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

Percentage Accurate: 77.2% → 99.3%

Time: 17.2s

Alternatives: 10

Speedup: 11.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.2% 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: 99.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{e^{-y}}{x}\\ \mathbf{if}\;x \leq -0.86:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.043:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (exp (- y)) x)))
   (if (<= x -0.86) t_0 (if (<= x 0.043) (/ 1.0 x) t_0))))

C

double code(double x, double y) {
	double t_0 = exp(-y) / x;
	double tmp;
	if (x <= -0.86) {
		tmp = t_0;
	} else if (x <= 0.043) {
		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 = exp(-y) / x
    if (x <= (-0.86d0)) then
        tmp = t_0
    else if (x <= 0.043d0) 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 = Math.exp(-y) / x;
	double tmp;
	if (x <= -0.86) {
		tmp = t_0;
	} else if (x <= 0.043) {
		tmp = 1.0 / x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.exp(-y) / x
	tmp = 0
	if x <= -0.86:
		tmp = t_0
	elif x <= 0.043:
		tmp = 1.0 / x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(exp(Float64(-y)) / x)
	tmp = 0.0
	if (x <= -0.86)
		tmp = t_0;
	elseif (x <= 0.043)
		tmp = Float64(1.0 / x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = exp(-y) / x;
	tmp = 0.0;
	if (x <= -0.86)
		tmp = t_0;
	elseif (x <= 0.043)
		tmp = 1.0 / x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Exp[(-y)], $MachinePrecision] / x), $MachinePrecision]}, If[LessEqual[x, -0.86], t$95$0, If[LessEqual[x, 0.043], N[(1.0 / x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.859999999999999987 or 0.042999999999999997 < x

   1. Initial program 81.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   if -0.859999999999999987 < x < 0.042999999999999997

   1. Initial program 85.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 85.6% accurate, 6.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{x + y \cdot \left(y \cdot \left(0.5 \cdot \left(1 + x\right)\right) - x\right)}{x}}{x}\\ \mathbf{if}\;x \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.041:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{1}{\left(1 + y\right) \cdot \left(1 + y \cdot y\right)}}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (/ (+ x (* y (- (* y (* 0.5 (+ 1.0 x))) x))) x) x)))
   (if (<= x -1.0)
     t_0
     (if (<= x 0.041)
       (/ 1.0 x)
       (if (<= x 1.4e+133) (/ (/ 1.0 (* (+ 1.0 y) (+ 1.0 (* y y)))) x) t_0)))))

C

double code(double x, double y) {
	double t_0 = ((x + (y * ((y * (0.5 * (1.0 + x))) - x))) / x) / x;
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= 0.041) {
		tmp = 1.0 / x;
	} else if (x <= 1.4e+133) {
		tmp = (1.0 / ((1.0 + y) * (1.0 + (y * y)))) / 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 = ((x + (y * ((y * (0.5d0 * (1.0d0 + x))) - x))) / x) / x
    if (x <= (-1.0d0)) then
        tmp = t_0
    else if (x <= 0.041d0) then
        tmp = 1.0d0 / x
    else if (x <= 1.4d+133) then
        tmp = (1.0d0 / ((1.0d0 + y) * (1.0d0 + (y * y)))) / x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((x + (y * ((y * (0.5 * (1.0 + x))) - x))) / x) / x;
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= 0.041) {
		tmp = 1.0 / x;
	} else if (x <= 1.4e+133) {
		tmp = (1.0 / ((1.0 + y) * (1.0 + (y * y)))) / x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((x + (y * ((y * (0.5 * (1.0 + x))) - x))) / x) / x
	tmp = 0
	if x <= -1.0:
		tmp = t_0
	elif x <= 0.041:
		tmp = 1.0 / x
	elif x <= 1.4e+133:
		tmp = (1.0 / ((1.0 + y) * (1.0 + (y * y)))) / x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(x + Float64(y * Float64(Float64(y * Float64(0.5 * Float64(1.0 + x))) - x))) / x) / x)
	tmp = 0.0
	if (x <= -1.0)
		tmp = t_0;
	elseif (x <= 0.041)
		tmp = Float64(1.0 / x);
	elseif (x <= 1.4e+133)
		tmp = Float64(Float64(1.0 / Float64(Float64(1.0 + y) * Float64(1.0 + Float64(y * y)))) / x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((x + (y * ((y * (0.5 * (1.0 + x))) - x))) / x) / x;
	tmp = 0.0;
	if (x <= -1.0)
		tmp = t_0;
	elseif (x <= 0.041)
		tmp = 1.0 / x;
	elseif (x <= 1.4e+133)
		tmp = (1.0 / ((1.0 + y) * (1.0 + (y * y)))) / x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(x + N[(y * N[(N[(y * N[(0.5 * N[(1.0 + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision]}, If[LessEqual[x, -1.0], t$95$0, If[LessEqual[x, 0.041], N[(1.0 / x), $MachinePrecision], If[LessEqual[x, 1.4e+133], N[(N[(1.0 / N[(N[(1.0 + y), $MachinePrecision] * N[(1.0 + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1 or 1.40000000000000008e133 < x

   1. Initial program 81.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -1 < x < 0.0410000000000000017

   1. Initial program 85.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 0.0410000000000000017 < x < 1.40000000000000008e133

   1. Initial program 84.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in y around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 84.0% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1 + y \cdot \left(-1 + y \cdot \left(0.5 + y \cdot -0.16666666666666666\right)\right)}{x}\\ \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{1}{\left(1 + y\right) \cdot \left(1 + y \cdot y\right)}}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0
         (/
          (+ 1.0 (* y (+ -1.0 (* y (+ 0.5 (* y -0.16666666666666666))))))
          x)))
   (if (<= x -0.75)
     t_0
     (if (<= x 8.6e-5)
       (/ 1.0 x)
       (if (<= x 1.4e+133) (/ (/ 1.0 (* (+ 1.0 y) (+ 1.0 (* y y)))) x) t_0)))))

C

double code(double x, double y) {
	double t_0 = (1.0 + (y * (-1.0 + (y * (0.5 + (y * -0.16666666666666666)))))) / x;
	double tmp;
	if (x <= -0.75) {
		tmp = t_0;
	} else if (x <= 8.6e-5) {
		tmp = 1.0 / x;
	} else if (x <= 1.4e+133) {
		tmp = (1.0 / ((1.0 + y) * (1.0 + (y * y)))) / 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 + (y * ((-1.0d0) + (y * (0.5d0 + (y * (-0.16666666666666666d0))))))) / x
    if (x <= (-0.75d0)) then
        tmp = t_0
    else if (x <= 8.6d-5) then
        tmp = 1.0d0 / x
    else if (x <= 1.4d+133) then
        tmp = (1.0d0 / ((1.0d0 + y) * (1.0d0 + (y * y)))) / 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 + (y * (-1.0 + (y * (0.5 + (y * -0.16666666666666666)))))) / x;
	double tmp;
	if (x <= -0.75) {
		tmp = t_0;
	} else if (x <= 8.6e-5) {
		tmp = 1.0 / x;
	} else if (x <= 1.4e+133) {
		tmp = (1.0 / ((1.0 + y) * (1.0 + (y * y)))) / x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (1.0 + (y * (-1.0 + (y * (0.5 + (y * -0.16666666666666666)))))) / x
	tmp = 0
	if x <= -0.75:
		tmp = t_0
	elif x <= 8.6e-5:
		tmp = 1.0 / x
	elif x <= 1.4e+133:
		tmp = (1.0 / ((1.0 + y) * (1.0 + (y * y)))) / x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 + Float64(y * Float64(-1.0 + Float64(y * Float64(0.5 + Float64(y * -0.16666666666666666)))))) / x)
	tmp = 0.0
	if (x <= -0.75)
		tmp = t_0;
	elseif (x <= 8.6e-5)
		tmp = Float64(1.0 / x);
	elseif (x <= 1.4e+133)
		tmp = Float64(Float64(1.0 / Float64(Float64(1.0 + y) * Float64(1.0 + Float64(y * y)))) / x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (1.0 + (y * (-1.0 + (y * (0.5 + (y * -0.16666666666666666)))))) / x;
	tmp = 0.0;
	if (x <= -0.75)
		tmp = t_0;
	elseif (x <= 8.6e-5)
		tmp = 1.0 / x;
	elseif (x <= 1.4e+133)
		tmp = (1.0 / ((1.0 + y) * (1.0 + (y * y)))) / x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 + N[(y * N[(-1.0 + N[(y * N[(0.5 + N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]}, If[LessEqual[x, -0.75], t$95$0, If[LessEqual[x, 8.6e-5], N[(1.0 / x), $MachinePrecision], If[LessEqual[x, 1.4e+133], N[(N[(1.0 / N[(N[(1.0 + y), $MachinePrecision] * N[(1.0 + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.75 or 1.40000000000000008e133 < x

   1. Initial program 81.1%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -0.75 < x < 8.6000000000000003e-5

   1. Initial program 85.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 8.6000000000000003e-5 < x < 1.40000000000000008e133

   1. Initial program 84.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in y around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 83.0% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.29:\\ \;\;\;\;\frac{1 - y}{x} + y \cdot \left(\frac{y}{x} \cdot \left(y \cdot -0.16666666666666666\right)\right)\\ \mathbf{elif}\;x \leq 0.043:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{1}{\left(1 + y\right) \cdot \left(1 + y \cdot y\right)}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - y\right)}{x}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.29)
   (+ (/ (- 1.0 y) x) (* y (* (/ y x) (* y -0.16666666666666666))))
   (if (<= x 0.043)
     (/ 1.0 x)
     (if (<= x 1.35e+133)
       (/ (/ 1.0 (* (+ 1.0 y) (+ 1.0 (* y y)))) x)
       (/ (/ (* x (- 1.0 y)) x) x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.29) {
		tmp = ((1.0 - y) / x) + (y * ((y / x) * (y * -0.16666666666666666)));
	} else if (x <= 0.043) {
		tmp = 1.0 / x;
	} else if (x <= 1.35e+133) {
		tmp = (1.0 / ((1.0 + y) * (1.0 + (y * y)))) / x;
	} else {
		tmp = ((x * (1.0 - y)) / x) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.29d0)) then
        tmp = ((1.0d0 - y) / x) + (y * ((y / x) * (y * (-0.16666666666666666d0))))
    else if (x <= 0.043d0) then
        tmp = 1.0d0 / x
    else if (x <= 1.35d+133) then
        tmp = (1.0d0 / ((1.0d0 + y) * (1.0d0 + (y * y)))) / x
    else
        tmp = ((x * (1.0d0 - y)) / x) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.29) {
		tmp = ((1.0 - y) / x) + (y * ((y / x) * (y * -0.16666666666666666)));
	} else if (x <= 0.043) {
		tmp = 1.0 / x;
	} else if (x <= 1.35e+133) {
		tmp = (1.0 / ((1.0 + y) * (1.0 + (y * y)))) / x;
	} else {
		tmp = ((x * (1.0 - y)) / x) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.29:
		tmp = ((1.0 - y) / x) + (y * ((y / x) * (y * -0.16666666666666666)))
	elif x <= 0.043:
		tmp = 1.0 / x
	elif x <= 1.35e+133:
		tmp = (1.0 / ((1.0 + y) * (1.0 + (y * y)))) / x
	else:
		tmp = ((x * (1.0 - y)) / x) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.29)
		tmp = Float64(Float64(Float64(1.0 - y) / x) + Float64(y * Float64(Float64(y / x) * Float64(y * -0.16666666666666666))));
	elseif (x <= 0.043)
		tmp = Float64(1.0 / x);
	elseif (x <= 1.35e+133)
		tmp = Float64(Float64(1.0 / Float64(Float64(1.0 + y) * Float64(1.0 + Float64(y * y)))) / x);
	else
		tmp = Float64(Float64(Float64(x * Float64(1.0 - y)) / x) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.29)
		tmp = ((1.0 - y) / x) + (y * ((y / x) * (y * -0.16666666666666666)));
	elseif (x <= 0.043)
		tmp = 1.0 / x;
	elseif (x <= 1.35e+133)
		tmp = (1.0 / ((1.0 + y) * (1.0 + (y * y)))) / x;
	else
		tmp = ((x * (1.0 - y)) / x) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.29], N[(N[(N[(1.0 - y), $MachinePrecision] / x), $MachinePrecision] + N[(y * N[(N[(y / x), $MachinePrecision] * N[(y * -0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.043], N[(1.0 / x), $MachinePrecision], If[LessEqual[x, 1.35e+133], N[(N[(1.0 / N[(N[(1.0 + y), $MachinePrecision] * N[(1.0 + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(N[(N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -0.28999999999999998

   1. Initial program 81.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if -0.28999999999999998 < x < 0.042999999999999997

   1. Initial program 85.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 0.042999999999999997 < x < 1.3500000000000001e133

   1. Initial program 84.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in y around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   if 1.3500000000000001e133 < x

   1. Initial program 80.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 5: 82.9% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.72:\\ \;\;\;\;\frac{1 + y \cdot \left(-1 + y \cdot 0.5\right)}{x}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-7}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{1}{\left(1 + y\right) \cdot \left(1 + y \cdot y\right)}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - y\right)}{x}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.72)
   (/ (+ 1.0 (* y (+ -1.0 (* y 0.5)))) x)
   (if (<= x 1.75e-7)
     (/ 1.0 x)
     (if (<= x 1.3e+133)
       (/ (/ 1.0 (* (+ 1.0 y) (+ 1.0 (* y y)))) x)
       (/ (/ (* x (- 1.0 y)) x) x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.72) {
		tmp = (1.0 + (y * (-1.0 + (y * 0.5)))) / x;
	} else if (x <= 1.75e-7) {
		tmp = 1.0 / x;
	} else if (x <= 1.3e+133) {
		tmp = (1.0 / ((1.0 + y) * (1.0 + (y * y)))) / x;
	} else {
		tmp = ((x * (1.0 - y)) / x) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.72d0)) then
        tmp = (1.0d0 + (y * ((-1.0d0) + (y * 0.5d0)))) / x
    else if (x <= 1.75d-7) then
        tmp = 1.0d0 / x
    else if (x <= 1.3d+133) then
        tmp = (1.0d0 / ((1.0d0 + y) * (1.0d0 + (y * y)))) / x
    else
        tmp = ((x * (1.0d0 - y)) / x) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.72) {
		tmp = (1.0 + (y * (-1.0 + (y * 0.5)))) / x;
	} else if (x <= 1.75e-7) {
		tmp = 1.0 / x;
	} else if (x <= 1.3e+133) {
		tmp = (1.0 / ((1.0 + y) * (1.0 + (y * y)))) / x;
	} else {
		tmp = ((x * (1.0 - y)) / x) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.72:
		tmp = (1.0 + (y * (-1.0 + (y * 0.5)))) / x
	elif x <= 1.75e-7:
		tmp = 1.0 / x
	elif x <= 1.3e+133:
		tmp = (1.0 / ((1.0 + y) * (1.0 + (y * y)))) / x
	else:
		tmp = ((x * (1.0 - y)) / x) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.72)
		tmp = Float64(Float64(1.0 + Float64(y * Float64(-1.0 + Float64(y * 0.5)))) / x);
	elseif (x <= 1.75e-7)
		tmp = Float64(1.0 / x);
	elseif (x <= 1.3e+133)
		tmp = Float64(Float64(1.0 / Float64(Float64(1.0 + y) * Float64(1.0 + Float64(y * y)))) / x);
	else
		tmp = Float64(Float64(Float64(x * Float64(1.0 - y)) / x) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.72)
		tmp = (1.0 + (y * (-1.0 + (y * 0.5)))) / x;
	elseif (x <= 1.75e-7)
		tmp = 1.0 / x;
	elseif (x <= 1.3e+133)
		tmp = (1.0 / ((1.0 + y) * (1.0 + (y * y)))) / x;
	else
		tmp = ((x * (1.0 - y)) / x) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.72], N[(N[(1.0 + N[(y * N[(-1.0 + N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 1.75e-7], N[(1.0 / x), $MachinePrecision], If[LessEqual[x, 1.3e+133], N[(N[(1.0 / N[(N[(1.0 + y), $MachinePrecision] * N[(1.0 + N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(N[(N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -0.71999999999999997

   1. Initial program 81.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -0.71999999999999997 < x < 1.74999999999999992e-7

   1. Initial program 85.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 1.74999999999999992e-7 < x < 1.2999999999999999e133

   1. Initial program 84.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in y around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   if 1.2999999999999999e133 < x

   1. Initial program 80.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 82.4% accurate, 8.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.034:\\ \;\;\;\;\frac{1 + y \cdot \left(-1 + y \cdot 0.5\right)}{x}\\ \mathbf{elif}\;x \leq 0.036:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+133}:\\ \;\;\;\;\frac{\frac{1}{1 + y \cdot \left(1 + y\right)}}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - y\right)}{x}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.034)
   (/ (+ 1.0 (* y (+ -1.0 (* y 0.5)))) x)
   (if (<= x 0.036)
     (/ 1.0 x)
     (if (<= x 1.08e+133)
       (/ (/ 1.0 (+ 1.0 (* y (+ 1.0 y)))) x)
       (/ (/ (* x (- 1.0 y)) x) x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.034) {
		tmp = (1.0 + (y * (-1.0 + (y * 0.5)))) / x;
	} else if (x <= 0.036) {
		tmp = 1.0 / x;
	} else if (x <= 1.08e+133) {
		tmp = (1.0 / (1.0 + (y * (1.0 + y)))) / x;
	} else {
		tmp = ((x * (1.0 - y)) / x) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.034d0)) then
        tmp = (1.0d0 + (y * ((-1.0d0) + (y * 0.5d0)))) / x
    else if (x <= 0.036d0) then
        tmp = 1.0d0 / x
    else if (x <= 1.08d+133) then
        tmp = (1.0d0 / (1.0d0 + (y * (1.0d0 + y)))) / x
    else
        tmp = ((x * (1.0d0 - y)) / x) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.034) {
		tmp = (1.0 + (y * (-1.0 + (y * 0.5)))) / x;
	} else if (x <= 0.036) {
		tmp = 1.0 / x;
	} else if (x <= 1.08e+133) {
		tmp = (1.0 / (1.0 + (y * (1.0 + y)))) / x;
	} else {
		tmp = ((x * (1.0 - y)) / x) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.034:
		tmp = (1.0 + (y * (-1.0 + (y * 0.5)))) / x
	elif x <= 0.036:
		tmp = 1.0 / x
	elif x <= 1.08e+133:
		tmp = (1.0 / (1.0 + (y * (1.0 + y)))) / x
	else:
		tmp = ((x * (1.0 - y)) / x) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.034)
		tmp = Float64(Float64(1.0 + Float64(y * Float64(-1.0 + Float64(y * 0.5)))) / x);
	elseif (x <= 0.036)
		tmp = Float64(1.0 / x);
	elseif (x <= 1.08e+133)
		tmp = Float64(Float64(1.0 / Float64(1.0 + Float64(y * Float64(1.0 + y)))) / x);
	else
		tmp = Float64(Float64(Float64(x * Float64(1.0 - y)) / x) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.034)
		tmp = (1.0 + (y * (-1.0 + (y * 0.5)))) / x;
	elseif (x <= 0.036)
		tmp = 1.0 / x;
	elseif (x <= 1.08e+133)
		tmp = (1.0 / (1.0 + (y * (1.0 + y)))) / x;
	else
		tmp = ((x * (1.0 - y)) / x) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.034], N[(N[(1.0 + N[(y * N[(-1.0 + N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 0.036], N[(1.0 / x), $MachinePrecision], If[LessEqual[x, 1.08e+133], N[(N[(1.0 / N[(1.0 + N[(y * N[(1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], N[(N[(N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -0.034000000000000002

   1. Initial program 81.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -0.034000000000000002 < x < 0.0359999999999999973

   1. Initial program 85.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 0.0359999999999999973 < x < 1.08e133

   1. Initial program 84.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in y around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]

   if 1.08e133 < x

   1. Initial program 80.6%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 76.8% accurate, 10.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+192}:\\ \;\;\;\;\frac{0.5 \cdot \left(y \cdot y\right)}{x}\\ \mathbf{elif}\;y \leq 4.5:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+178}:\\ \;\;\;\;\frac{x}{x \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -8.5e+192)
   (/ (* 0.5 (* y y)) x)
   (if (<= y 4.5) (/ 1.0 x) (if (<= y 8e+178) (/ x (* x x)) (/ 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -8.5e+192) {
		tmp = (0.5 * (y * y)) / x;
	} else if (y <= 4.5) {
		tmp = 1.0 / x;
	} else if (y <= 8e+178) {
		tmp = x / (x * x);
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-8.5d+192)) then
        tmp = (0.5d0 * (y * y)) / x
    else if (y <= 4.5d0) then
        tmp = 1.0d0 / x
    else if (y <= 8d+178) then
        tmp = x / (x * x)
    else
        tmp = 1.0d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -8.5e+192) {
		tmp = (0.5 * (y * y)) / x;
	} else if (y <= 4.5) {
		tmp = 1.0 / x;
	} else if (y <= 8e+178) {
		tmp = x / (x * x);
	} else {
		tmp = 1.0 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -8.5e+192:
		tmp = (0.5 * (y * y)) / x
	elif y <= 4.5:
		tmp = 1.0 / x
	elif y <= 8e+178:
		tmp = x / (x * x)
	else:
		tmp = 1.0 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -8.5e+192)
		tmp = Float64(Float64(0.5 * Float64(y * y)) / x);
	elseif (y <= 4.5)
		tmp = Float64(1.0 / x);
	elseif (y <= 8e+178)
		tmp = Float64(x / Float64(x * x));
	else
		tmp = Float64(1.0 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -8.5e+192)
		tmp = (0.5 * (y * y)) / x;
	elseif (y <= 4.5)
		tmp = 1.0 / x;
	elseif (y <= 8e+178)
		tmp = x / (x * x);
	else
		tmp = 1.0 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -8.5e+192], N[(N[(0.5 * N[(y * y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[y, 4.5], N[(1.0 / x), $MachinePrecision], If[LessEqual[y, 8e+178], N[(x / N[(x * x), $MachinePrecision]), $MachinePrecision], N[(1.0 / x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.49999999999999965e192

   1. Initial program 72.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   11. Taylor expanded in y around inf 0

       \[\leadsto expr\]

   13. Simplified 0

       \[\leadsto expr\]

   if -8.49999999999999965e192 < y < 4.5 or 8.0000000000000004e178 < y

   1. Initial program 87.9%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 4.5 < y < 8.0000000000000004e178

   1. Initial program 45.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   10. Taylor expanded in y around 0 0

       \[\leadsto expr\]

   12. Simplified 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 8: 80.4% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.9:\\ \;\;\;\;\frac{1 + y \cdot \left(-1 + y \cdot 0.5\right)}{x}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+77}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(1 - y\right)}{x}}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.9)
   (/ (+ 1.0 (* y (+ -1.0 (* y 0.5)))) x)
   (if (<= x 3e+77) (/ 1.0 x) (/ (/ (* x (- 1.0 y)) x) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.9) {
		tmp = (1.0 + (y * (-1.0 + (y * 0.5)))) / x;
	} else if (x <= 3e+77) {
		tmp = 1.0 / x;
	} else {
		tmp = ((x * (1.0 - y)) / x) / x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.9d0)) then
        tmp = (1.0d0 + (y * ((-1.0d0) + (y * 0.5d0)))) / x
    else if (x <= 3d+77) then
        tmp = 1.0d0 / x
    else
        tmp = ((x * (1.0d0 - y)) / x) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.9) {
		tmp = (1.0 + (y * (-1.0 + (y * 0.5)))) / x;
	} else if (x <= 3e+77) {
		tmp = 1.0 / x;
	} else {
		tmp = ((x * (1.0 - y)) / x) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.9:
		tmp = (1.0 + (y * (-1.0 + (y * 0.5)))) / x
	elif x <= 3e+77:
		tmp = 1.0 / x
	else:
		tmp = ((x * (1.0 - y)) / x) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.9)
		tmp = Float64(Float64(1.0 + Float64(y * Float64(-1.0 + Float64(y * 0.5)))) / x);
	elseif (x <= 3e+77)
		tmp = Float64(1.0 / x);
	else
		tmp = Float64(Float64(Float64(x * Float64(1.0 - y)) / x) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.9)
		tmp = (1.0 + (y * (-1.0 + (y * 0.5)))) / x;
	elseif (x <= 3e+77)
		tmp = 1.0 / x;
	else
		tmp = ((x * (1.0 - y)) / x) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.9], N[(N[(1.0 + N[(y * N[(-1.0 + N[(y * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 3e+77], N[(1.0 / x), $MachinePrecision], N[(N[(N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.900000000000000022

   1. Initial program 81.4%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   8. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   10. Simplified 0

       \[\leadsto expr\]

   if -0.900000000000000022 < x < 2.9999999999999998e77

   1. Initial program 85.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   if 2.9999999999999998e77 < x

   1. Initial program 80.8%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 80.4% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{x \cdot \left(1 - y\right)}{x}}{x}\\ \mathbf{if}\;x \leq -0.18:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+80}:\\ \;\;\;\;\frac{1}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (/ (* x (- 1.0 y)) x) x)))
   (if (<= x -0.18) t_0 (if (<= x 2.3e+80) (/ 1.0 x) t_0))))

C

double code(double x, double y) {
	double t_0 = ((x * (1.0 - y)) / x) / x;
	double tmp;
	if (x <= -0.18) {
		tmp = t_0;
	} else if (x <= 2.3e+80) {
		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 = ((x * (1.0d0 - y)) / x) / x
    if (x <= (-0.18d0)) then
        tmp = t_0
    else if (x <= 2.3d+80) 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 = ((x * (1.0 - y)) / x) / x;
	double tmp;
	if (x <= -0.18) {
		tmp = t_0;
	} else if (x <= 2.3e+80) {
		tmp = 1.0 / x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((x * (1.0 - y)) / x) / x
	tmp = 0
	if x <= -0.18:
		tmp = t_0
	elif x <= 2.3e+80:
		tmp = 1.0 / x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(x * Float64(1.0 - y)) / x) / x)
	tmp = 0.0
	if (x <= -0.18)
		tmp = t_0;
	elseif (x <= 2.3e+80)
		tmp = Float64(1.0 / x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((x * (1.0 - y)) / x) / x;
	tmp = 0.0;
	if (x <= -0.18)
		tmp = t_0;
	elseif (x <= 2.3e+80)
		tmp = 1.0 / x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] / x), $MachinePrecision]}, If[LessEqual[x, -0.18], t$95$0, If[LessEqual[x, 2.3e+80], N[(1.0 / x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -0.17999999999999999 or 2.30000000000000004e80 < x

   1. Initial program 81.2%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]

   9. Applied egg-rr 0

      \[\leadsto expr\]

   11. Applied egg-rr 0

       \[\leadsto expr\]

   if -0.17999999999999999 < x < 2.30000000000000004e80

   1. Initial program 85.5%

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

   3. Simplified 0

      \[\leadsto expr\]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   7. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 74.2% 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 83.2%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

5. Taylor expanded in x around 0 0

   \[\leadsto expr\]

7. Simplified 0

   \[\leadsto expr\]
8. Add Preprocessing

Developer target: 77.2% 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 2024110 
(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))