ x (+ x y)))) x)
     (/ 1.0 (/ (exp y) (/ 1.0 x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5e+60) {
		tmp = exp(-y) / x;
	} else if (x <= 7.6e-12) {
		tmp = pow(exp(x), log((x / (x + y)))) / x;
	} else {
		tmp = 1.0 / (exp(y) / (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 <= (-5d+60)) then
        tmp = exp(-y) / x
    else if (x <= 7.6d-12) then
        tmp = (exp(x) ** log((x / (x + y)))) / x
    else
        tmp = 1.0d0 / (exp(y) / (1.0d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5e+60) {
		tmp = Math.exp(-y) / x;
	} else if (x <= 7.6e-12) {
		tmp = Math.pow(Math.exp(x), Math.log((x / (x + y)))) / x;
	} else {
		tmp = 1.0 / (Math.exp(y) / (1.0 / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5e+60:
		tmp = math.exp(-y) / x
	elif x <= 7.6e-12:
		tmp = math.pow(math.exp(x), math.log((x / (x + y)))) / x
	else:
		tmp = 1.0 / (math.exp(y) / (1.0 / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5e+60)
		tmp = Float64(exp(Float64(-y)) / x);
	elseif (x <= 7.6e-12)
		tmp = Float64((exp(x) ^ log(Float64(x / Float64(x + y)))) / x);
	else
		tmp = Float64(1.0 / Float64(exp(y) / Float64(1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5e+60)
		tmp = exp(-y) / x;
	elseif (x <= 7.6e-12)
		tmp = (exp(x) ^ log((x / (x + y)))) / x;
	else
		tmp = 1.0 / (exp(y) / (1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5e+60], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 7.6e-12], N[(N[Power[N[Exp[x], $MachinePrecision], N[Log[N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision] / x), $MachinePrecision], N[(1.0 / N[(N[Exp[y], $MachinePrecision] / N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.99999999999999975e60

   1. Initial program 58.4%

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

      1. *-commutative 58.4%

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

      2. exp-to-pow 58.4%

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

   3. Simplified 58.4%

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

   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 -4.99999999999999975e60 < x < 7.59999999999999993e-12

   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%

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

   if 7.59999999999999993e-12 < x

   1. Initial program 70.6%

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

      1. *-commutative 70.6%

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

      2. exp-to-pow 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in x around inf 99.9%

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

      1. mul-1-neg 99.9%

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

   6. Simplified 99.9%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. exp-neg 99.9%

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

      4. associate-/r/ 100.0%

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

      5. /-rgt-identity 100.0%

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

   8. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

   10. Simplified 100.0%

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

       1. /-rgt-identity 100.0%

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

       2. *-commutative 100.0%

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

       3. associate-/l* 100.0%

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

   12. Applied egg-rr 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+60}:\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{{\left(e^{x}\right)}^{\log \left(\frac{x}{x + y}\right)}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{e^{y}}{\frac{1}{x}}}\\ \end{array} \]

Alternative 2: 99.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -940000:\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{e^{y}}{\frac{1}{x}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -940000.0)
   (/ (exp (- y)) x)
   (if (<= x 7.6e-12) (/ 1.0 x) (/ 1.0 (/ (exp y) (/ 1.0 x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -940000.0) {
		tmp = exp(-y) / x;
	} else if (x <= 7.6e-12) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (exp(y) / (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 <= (-940000.0d0)) then
        tmp = exp(-y) / x
    else if (x <= 7.6d-12) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (exp(y) / (1.0d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -940000.0) {
		tmp = Math.exp(-y) / x;
	} else if (x <= 7.6e-12) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (Math.exp(y) / (1.0 / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -940000.0:
		tmp = math.exp(-y) / x
	elif x <= 7.6e-12:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (math.exp(y) / (1.0 / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -940000.0)
		tmp = Float64(exp(Float64(-y)) / x);
	elseif (x <= 7.6e-12)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(exp(y) / Float64(1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -940000.0)
		tmp = exp(-y) / x;
	elseif (x <= 7.6e-12)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (exp(y) / (1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -940000.0], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 7.6e-12], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(N[Exp[y], $MachinePrecision] / N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.4e5

   1. Initial program 67.5%

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

      1. *-commutative 67.5%

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

      2. exp-to-pow 67.5%

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

   3. Simplified 67.5%

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

   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 -9.4e5 < x < 7.59999999999999993e-12

   1. Initial program 84.6%

      \[\frac{e^{x \cdot \log \left(\frac{x}{x + y}\right)}}{x} \]
   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 99.6%

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

   if 7.59999999999999993e-12 < x

   1. Initial program 70.6%

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

      1. *-commutative 70.6%

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

      2. exp-to-pow 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in x around inf 99.9%

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

      1. mul-1-neg 99.9%

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

   6. Simplified 99.9%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. exp-neg 99.9%

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

      4. associate-/r/ 100.0%

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

      5. /-rgt-identity 100.0%

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

   8. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

   10. Simplified 100.0%

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

       1. /-rgt-identity 100.0%

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

       2. *-commutative 100.0%

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

       3. associate-/l* 100.0%

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

   12. Applied egg-rr 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -940000:\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{e^{y}}{\frac{1}{x}}}\\ \end{array} \]

Alternative 3: 99.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -940000:\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot e^{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -940000.0)
   (/ (exp (- y)) x)
   (if (<= x 7.6e-12) (/ 1.0 x) (/ 1.0 (* x (exp y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -940000.0) {
		tmp = exp(-y) / x;
	} else if (x <= 7.6e-12) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x * exp(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 <= (-940000.0d0)) then
        tmp = exp(-y) / x
    else if (x <= 7.6d-12) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (x * exp(y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -940000.0) {
		tmp = Math.exp(-y) / x;
	} else if (x <= 7.6e-12) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x * Math.exp(y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -940000.0:
		tmp = math.exp(-y) / x
	elif x <= 7.6e-12:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x * math.exp(y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -940000.0)
		tmp = Float64(exp(Float64(-y)) / x);
	elseif (x <= 7.6e-12)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(x * exp(y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -940000.0)
		tmp = exp(-y) / x;
	elseif (x <= 7.6e-12)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x * exp(y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -940000.0], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 7.6e-12], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x * N[Exp[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.4e5

   1. Initial program 67.5%

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

      1. *-commutative 67.5%

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

      2. exp-to-pow 67.5%

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

   3. Simplified 67.5%

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

   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 -9.4e5 < x < 7.59999999999999993e-12

   1. Initial program 84.6%

      \[\frac{e^{x \cdot \log \left(\frac{x}{x + y}\right)}}{x} \]
   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 99.6%

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

   if 7.59999999999999993e-12 < x

   1. Initial program 70.6%

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

      1. *-commutative 70.6%

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

      2. exp-to-pow 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in x around inf 99.9%

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

      1. mul-1-neg 99.9%

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

   6. Simplified 99.9%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. exp-neg 99.9%

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

      4. associate-/r/ 100.0%

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

      5. /-rgt-identity 100.0%

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

   8. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -940000:\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x \cdot e^{y}}\\ \end{array} \]

Alternative 4: 99.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -940000 \lor \neg \left(x \leq 7.6 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -940000.0) (not (<= x 7.6e-12))) (/ (exp (- y)) x) (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -940000.0) || !(x <= 7.6e-12)) {
		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 <= (-940000.0d0)) .or. (.not. (x <= 7.6d-12))) 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 <= -940000.0) || !(x <= 7.6e-12)) {
		tmp = Math.exp(-y) / x;
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -940000.0) or not (x <= 7.6e-12):
		tmp = math.exp(-y) / x
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -940000.0) || !(x <= 7.6e-12))
		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 <= -940000.0) || ~((x <= 7.6e-12)))
		tmp = exp(-y) / x;
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -940000.0], N[Not[LessEqual[x, 7.6e-12]], $MachinePrecision]], N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.4e5 or 7.59999999999999993e-12 < x

   1. Initial program 69.3%

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

      1. *-commutative 69.3%

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

      2. exp-to-pow 69.3%

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

   3. Simplified 69.3%

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

   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 -9.4e5 < x < 7.59999999999999993e-12

   1. Initial program 84.6%

      \[\frac{e^{x \cdot \log \left(\frac{x}{x + y}\right)}}{x} \]
   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 99.6%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -940000 \lor \neg \left(x \leq 7.6 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{e^{-y}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]

Alternative 5: 85.8% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -940000:\\ \;\;\;\;\frac{1 - y}{x} + \frac{y \cdot y}{x}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot \left(y + \left(y \cdot y\right) \cdot \left(0.5 + y \cdot 0.16666666666666666\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -940000.0)
   (+ (/ (- 1.0 y) x) (/ (* y y) x))
   (if (<= x 7.6e-12)
     (/ 1.0 x)
     (/ 1.0 (+ x (* x (+ y (* (* y y) (+ 0.5 (* y 0.16666666666666666))))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -940000.0) {
		tmp = ((1.0 - y) / x) + ((y * y) / x);
	} else if (x <= 7.6e-12) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (x * (y + ((y * y) * (0.5 + (y * 0.16666666666666666))))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-940000.0d0)) then
        tmp = ((1.0d0 - y) / x) + ((y * y) / x)
    else if (x <= 7.6d-12) then
        tmp = 1.0d0 / x
    else
        tmp = 1.0d0 / (x + (x * (y + ((y * y) * (0.5d0 + (y * 0.16666666666666666d0))))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -940000.0) {
		tmp = ((1.0 - y) / x) + ((y * y) / x);
	} else if (x <= 7.6e-12) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (x * (y + ((y * y) * (0.5 + (y * 0.16666666666666666))))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -940000.0:
		tmp = ((1.0 - y) / x) + ((y * y) / x)
	elif x <= 7.6e-12:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (x * (y + ((y * y) * (0.5 + (y * 0.16666666666666666))))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -940000.0)
		tmp = Float64(Float64(Float64(1.0 - y) / x) + Float64(Float64(y * y) / x));
	elseif (x <= 7.6e-12)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(1.0 / Float64(x + Float64(x * Float64(y + Float64(Float64(y * y) * Float64(0.5 + Float64(y * 0.16666666666666666)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -940000.0)
		tmp = ((1.0 - y) / x) + ((y * y) / x);
	elseif (x <= 7.6e-12)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (x * (y + ((y * y) * (0.5 + (y * 0.16666666666666666))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -940000.0], N[(N[(N[(1.0 - y), $MachinePrecision] / x), $MachinePrecision] + N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.6e-12], N[(1.0 / x), $MachinePrecision], N[(1.0 / N[(x + N[(x * N[(y + N[(N[(y * y), $MachinePrecision] * N[(0.5 + N[(y * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.4e5

   1. Initial program 67.5%

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

      1. *-commutative 67.5%

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

      2. exp-to-pow 67.5%

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

   3. Simplified 67.5%

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

   4. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. exp-neg 100.0%

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

      4. associate-/r/ 100.0%

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

      5. /-rgt-identity 100.0%

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

   8. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

   10. Simplified 100.0%

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

   11. Taylor expanded in y around 0 49.1%

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

   12. Taylor expanded in y around 0 70.9%

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

       1. +-commutative 70.9%

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

       2. mul-1-neg 70.9%

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

       3. sub-neg 70.9%

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

       4. div-sub 70.9%

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

       5. unpow2 70.9%

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

   14. Simplified 70.9%

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

   if -9.4e5 < x < 7.59999999999999993e-12

   1. Initial program 84.6%

      \[\frac{e^{x \cdot \log \left(\frac{x}{x + y}\right)}}{x} \]
   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 99.6%

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

   if 7.59999999999999993e-12 < x

   1. Initial program 70.6%

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

      1. *-commutative 70.6%

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

      2. exp-to-pow 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in x around inf 99.9%

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

      1. mul-1-neg 99.9%

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

   6. Simplified 99.9%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. exp-neg 99.9%

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

      4. associate-/r/ 100.0%

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

      5. /-rgt-identity 100.0%

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

   8. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

   10. Simplified 100.0%

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

       1. /-rgt-identity 100.0%

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

       2. *-commutative 100.0%

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

       3. associate-/l* 100.0%

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

   12. Applied egg-rr 100.0%

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

   13. Taylor expanded in y around 0 81.9%

       \[\leadsto \frac{1}{\color{blue}{y \cdot x + \left(0.5 \cdot \left({y}^{2} \cdot x\right) + \left(0.16666666666666666 \cdot \left({y}^{3} \cdot x\right) + x\right)\right)}} \]
   14. Step-by-step derivation

       1. associate-+r+ 81.9%

          \[\leadsto \frac{1}{y \cdot x + \color{blue}{\left(\left(0.5 \cdot \left({y}^{2} \cdot x\right) + 0.16666666666666666 \cdot \left({y}^{3} \cdot x\right)\right) + x\right)}} \]

       2. associate-+r+ 81.9%

          \[\leadsto \frac{1}{\color{blue}{\left(y \cdot x + \left(0.5 \cdot \left({y}^{2} \cdot x\right) + 0.16666666666666666 \cdot \left({y}^{3} \cdot x\right)\right)\right) + x}} \]

       3. *-commutative 81.9%

          \[\leadsto \frac{1}{\left(\color{blue}{x \cdot y} + \left(0.5 \cdot \left({y}^{2} \cdot x\right) + 0.16666666666666666 \cdot \left({y}^{3} \cdot x\right)\right)\right) + x} \]

       4. unpow2 81.9%

          \[\leadsto \frac{1}{\left(x \cdot y + \left(0.5 \cdot \left(\color{blue}{\left(y \cdot y\right)} \cdot x\right) + 0.16666666666666666 \cdot \left({y}^{3} \cdot x\right)\right)\right) + x} \]

       5. associate-*r* 81.9%

          \[\leadsto \frac{1}{\left(x \cdot y + \left(\color{blue}{\left(0.5 \cdot \left(y \cdot y\right)\right) \cdot x} + 0.16666666666666666 \cdot \left({y}^{3} \cdot x\right)\right)\right) + x} \]

       6. associate-*r* 81.9%

          \[\leadsto \frac{1}{\left(x \cdot y + \left(\left(0.5 \cdot \left(y \cdot y\right)\right) \cdot x + \color{blue}{\left(0.16666666666666666 \cdot {y}^{3}\right) \cdot x}\right)\right) + x} \]

       7. distribute-rgt-out 82.0%

          \[\leadsto \frac{1}{\left(x \cdot y + \color{blue}{x \cdot \left(0.5 \cdot \left(y \cdot y\right) + 0.16666666666666666 \cdot {y}^{3}\right)}\right) + x} \]

       8. distribute-lft-out 82.0%

          \[\leadsto \frac{1}{\color{blue}{x \cdot \left(y + \left(0.5 \cdot \left(y \cdot y\right) + 0.16666666666666666 \cdot {y}^{3}\right)\right)} + x} \]

       9. cube-mult 82.0%

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

       10. associate-*r* 82.0%

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

       11. distribute-rgt-out 82.1%

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

   15. Simplified 82.1%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -940000:\\ \;\;\;\;\frac{1 - y}{x} + \frac{y \cdot y}{x}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot \left(y + \left(y \cdot y\right) \cdot \left(0.5 + y \cdot 0.16666666666666666\right)\right)}\\ \end{array} \]

Alternative 6: 82.3% accurate, 15.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{x + x \cdot y}\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+129}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+28}:\\ \;\;\;\;\frac{x - x \cdot y}{x \cdot x}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ 1.0 (+ x (* x y)))))
   (if (<= x -2.4e+129)
     t_0
     (if (<= x -5.8e+28)
       (/ (- x (* x y)) (* x x))
       (if (<= x 7.6e-12) (/ 1.0 x) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 / (x + (x * y));
	double tmp;
	if (x <= -2.4e+129) {
		tmp = t_0;
	} else if (x <= -5.8e+28) {
		tmp = (x - (x * y)) / (x * x);
	} else if (x <= 7.6e-12) {
		tmp = 1.0 / x;
	} 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) :: tmp
    t_0 = 1.0d0 / (x + (x * y))
    if (x <= (-2.4d+129)) then
        tmp = t_0
    else if (x <= (-5.8d+28)) then
        tmp = (x - (x * y)) / (x * x)
    else if (x <= 7.6d-12) then
        tmp = 1.0d0 / x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 / (x + (x * y));
	double tmp;
	if (x <= -2.4e+129) {
		tmp = t_0;
	} else if (x <= -5.8e+28) {
		tmp = (x - (x * y)) / (x * x);
	} else if (x <= 7.6e-12) {
		tmp = 1.0 / x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 / (x + (x * y))
	tmp = 0
	if x <= -2.4e+129:
		tmp = t_0
	elif x <= -5.8e+28:
		tmp = (x - (x * y)) / (x * x)
	elif x <= 7.6e-12:
		tmp = 1.0 / x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 / Float64(x + Float64(x * y)))
	tmp = 0.0
	if (x <= -2.4e+129)
		tmp = t_0;
	elseif (x <= -5.8e+28)
		tmp = Float64(Float64(x - Float64(x * y)) / Float64(x * x));
	elseif (x <= 7.6e-12)
		tmp = Float64(1.0 / x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 / (x + (x * y));
	tmp = 0.0;
	if (x <= -2.4e+129)
		tmp = t_0;
	elseif (x <= -5.8e+28)
		tmp = (x - (x * y)) / (x * x);
	elseif (x <= 7.6e-12)
		tmp = 1.0 / x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 / N[(x + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e+129], t$95$0, If[LessEqual[x, -5.8e+28], N[(N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.6e-12], N[(1.0 / x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.3999999999999999e129 or 7.59999999999999993e-12 < x

   1. Initial program 65.4%

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

      1. *-commutative 65.4%

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

      2. exp-to-pow 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. exp-neg 99.9%

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

      4. associate-/r/ 100.0%

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

      5. /-rgt-identity 100.0%

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

   8. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

   10. Simplified 100.0%

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

   11. Taylor expanded in y around 0 64.0%

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

   if -2.3999999999999999e129 < x < -5.8000000000000002e28

   1. Initial program 77.8%

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

      1. exp-prod 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in x around inf 44.7%

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

      1. mul-1-neg 44.7%

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

      2. unsub-neg 44.7%

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

   6. Simplified 44.7%

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

      1. frac-sub 59.2%

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

      2. *-un-lft-identity 59.2%

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

      3. *-commutative 59.2%

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

   8. Applied egg-rr 59.2%

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

   if -5.8000000000000002e28 < x < 7.59999999999999993e-12

   1. Initial program 85.4%

      \[\frac{e^{x \cdot \log \left(\frac{x}{x + y}\right)}}{x} \]
   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 98.8%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+129}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+28}:\\ \;\;\;\;\frac{x - x \cdot y}{x \cdot x}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \end{array} \]

Alternative 7: 83.3% accurate, 16.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -940000:\\ \;\;\;\;\frac{1 - y}{x} + \frac{y \cdot y}{x}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -940000.0)
   (+ (/ (- 1.0 y) x) (/ (* y y) x))
   (if (<= x 7.6e-12) (/ 1.0 x) (/ 1.0 (+ x (* x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -940000.0) {
		tmp = ((1.0 - y) / x) + ((y * y) / x);
	} else if (x <= 7.6e-12) {
		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 <= (-940000.0d0)) then
        tmp = ((1.0d0 - y) / x) + ((y * y) / x)
    else if (x <= 7.6d-12) 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 <= -940000.0) {
		tmp = ((1.0 - y) / x) + ((y * y) / x);
	} else if (x <= 7.6e-12) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (x * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -940000.0:
		tmp = ((1.0 - y) / x) + ((y * y) / x)
	elif x <= 7.6e-12:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (x * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -940000.0)
		tmp = Float64(Float64(Float64(1.0 - y) / x) + Float64(Float64(y * y) / x));
	elseif (x <= 7.6e-12)
		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 <= -940000.0)
		tmp = ((1.0 - y) / x) + ((y * y) / x);
	elseif (x <= 7.6e-12)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -940000.0], N[(N[(N[(1.0 - y), $MachinePrecision] / x), $MachinePrecision] + N[(N[(y * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.6e-12], 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 < -9.4e5

   1. Initial program 67.5%

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

      1. *-commutative 67.5%

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

      2. exp-to-pow 67.5%

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

   3. Simplified 67.5%

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

   4. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

   6. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. exp-neg 100.0%

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

      4. associate-/r/ 100.0%

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

      5. /-rgt-identity 100.0%

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

   8. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

   10. Simplified 100.0%

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

   11. Taylor expanded in y around 0 49.1%

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

   12. Taylor expanded in y around 0 70.9%

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

       1. +-commutative 70.9%

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

       2. mul-1-neg 70.9%

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

       3. sub-neg 70.9%

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

       4. div-sub 70.9%

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

       5. unpow2 70.9%

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

   14. Simplified 70.9%

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

   if -9.4e5 < x < 7.59999999999999993e-12

   1. Initial program 84.6%

      \[\frac{e^{x \cdot \log \left(\frac{x}{x + y}\right)}}{x} \]
   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 99.6%

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

   if 7.59999999999999993e-12 < x

   1. Initial program 70.6%

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

      1. *-commutative 70.6%

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

      2. exp-to-pow 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in x around inf 99.9%

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

      1. mul-1-neg 99.9%

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

   6. Simplified 99.9%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. exp-neg 99.9%

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

      4. associate-/r/ 100.0%

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

      5. /-rgt-identity 100.0%

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

   8. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

   10. Simplified 100.0%

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

   11. Taylor expanded in y around 0 70.0%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -940000:\\ \;\;\;\;\frac{1 - y}{x} + \frac{y \cdot y}{x}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \end{array} \]

Alternative 8: 83.4% accurate, 18.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -940000:\\ \;\;\;\;\frac{\frac{x - x \cdot y}{x}}{x}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -940000.0)
   (/ (/ (- x (* x y)) x) x)
   (if (<= x 7.6e-12) (/ 1.0 x) (/ 1.0 (+ x (* x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -940000.0) {
		tmp = ((x - (x * y)) / x) / x;
	} else if (x <= 7.6e-12) {
		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 <= (-940000.0d0)) then
        tmp = ((x - (x * y)) / x) / x
    else if (x <= 7.6d-12) 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 <= -940000.0) {
		tmp = ((x - (x * y)) / x) / x;
	} else if (x <= 7.6e-12) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (x * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -940000.0:
		tmp = ((x - (x * y)) / x) / x
	elif x <= 7.6e-12:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (x * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -940000.0)
		tmp = Float64(Float64(Float64(x - Float64(x * y)) / x) / x);
	elseif (x <= 7.6e-12)
		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 <= -940000.0)
		tmp = ((x - (x * y)) / x) / x;
	elseif (x <= 7.6e-12)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -940000.0], N[(N[(N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 7.6e-12], 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 < -9.4e5

   1. Initial program 67.5%

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

      1. exp-prod 67.5%

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

   3. Simplified 67.5%

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

   4. Taylor expanded in x around inf 44.9%

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

      1. mul-1-neg 44.9%

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

      2. unsub-neg 44.9%

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

   6. Simplified 44.9%

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

      1. frac-sub 40.6%

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

      2. associate-/r* 67.7%

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

      3. *-un-lft-identity 67.7%

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

      4. *-commutative 67.7%

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

   8. Applied egg-rr 67.7%

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

   if -9.4e5 < x < 7.59999999999999993e-12

   1. Initial program 84.6%

      \[\frac{e^{x \cdot \log \left(\frac{x}{x + y}\right)}}{x} \]
   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 99.6%

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

   if 7.59999999999999993e-12 < x

   1. Initial program 70.6%

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

      1. *-commutative 70.6%

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

      2. exp-to-pow 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in x around inf 99.9%

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

      1. mul-1-neg 99.9%

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

   6. Simplified 99.9%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. exp-neg 99.9%

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

      4. associate-/r/ 100.0%

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

      5. /-rgt-identity 100.0%

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

   8. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

   10. Simplified 100.0%

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

   11. Taylor expanded in y around 0 70.0%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -940000:\\ \;\;\;\;\frac{\frac{x - x \cdot y}{x}}{x}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \end{array} \]

Alternative 9: 79.4% accurate, 23.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 7.6e-12) (/ 1.0 x) (/ 1.0 (+ x (* x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 7.6e-12) {
		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 <= 7.6d-12) 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 <= 7.6e-12) {
		tmp = 1.0 / x;
	} else {
		tmp = 1.0 / (x + (x * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 7.6e-12:
		tmp = 1.0 / x
	else:
		tmp = 1.0 / (x + (x * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 7.6e-12)
		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 <= 7.6e-12)
		tmp = 1.0 / x;
	else
		tmp = 1.0 / (x + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 7.6e-12], 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 < 7.59999999999999993e-12

   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 89.2%

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

   3. Simplified 89.2%

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

   4. Taylor expanded in x around 0 81.3%

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

   if 7.59999999999999993e-12 < x

   1. Initial program 70.6%

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

      1. *-commutative 70.6%

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

      2. exp-to-pow 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in x around inf 99.9%

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

      1. mul-1-neg 99.9%

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

   6. Simplified 99.9%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. exp-neg 99.9%

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

      4. associate-/r/ 100.0%

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

      5. /-rgt-identity 100.0%

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

   8. Applied egg-rr 100.0%

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

      1. unpow-1 100.0%

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

   10. Simplified 100.0%

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

   11. Taylor expanded in y around 0 70.0%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.6 \cdot 10^{-12}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + x \cdot y}\\ \end{array} \]

Alternative 10: 75.0% accurate, 29.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.65e+157) (* y (- -1.0 y)) (/ 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.65e+157) {
		tmp = y * (-1.0 - 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 <= (-2.65d+157)) then
        tmp = y * ((-1.0d0) - 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 <= -2.65e+157) {
		tmp = y * (-1.0 - y);
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.65e+157:
		tmp = y * (-1.0 - y)
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.65e+157)
		tmp = Float64(y * Float64(-1.0 - y));
	else
		tmp = Float64(1.0 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.65e+157)
		tmp = y * (-1.0 - y);
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.65e+157], N[(y * N[(-1.0 - y), $MachinePrecision]), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6499999999999999e157

   1. Initial program 59.4%

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

      1. exp-prod 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in x around inf 4.4%

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

      1. mul-1-neg 4.4%

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

      2. unsub-neg 4.4%

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

   6. Simplified 4.4%

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

      1. clear-num 4.4%

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

      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%

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

   8. Applied egg-rr 4.2%

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

      1. associate-*r/ 3.7%

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

   10. Applied egg-rr 3.7%

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

   12. Applied egg-rr 63.0%

       \[\leadsto \color{blue}{-1 \cdot \mathsf{fma}\left(y, y, y\right)} \]
   13. Step-by-step derivation

       1. fma-def 63.0%

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

       2. +-commutative 63.0%

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

       3. distribute-lft-in 63.0%

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

       4. neg-mul-1 63.0%

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

       5. distribute-lft-neg-in 63.0%

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

       6. distribute-rgt-out 63.0%

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

       7. sub-neg 63.0%

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

   14. Simplified 63.0%

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

   if -2.6499999999999999e157 < y

   1. Initial program 78.4%

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

      1. exp-prod 83.6%

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

   3. Simplified 83.6%

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

   4. Taylor expanded in x around 0 78.8%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+157}:\\ \;\;\;\;y \cdot \left(-1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \]

Alternative 11: 74.9% 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 76.4%

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

   1. exp-prod 83.3%

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

3. Simplified 83.3%

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

4. Taylor expanded in x around 0 73.5%

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

5. Final simplification 73.5%

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

Alternative 12: 4.2% accurate, 209.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 y)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

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

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 76.4%

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

   1. exp-prod 83.3%

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

3. Simplified 83.3%

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

4. Taylor expanded in x around inf 56.9%

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

   1. mul-1-neg 56.9%

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

   2. unsub-neg 56.9%

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

6. Simplified 56.9%

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

   1. frac-sub 38.7%

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

   2. *-un-lft-identity 38.7%

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

   3. *-commutative 38.7%

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

8. Applied egg-rr 38.7%

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

9. Taylor expanded in y around inf 6.4%

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

    1. mul-1-neg 6.4%

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

    2. distribute-rgt-neg-in 6.4%

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

11. Simplified 6.4%

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

13. Applied egg-rr 4.1%

    \[\leadsto \color{blue}{y + 0} \]
14. Step-by-step derivation

    1. +-rgt-identity 4.1%

       \[\leadsto \color{blue}{y} \]

15. Simplified 4.1%

    \[\leadsto \color{blue}{y} \]

16. Final simplification 4.1%

    \[\leadsto y \]

Developer target: 77.8% 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 2023238 
(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))