Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, A

Percentage Accurate: 68.5% → 99.8%

Time: 12.7s

Alternatives: 15

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y}{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(\left(x + y\right) + 1\right)} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{y}{y + \left(x + 1\right)} \cdot \frac{\frac{x}{y + x}}{y + x} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.0%

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

   1. associate-/l* 83.6%

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

   2. associate-+l+ 83.6%

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

3. Simplified 83.6%

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

   1. associate-*r/ 65.0%

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

   2. associate-+r+ 65.0%

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

   3. associate-*l* 65.0%

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

   4. associate-/r* 70.7%

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

   5. *-commutative 70.7%

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

   6. +-commutative 70.7%

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

   7. +-commutative 70.7%

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

   8. associate-+r+ 70.7%

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

   9. +-commutative 70.7%

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

   10. associate-+l+ 70.7%

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

6. Applied egg-rr 70.7%

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

   1. associate-/l* 94.4%

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

   2. *-commutative 94.4%

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

   3. +-commutative 94.4%

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

   4. times-frac 99.8%

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

   5. +-commutative 99.8%

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

   6. +-commutative 99.8%

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

8. Applied egg-rr 99.8%

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

9. Final simplification 99.8%

   \[\leadsto \frac{y}{y + \left(x + 1\right)} \cdot \frac{\frac{x}{y + x}}{y + x} \]
10. Add Preprocessing

Alternative 2: 89.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y + x}\\ \mathbf{if}\;y \leq 1.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{t\_0}{y + x} \cdot \frac{y}{x + 1}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \frac{y}{\left(\left(y + x\right) \cdot \left(y + x\right)\right) \cdot \left(x + \left(y + 1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0 \cdot \frac{1}{y + \left(x + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ y x))))
   (if (<= y 1.8e-16)
     (* (/ t_0 (+ y x)) (/ y (+ x 1.0)))
     (if (<= y 4.2e+119)
       (* x (/ y (* (* (+ y x) (+ y x)) (+ x (+ y 1.0)))))
       (* t_0 (/ 1.0 (+ y (+ x 1.0))))))))

C

double code(double x, double y) {
	double t_0 = x / (y + x);
	double tmp;
	if (y <= 1.8e-16) {
		tmp = (t_0 / (y + x)) * (y / (x + 1.0));
	} else if (y <= 4.2e+119) {
		tmp = x * (y / (((y + x) * (y + x)) * (x + (y + 1.0))));
	} else {
		tmp = t_0 * (1.0 / (y + (x + 1.0)));
	}
	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 + x)
    if (y <= 1.8d-16) then
        tmp = (t_0 / (y + x)) * (y / (x + 1.0d0))
    else if (y <= 4.2d+119) then
        tmp = x * (y / (((y + x) * (y + x)) * (x + (y + 1.0d0))))
    else
        tmp = t_0 * (1.0d0 / (y + (x + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y + x);
	double tmp;
	if (y <= 1.8e-16) {
		tmp = (t_0 / (y + x)) * (y / (x + 1.0));
	} else if (y <= 4.2e+119) {
		tmp = x * (y / (((y + x) * (y + x)) * (x + (y + 1.0))));
	} else {
		tmp = t_0 * (1.0 / (y + (x + 1.0)));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y + x)
	tmp = 0
	if y <= 1.8e-16:
		tmp = (t_0 / (y + x)) * (y / (x + 1.0))
	elif y <= 4.2e+119:
		tmp = x * (y / (((y + x) * (y + x)) * (x + (y + 1.0))))
	else:
		tmp = t_0 * (1.0 / (y + (x + 1.0)))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y + x))
	tmp = 0.0
	if (y <= 1.8e-16)
		tmp = Float64(Float64(t_0 / Float64(y + x)) * Float64(y / Float64(x + 1.0)));
	elseif (y <= 4.2e+119)
		tmp = Float64(x * Float64(y / Float64(Float64(Float64(y + x) * Float64(y + x)) * Float64(x + Float64(y + 1.0)))));
	else
		tmp = Float64(t_0 * Float64(1.0 / Float64(y + Float64(x + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y + x);
	tmp = 0.0;
	if (y <= 1.8e-16)
		tmp = (t_0 / (y + x)) * (y / (x + 1.0));
	elseif (y <= 4.2e+119)
		tmp = x * (y / (((y + x) * (y + x)) * (x + (y + 1.0))));
	else
		tmp = t_0 * (1.0 / (y + (x + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 1.8e-16], N[(N[(t$95$0 / N[(y + x), $MachinePrecision]), $MachinePrecision] * N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e+119], N[(x * N[(y / N[(N[(N[(y + x), $MachinePrecision] * N[(y + x), $MachinePrecision]), $MachinePrecision] * N[(x + N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 * N[(1.0 / N[(y + N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 1.79999999999999991e-16

   1. Initial program 64.4%

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

      1. associate-/l* 83.0%

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

      2. associate-+l+ 83.0%

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

   3. Simplified 83.0%

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

      1. associate-*r/ 64.4%

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

      2. associate-+r+ 64.4%

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

      3. associate-*l* 64.4%

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

      4. associate-/r* 69.4%

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

      5. *-commutative 69.4%

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

      6. +-commutative 69.4%

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

      7. +-commutative 69.4%

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

      8. associate-+r+ 69.4%

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

      9. +-commutative 69.4%

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

      10. associate-+l+ 69.4%

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

   6. Applied egg-rr 69.4%

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

      1. associate-/l* 95.5%

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

      2. *-commutative 95.5%

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

      3. +-commutative 95.5%

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

      4. times-frac 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in y around 0 90.4%

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

       1. +-commutative 90.4%

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

   11. Simplified 90.4%

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

   if 1.79999999999999991e-16 < y < 4.19999999999999966e119

   1. Initial program 74.6%

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

      1. associate-/l* 90.9%

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

      2. associate-+l+ 90.9%

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

   3. Simplified 90.9%

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

   if 4.19999999999999966e119 < y

   1. Initial program 61.0%

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

      1. associate-/l* 81.4%

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

      2. associate-+l+ 81.4%

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

   3. Simplified 81.4%

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

      1. associate-*r/ 61.0%

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

      2. associate-+r+ 61.0%

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

      3. associate-*l* 61.0%

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

      4. associate-/r* 68.6%

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

      5. *-commutative 68.6%

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

      6. +-commutative 68.6%

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

      7. +-commutative 68.6%

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

      8. associate-+r+ 68.6%

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

      9. +-commutative 68.6%

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

      10. associate-+l+ 68.6%

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

   6. Applied egg-rr 68.6%

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

   7. Taylor expanded in y around inf 88.1%

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

      1. associate-/r* 95.1%

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

      2. +-commutative 95.1%

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

      3. +-commutative 95.1%

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

      4. div-inv 95.1%

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

      5. +-commutative 95.1%

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

   9. Applied egg-rr 95.1%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.8 \cdot 10^{-16}:\\ \;\;\;\;\frac{\frac{x}{y + x}}{y + x} \cdot \frac{y}{x + 1}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+119}:\\ \;\;\;\;x \cdot \frac{y}{\left(\left(y + x\right) \cdot \left(y + x\right)\right) \cdot \left(x + \left(y + 1\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + x} \cdot \frac{1}{y + \left(x + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y + \left(x + 1\right)\\ t_1 := \frac{x}{y + x}\\ \mathbf{if}\;y \leq 2.05 \cdot 10^{-11}:\\ \;\;\;\;\frac{t\_1}{y + x} \cdot \frac{y}{x + 1}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{t\_0 \cdot \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \frac{1}{t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ y (+ x 1.0))) (t_1 (/ x (+ y x))))
   (if (<= y 2.05e-11)
     (* (/ t_1 (+ y x)) (/ y (+ x 1.0)))
     (if (<= y 1.9e+123) (/ x (* t_0 (+ y x))) (* t_1 (/ 1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = y + (x + 1.0);
	double t_1 = x / (y + x);
	double tmp;
	if (y <= 2.05e-11) {
		tmp = (t_1 / (y + x)) * (y / (x + 1.0));
	} else if (y <= 1.9e+123) {
		tmp = x / (t_0 * (y + x));
	} else {
		tmp = t_1 * (1.0 / 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 = y + (x + 1.0d0)
    t_1 = x / (y + x)
    if (y <= 2.05d-11) then
        tmp = (t_1 / (y + x)) * (y / (x + 1.0d0))
    else if (y <= 1.9d+123) then
        tmp = x / (t_0 * (y + x))
    else
        tmp = t_1 * (1.0d0 / t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y + (x + 1.0);
	double t_1 = x / (y + x);
	double tmp;
	if (y <= 2.05e-11) {
		tmp = (t_1 / (y + x)) * (y / (x + 1.0));
	} else if (y <= 1.9e+123) {
		tmp = x / (t_0 * (y + x));
	} else {
		tmp = t_1 * (1.0 / t_0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y + (x + 1.0)
	t_1 = x / (y + x)
	tmp = 0
	if y <= 2.05e-11:
		tmp = (t_1 / (y + x)) * (y / (x + 1.0))
	elif y <= 1.9e+123:
		tmp = x / (t_0 * (y + x))
	else:
		tmp = t_1 * (1.0 / t_0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y + Float64(x + 1.0))
	t_1 = Float64(x / Float64(y + x))
	tmp = 0.0
	if (y <= 2.05e-11)
		tmp = Float64(Float64(t_1 / Float64(y + x)) * Float64(y / Float64(x + 1.0)));
	elseif (y <= 1.9e+123)
		tmp = Float64(x / Float64(t_0 * Float64(y + x)));
	else
		tmp = Float64(t_1 * Float64(1.0 / t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y + (x + 1.0);
	t_1 = x / (y + x);
	tmp = 0.0;
	if (y <= 2.05e-11)
		tmp = (t_1 / (y + x)) * (y / (x + 1.0));
	elseif (y <= 1.9e+123)
		tmp = x / (t_0 * (y + x));
	else
		tmp = t_1 * (1.0 / t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y + N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(y + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 2.05e-11], N[(N[(t$95$1 / N[(y + x), $MachinePrecision]), $MachinePrecision] * N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+123], N[(x / N[(t$95$0 * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 2.05e-11

   1. Initial program 64.6%

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

      1. associate-/l* 83.1%

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

      2. associate-+l+ 83.0%

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

   3. Simplified 83.0%

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

      1. associate-*r/ 64.6%

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

      2. associate-+r+ 64.6%

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

      3. associate-*l* 64.6%

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

      4. associate-/r* 69.6%

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

      5. *-commutative 69.6%

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

      6. +-commutative 69.6%

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

      7. +-commutative 69.6%

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

      8. associate-+r+ 69.6%

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

      9. +-commutative 69.6%

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

      10. associate-+l+ 69.6%

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

   6. Applied egg-rr 69.6%

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

      1. associate-/l* 95.5%

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

      2. *-commutative 95.5%

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

      3. +-commutative 95.5%

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

      4. times-frac 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in y around 0 90.5%

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

       1. +-commutative 90.5%

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

   11. Simplified 90.5%

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

   if 2.05e-11 < y < 1.89999999999999997e123

   1. Initial program 73.8%

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

      1. associate-/l* 90.6%

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

      2. associate-+l+ 90.6%

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

   3. Simplified 90.6%

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

      1. associate-*r/ 73.8%

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

      2. associate-+r+ 73.8%

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

      3. associate-*l* 73.9%

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

      4. associate-/r* 80.1%

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

      5. *-commutative 80.1%

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

      6. +-commutative 80.1%

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

      7. +-commutative 80.1%

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

      8. associate-+r+ 80.1%

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

      9. +-commutative 80.1%

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

      10. associate-+l+ 80.1%

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

   6. Applied egg-rr 80.1%

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

   7. Taylor expanded in y around inf 89.3%

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

   if 1.89999999999999997e123 < y

   1. Initial program 61.0%

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

      1. associate-/l* 81.4%

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

      2. associate-+l+ 81.4%

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

   3. Simplified 81.4%

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

      1. associate-*r/ 61.0%

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

      2. associate-+r+ 61.0%

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

      3. associate-*l* 61.0%

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

      4. associate-/r* 68.6%

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

      5. *-commutative 68.6%

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

      6. +-commutative 68.6%

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

      7. +-commutative 68.6%

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

      8. associate-+r+ 68.6%

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

      9. +-commutative 68.6%

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

      10. associate-+l+ 68.6%

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

   6. Applied egg-rr 68.6%

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

   7. Taylor expanded in y around inf 88.1%

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

      1. associate-/r* 95.1%

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

      2. +-commutative 95.1%

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

      3. +-commutative 95.1%

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

      4. div-inv 95.1%

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

      5. +-commutative 95.1%

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

   9. Applied egg-rr 95.1%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.05 \cdot 10^{-11}:\\ \;\;\;\;\frac{\frac{x}{y + x}}{y + x} \cdot \frac{y}{x + 1}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{\left(y + \left(x + 1\right)\right) \cdot \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + x} \cdot \frac{1}{y + \left(x + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y + \left(x + 1\right)\\ \mathbf{if}\;y \leq 3.5 \cdot 10^{-239}:\\ \;\;\;\;\frac{\frac{y}{x}}{x + 1}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{t\_0 \cdot \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + x} \cdot \frac{1}{t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ y (+ x 1.0))))
   (if (<= y 3.5e-239)
     (/ (/ y x) (+ x 1.0))
     (if (<= y 1.9e+123)
       (/ x (* t_0 (+ y x)))
       (* (/ x (+ y x)) (/ 1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = y + (x + 1.0);
	double tmp;
	if (y <= 3.5e-239) {
		tmp = (y / x) / (x + 1.0);
	} else if (y <= 1.9e+123) {
		tmp = x / (t_0 * (y + x));
	} else {
		tmp = (x / (y + x)) * (1.0 / 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 = y + (x + 1.0d0)
    if (y <= 3.5d-239) then
        tmp = (y / x) / (x + 1.0d0)
    else if (y <= 1.9d+123) then
        tmp = x / (t_0 * (y + x))
    else
        tmp = (x / (y + x)) * (1.0d0 / t_0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y + (x + 1.0);
	double tmp;
	if (y <= 3.5e-239) {
		tmp = (y / x) / (x + 1.0);
	} else if (y <= 1.9e+123) {
		tmp = x / (t_0 * (y + x));
	} else {
		tmp = (x / (y + x)) * (1.0 / t_0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y + (x + 1.0)
	tmp = 0
	if y <= 3.5e-239:
		tmp = (y / x) / (x + 1.0)
	elif y <= 1.9e+123:
		tmp = x / (t_0 * (y + x))
	else:
		tmp = (x / (y + x)) * (1.0 / t_0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y + Float64(x + 1.0))
	tmp = 0.0
	if (y <= 3.5e-239)
		tmp = Float64(Float64(y / x) / Float64(x + 1.0));
	elseif (y <= 1.9e+123)
		tmp = Float64(x / Float64(t_0 * Float64(y + x)));
	else
		tmp = Float64(Float64(x / Float64(y + x)) * Float64(1.0 / t_0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y + (x + 1.0);
	tmp = 0.0;
	if (y <= 3.5e-239)
		tmp = (y / x) / (x + 1.0);
	elseif (y <= 1.9e+123)
		tmp = x / (t_0 * (y + x));
	else
		tmp = (x / (y + x)) * (1.0 / t_0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y + N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 3.5e-239], N[(N[(y / x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+123], N[(x / N[(t$95$0 * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y + x), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.50000000000000005e-239

   1. Initial program 63.4%

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

      1. associate-/l* 83.5%

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

      2. associate-+l+ 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in y around 0 59.6%

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

      1. associate-/r* 56.9%

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

      2. +-commutative 56.9%

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

   7. Simplified 56.9%

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

   if 3.50000000000000005e-239 < y < 1.89999999999999997e123

   1. Initial program 71.3%

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

      1. associate-/l* 85.5%

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

      2. associate-+l+ 85.5%

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

   3. Simplified 85.5%

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

      1. associate-*r/ 71.3%

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

      2. associate-+r+ 71.3%

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

      3. associate-*l* 71.4%

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

      4. associate-/r* 75.8%

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

      5. *-commutative 75.8%

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

      6. +-commutative 75.8%

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

      7. +-commutative 75.8%

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

      8. associate-+r+ 75.8%

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

      9. +-commutative 75.8%

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

      10. associate-+l+ 75.8%

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

   6. Applied egg-rr 75.8%

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

   7. Taylor expanded in y around inf 78.3%

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

   if 1.89999999999999997e123 < y

   1. Initial program 61.0%

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

      1. associate-/l* 81.4%

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

      2. associate-+l+ 81.4%

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

   3. Simplified 81.4%

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

      1. associate-*r/ 61.0%

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

      2. associate-+r+ 61.0%

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

      3. associate-*l* 61.0%

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

      4. associate-/r* 68.6%

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

      5. *-commutative 68.6%

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

      6. +-commutative 68.6%

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

      7. +-commutative 68.6%

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

      8. associate-+r+ 68.6%

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

      9. +-commutative 68.6%

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

      10. associate-+l+ 68.6%

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

   6. Applied egg-rr 68.6%

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

   7. Taylor expanded in y around inf 88.1%

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

      1. associate-/r* 95.1%

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

      2. +-commutative 95.1%

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

      3. +-commutative 95.1%

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

      4. div-inv 95.1%

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

      5. +-commutative 95.1%

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

   9. Applied egg-rr 95.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{-239}:\\ \;\;\;\;\frac{\frac{y}{x}}{x + 1}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+123}:\\ \;\;\;\;\frac{x}{\left(y + \left(x + 1\right)\right) \cdot \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + x} \cdot \frac{1}{y + \left(x + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+73}:\\ \;\;\;\;\frac{\frac{x}{y + x}}{y + x} \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\frac{y}{y + x}}{y + \left(x + 1\right)}}{y + x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5.2e+73)
   (* (/ (/ x (+ y x)) (+ y x)) (/ y x))
   (* x (/ (/ (/ y (+ y x)) (+ y (+ x 1.0))) (+ y x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.2e+73) {
		tmp = ((x / (y + x)) / (y + x)) * (y / x);
	} else {
		tmp = x * (((y / (y + x)) / (y + (x + 1.0))) / (y + x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-5.2d+73)) then
        tmp = ((x / (y + x)) / (y + x)) * (y / x)
    else
        tmp = x * (((y / (y + x)) / (y + (x + 1.0d0))) / (y + x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5.2e+73) {
		tmp = ((x / (y + x)) / (y + x)) * (y / x);
	} else {
		tmp = x * (((y / (y + x)) / (y + (x + 1.0))) / (y + x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.2e+73:
		tmp = ((x / (y + x)) / (y + x)) * (y / x)
	else:
		tmp = x * (((y / (y + x)) / (y + (x + 1.0))) / (y + x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.2e+73)
		tmp = Float64(Float64(Float64(x / Float64(y + x)) / Float64(y + x)) * Float64(y / x));
	else
		tmp = Float64(x * Float64(Float64(Float64(y / Float64(y + x)) / Float64(y + Float64(x + 1.0))) / Float64(y + x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5.2e+73)
		tmp = ((x / (y + x)) / (y + x)) * (y / x);
	else
		tmp = x * (((y / (y + x)) / (y + (x + 1.0))) / (y + x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.2e+73], N[(N[(N[(x / N[(y + x), $MachinePrecision]), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(N[(y / N[(y + x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.2000000000000001e73

   1. Initial program 47.2%

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

      1. associate-/l* 78.0%

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

      2. associate-+l+ 78.0%

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

   3. Simplified 78.0%

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

      1. associate-*r/ 47.2%

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

      2. associate-+r+ 47.2%

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

      3. associate-*l* 47.2%

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

      4. associate-/r* 56.2%

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

      5. *-commutative 56.2%

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

      6. +-commutative 56.2%

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

      7. +-commutative 56.2%

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

      8. associate-+r+ 56.2%

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

      9. +-commutative 56.2%

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

      10. associate-+l+ 56.2%

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

   6. Applied egg-rr 56.2%

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

      1. associate-/l* 89.1%

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

      2. *-commutative 89.1%

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

      3. +-commutative 89.1%

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

      4. times-frac 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in x around inf 92.6%

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

   if -5.2000000000000001e73 < x

   1. Initial program 69.5%

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

      1. associate-/l* 85.1%

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

      2. associate-+l+ 85.0%

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

   3. Simplified 85.0%

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

      1. *-un-lft-identity 85.0%

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

      2. associate-+r+ 85.1%

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

      3. associate-*l* 85.0%

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

      4. times-frac 94.5%

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

      5. +-commutative 94.5%

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

      6. +-commutative 94.5%

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

      7. associate-+r+ 94.5%

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

      8. +-commutative 94.5%

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

      9. associate-+l+ 94.5%

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

   6. Applied egg-rr 94.5%

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

      1. associate-*l/ 94.5%

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

      2. *-lft-identity 94.5%

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

      3. associate-/r* 94.5%

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

      4. +-commutative 94.5%

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

   8. Simplified 94.5%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+73}:\\ \;\;\;\;\frac{\frac{x}{y + x}}{y + x} \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\frac{\frac{y}{y + x}}{y + \left(x + 1\right)}}{y + x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{-239}:\\ \;\;\;\;\frac{\frac{y}{x}}{x + 1}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{\left(y + \left(x + 1\right)\right) \cdot \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 3.5e-239)
   (/ (/ y x) (+ x 1.0))
   (if (<= y 3.5e+151)
     (/ x (* (+ y (+ x 1.0)) (+ y x)))
     (* (/ 1.0 y) (/ x (+ y 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 3.5e-239) {
		tmp = (y / x) / (x + 1.0);
	} else if (y <= 3.5e+151) {
		tmp = x / ((y + (x + 1.0)) * (y + x));
	} else {
		tmp = (1.0 / y) * (x / (y + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 3.5d-239) then
        tmp = (y / x) / (x + 1.0d0)
    else if (y <= 3.5d+151) then
        tmp = x / ((y + (x + 1.0d0)) * (y + x))
    else
        tmp = (1.0d0 / y) * (x / (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 3.5e-239) {
		tmp = (y / x) / (x + 1.0);
	} else if (y <= 3.5e+151) {
		tmp = x / ((y + (x + 1.0)) * (y + x));
	} else {
		tmp = (1.0 / y) * (x / (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 3.5e-239:
		tmp = (y / x) / (x + 1.0)
	elif y <= 3.5e+151:
		tmp = x / ((y + (x + 1.0)) * (y + x))
	else:
		tmp = (1.0 / y) * (x / (y + 1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 3.5e-239)
		tmp = Float64(Float64(y / x) / Float64(x + 1.0));
	elseif (y <= 3.5e+151)
		tmp = Float64(x / Float64(Float64(y + Float64(x + 1.0)) * Float64(y + x)));
	else
		tmp = Float64(Float64(1.0 / y) * Float64(x / Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 3.5e-239)
		tmp = (y / x) / (x + 1.0);
	elseif (y <= 3.5e+151)
		tmp = x / ((y + (x + 1.0)) * (y + x));
	else
		tmp = (1.0 / y) * (x / (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 3.5e-239], N[(N[(y / x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+151], N[(x / N[(N[(y + N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / y), $MachinePrecision] * N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 3.50000000000000005e-239

   1. Initial program 63.4%

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

      1. associate-/l* 83.5%

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

      2. associate-+l+ 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in y around 0 59.6%

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

      1. associate-/r* 56.9%

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

      2. +-commutative 56.9%

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

   7. Simplified 56.9%

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

   if 3.50000000000000005e-239 < y < 3.5000000000000003e151

   1. Initial program 66.6%

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

      1. associate-/l* 81.3%

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

      2. associate-+l+ 81.3%

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

   3. Simplified 81.3%

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

      1. associate-*r/ 66.6%

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

      2. associate-+r+ 66.6%

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

      3. associate-*l* 66.7%

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

      4. associate-/r* 76.1%

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

      5. *-commutative 76.1%

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

      6. +-commutative 76.1%

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

      7. +-commutative 76.1%

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

      8. associate-+r+ 76.1%

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

      9. +-commutative 76.1%

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

      10. associate-+l+ 76.1%

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

   6. Applied egg-rr 76.1%

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

   7. Taylor expanded in y around inf 79.1%

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

   if 3.5000000000000003e151 < y

   1. Initial program 67.4%

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

      1. associate-/l* 87.9%

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

      2. associate-+l+ 87.9%

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

   3. Simplified 87.9%

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

   5. Taylor expanded in x around 0 87.9%

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

      1. +-commutative 87.9%

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

   7. Simplified 87.9%

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

      1. *-un-lft-identity 87.9%

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

      2. times-frac 97.8%

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

   9. Applied egg-rr 97.8%

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

4. Final simplification 70.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{-239}:\\ \;\;\;\;\frac{\frac{y}{x}}{x + 1}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{\left(y + \left(x + 1\right)\right) \cdot \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} \cdot \frac{x}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{y}{x} \cdot \frac{1}{x}\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{y}{x} - y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(y + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.0)
   (* (/ y x) (/ 1.0 x))
   (if (<= x -5.5e-29) (- (/ y x) y) (/ x (* y (+ y 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = (y / x) * (1.0 / x);
	} else if (x <= -5.5e-29) {
		tmp = (y / x) - y;
	} else {
		tmp = x / (y * (y + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.0d0)) then
        tmp = (y / x) * (1.0d0 / x)
    else if (x <= (-5.5d-29)) then
        tmp = (y / x) - y
    else
        tmp = x / (y * (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = (y / x) * (1.0 / x);
	} else if (x <= -5.5e-29) {
		tmp = (y / x) - y;
	} else {
		tmp = x / (y * (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = (y / x) * (1.0 / x)
	elif x <= -5.5e-29:
		tmp = (y / x) - y
	else:
		tmp = x / (y * (y + 1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(Float64(y / x) * Float64(1.0 / x));
	elseif (x <= -5.5e-29)
		tmp = Float64(Float64(y / x) - y);
	else
		tmp = Float64(x / Float64(y * Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = (y / x) * (1.0 / x);
	elseif (x <= -5.5e-29)
		tmp = (y / x) - y;
	else
		tmp = x / (y * (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.0], N[(N[(y / x), $MachinePrecision] * N[(1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.5e-29], N[(N[(y / x), $MachinePrecision] - y), $MachinePrecision], N[(x / N[(y * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 51.1%

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

      1. associate-/l* 75.2%

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

      2. associate-+l+ 75.2%

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

   3. Simplified 75.2%

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

      1. associate-*r/ 51.1%

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

      2. associate-+r+ 51.1%

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

      3. associate-*l* 51.1%

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

      4. associate-/r* 64.9%

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

      5. *-commutative 64.9%

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

      6. +-commutative 64.9%

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

      7. +-commutative 64.9%

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

      8. associate-+r+ 64.9%

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

      9. +-commutative 64.9%

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

      10. associate-+l+ 64.9%

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

   6. Applied egg-rr 64.9%

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

      1. associate-/l* 91.6%

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

      2. *-commutative 91.6%

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

      3. +-commutative 91.6%

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

      4. times-frac 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in x around inf 85.9%

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

   10. Taylor expanded in x around inf 67.2%

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

   if -1 < x < -5.4999999999999999e-29

   1. Initial program 79.9%

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

      1. associate-/l* 89.6%

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

      2. associate-+l+ 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in y around 0 59.6%

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

      1. associate-/r* 59.8%

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

      2. +-commutative 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in x around 0 55.0%

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

      1. associate-*r* 55.0%

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

      2. mul-1-neg 55.0%

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

   10. Simplified 55.0%

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

   11. Taylor expanded in x around inf 55.0%

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

       1. neg-mul-1 55.0%

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

       2. +-commutative 55.0%

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

       3. unsub-neg 55.0%

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

   13. Simplified 55.0%

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

   if -5.4999999999999999e-29 < x

   1. Initial program 69.5%

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

      1. associate-/l* 86.5%

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

      2. associate-+l+ 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in x around 0 65.1%

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

      1. +-commutative 65.1%

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

   7. Simplified 65.1%

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

Alternative 8: 45.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{y}{x} \cdot \frac{1}{x}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-158}:\\ \;\;\;\;\frac{y}{x} - y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.0)
   (* (/ y x) (/ 1.0 x))
   (if (<= x -6e-158) (- (/ y x) y) (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = (y / x) * (1.0 / x);
	} else if (x <= -6e-158) {
		tmp = (y / x) - y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.0d0)) then
        tmp = (y / x) * (1.0d0 / x)
    else if (x <= (-6d-158)) then
        tmp = (y / x) - y
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = (y / x) * (1.0 / x);
	} else if (x <= -6e-158) {
		tmp = (y / x) - y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = (y / x) * (1.0 / x)
	elif x <= -6e-158:
		tmp = (y / x) - y
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(Float64(y / x) * Float64(1.0 / x));
	elseif (x <= -6e-158)
		tmp = Float64(Float64(y / x) - y);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = (y / x) * (1.0 / x);
	elseif (x <= -6e-158)
		tmp = (y / x) - y;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.0], N[(N[(y / x), $MachinePrecision] * N[(1.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6e-158], N[(N[(y / x), $MachinePrecision] - y), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 51.1%

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

      1. associate-/l* 75.2%

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

      2. associate-+l+ 75.2%

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

   3. Simplified 75.2%

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

      1. associate-*r/ 51.1%

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

      2. associate-+r+ 51.1%

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

      3. associate-*l* 51.1%

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

      4. associate-/r* 64.9%

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

      5. *-commutative 64.9%

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

      6. +-commutative 64.9%

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

      7. +-commutative 64.9%

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

      8. associate-+r+ 64.9%

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

      9. +-commutative 64.9%

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

      10. associate-+l+ 64.9%

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

   6. Applied egg-rr 64.9%

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

      1. associate-/l* 91.6%

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

      2. *-commutative 91.6%

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

      3. +-commutative 91.6%

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

      4. times-frac 99.8%

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

      5. +-commutative 99.8%

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

      6. +-commutative 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in x around inf 85.9%

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

   10. Taylor expanded in x around inf 67.2%

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

   if -1 < x < -6e-158

   1. Initial program 83.7%

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

      1. associate-/l* 96.5%

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

      2. associate-+l+ 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in y around 0 40.9%

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

      1. associate-/r* 40.9%

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

      2. +-commutative 40.9%

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

   7. Simplified 40.9%

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

   8. Taylor expanded in x around 0 39.4%

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

      1. associate-*r* 39.4%

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

      2. mul-1-neg 39.4%

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

   10. Simplified 39.4%

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

   11. Taylor expanded in x around inf 39.4%

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

       1. neg-mul-1 39.4%

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

       2. +-commutative 39.4%

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

       3. unsub-neg 39.4%

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

   13. Simplified 39.4%

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

   if -6e-158 < x

   1. Initial program 67.5%

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

      1. associate-/l* 84.9%

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

      2. associate-+l+ 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in x around 0 64.5%

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

      1. +-commutative 64.5%

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

   7. Simplified 64.5%

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

   8. Taylor expanded in y around 0 41.3%

      \[\leadsto \color{blue}{\frac{x}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 9: 60.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{\frac{y}{x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + 1}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 3.5e-94) (/ (/ y x) (+ x 1.0)) (/ (/ x (+ y 1.0)) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 3.5e-94) {
		tmp = (y / x) / (x + 1.0);
	} else {
		tmp = (x / (y + 1.0)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 3.5d-94) then
        tmp = (y / x) / (x + 1.0d0)
    else
        tmp = (x / (y + 1.0d0)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 3.5e-94) {
		tmp = (y / x) / (x + 1.0);
	} else {
		tmp = (x / (y + 1.0)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 3.5e-94:
		tmp = (y / x) / (x + 1.0)
	else:
		tmp = (x / (y + 1.0)) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 3.5e-94)
		tmp = Float64(Float64(y / x) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x / Float64(y + 1.0)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 3.5e-94)
		tmp = (y / x) / (x + 1.0);
	else
		tmp = (x / (y + 1.0)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 3.5e-94], N[(N[(y / x), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.49999999999999998e-94

   1. Initial program 63.7%

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

      1. associate-/l* 82.3%

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

      2. associate-+l+ 82.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in y around 0 60.6%

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

      1. associate-/r* 58.3%

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

      2. +-commutative 58.3%

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

   7. Simplified 58.3%

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

   if 3.49999999999999998e-94 < y

   1. Initial program 67.2%

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

      1. associate-/l* 86.0%

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

      2. associate-+l+ 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in x around 0 76.2%

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

      1. +-commutative 76.2%

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

   7. Simplified 76.2%

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

      1. *-un-lft-identity 76.2%

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

      2. times-frac 80.8%

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

   9. Applied egg-rr 80.8%

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

       1. associate-*l/ 80.9%

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

       2. *-un-lft-identity 80.9%

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

   11. Applied egg-rr 80.9%

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

Alternative 10: 60.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.1 \cdot 10^{-94}:\\ \;\;\;\;\frac{y}{x \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + 1}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 2.1e-94) (/ y (* x (+ x 1.0))) (/ (/ x (+ y 1.0)) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2.1e-94) {
		tmp = y / (x * (x + 1.0));
	} else {
		tmp = (x / (y + 1.0)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 2.1d-94) then
        tmp = y / (x * (x + 1.0d0))
    else
        tmp = (x / (y + 1.0d0)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 2.1e-94) {
		tmp = y / (x * (x + 1.0));
	} else {
		tmp = (x / (y + 1.0)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2.1e-94:
		tmp = y / (x * (x + 1.0))
	else:
		tmp = (x / (y + 1.0)) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2.1e-94)
		tmp = Float64(y / Float64(x * Float64(x + 1.0)));
	else
		tmp = Float64(Float64(x / Float64(y + 1.0)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.1e-94)
		tmp = y / (x * (x + 1.0));
	else
		tmp = (x / (y + 1.0)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2.1e-94], N[(y / N[(x * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.1000000000000001e-94

   1. Initial program 63.7%

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

      1. associate-/l* 82.3%

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

      2. associate-+l+ 82.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in y around 0 60.6%

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

   if 2.1000000000000001e-94 < y

   1. Initial program 67.2%

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

      1. associate-/l* 86.0%

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

      2. associate-+l+ 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in x around 0 76.2%

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

      1. +-commutative 76.2%

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

   7. Simplified 76.2%

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

      1. *-un-lft-identity 76.2%

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

      2. times-frac 80.8%

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

   9. Applied egg-rr 80.8%

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

       1. associate-*l/ 80.9%

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

       2. *-un-lft-identity 80.9%

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

   11. Applied egg-rr 80.9%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.1 \cdot 10^{-94}:\\ \;\;\;\;\frac{y}{x \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y + 1}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{y}{x \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(y + 1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 3.5e-94) (/ y (* x (+ x 1.0))) (/ x (* y (+ y 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 3.5e-94) {
		tmp = y / (x * (x + 1.0));
	} else {
		tmp = x / (y * (y + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 3.5d-94) then
        tmp = y / (x * (x + 1.0d0))
    else
        tmp = x / (y * (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 3.5e-94) {
		tmp = y / (x * (x + 1.0));
	} else {
		tmp = x / (y * (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 3.5e-94:
		tmp = y / (x * (x + 1.0))
	else:
		tmp = x / (y * (y + 1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 3.5e-94)
		tmp = Float64(y / Float64(x * Float64(x + 1.0)));
	else
		tmp = Float64(x / Float64(y * Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 3.5e-94)
		tmp = y / (x * (x + 1.0));
	else
		tmp = x / (y * (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 3.5e-94], N[(y / N[(x * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(y * N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.49999999999999998e-94

   1. Initial program 63.7%

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

      1. associate-/l* 82.3%

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

      2. associate-+l+ 82.3%

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

   3. Simplified 82.3%

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

   5. Taylor expanded in y around 0 60.6%

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

   if 3.49999999999999998e-94 < y

   1. Initial program 67.2%

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

      1. associate-/l* 86.0%

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

      2. associate-+l+ 86.0%

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

   3. Simplified 86.0%

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

   5. Taylor expanded in x around 0 76.2%

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

      1. +-commutative 76.2%

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

   7. Simplified 76.2%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{y}{x \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(y + 1\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 22.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{-239}:\\ \;\;\;\;\frac{y}{x} - y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 3.5e-239) (- (/ y x) y) (/ x y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 3.5e-239) {
		tmp = (y / x) - y;
	} else {
		tmp = 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 (y <= 3.5d-239) then
        tmp = (y / x) - y
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 3.5e-239) {
		tmp = (y / x) - y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 3.5e-239:
		tmp = (y / x) - y
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 3.5e-239)
		tmp = Float64(Float64(y / x) - y);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 3.5e-239)
		tmp = (y / x) - y;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 3.5e-239], N[(N[(y / x), $MachinePrecision] - y), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.50000000000000005e-239

   1. Initial program 63.4%

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

      1. associate-/l* 83.5%

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

      2. associate-+l+ 83.5%

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

   3. Simplified 83.5%

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

   5. Taylor expanded in y around 0 59.6%

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

      1. associate-/r* 56.9%

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

      2. +-commutative 56.9%

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

   7. Simplified 56.9%

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

   8. Taylor expanded in x around 0 18.4%

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

      1. associate-*r* 18.4%

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

      2. mul-1-neg 18.4%

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

   10. Simplified 18.4%

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

   11. Taylor expanded in x around inf 18.5%

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

       1. neg-mul-1 18.5%

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

       2. +-commutative 18.5%

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

       3. unsub-neg 18.5%

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

   13. Simplified 18.5%

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

   if 3.50000000000000005e-239 < y

   1. Initial program 66.9%

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

      1. associate-/l* 83.8%

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

      2. associate-+l+ 83.8%

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

   3. Simplified 83.8%

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

   5. Taylor expanded in x around 0 67.7%

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

      1. +-commutative 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in y around 0 36.4%

      \[\leadsto \color{blue}{\frac{x}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 26.2% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.0%

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

   1. associate-/l* 83.6%

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

   2. associate-+l+ 83.6%

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

3. Simplified 83.6%

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

5. Taylor expanded in x around 0 55.5%

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

   1. +-commutative 55.5%

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

7. Simplified 55.5%

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

8. Taylor expanded in y around 0 29.0%

   \[\leadsto \color{blue}{\frac{x}{y}} \]
9. Add Preprocessing

Alternative 14: 4.2% accurate, 5.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 65.0%

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

   1. associate-/l* 83.6%

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

   2. associate-+l+ 83.6%

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

3. Simplified 83.6%

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

   1. associate-*r/ 65.0%

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

   2. associate-+r+ 65.0%

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

   3. associate-*l* 65.0%

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

   4. associate-/r* 70.7%

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

   5. *-commutative 70.7%

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

   6. +-commutative 70.7%

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

   7. +-commutative 70.7%

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

   8. associate-+r+ 70.7%

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

   9. +-commutative 70.7%

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

   10. associate-+l+ 70.7%

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

6. Applied egg-rr 70.7%

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

   1. associate-/l* 94.4%

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

   2. *-commutative 94.4%

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

   3. +-commutative 94.4%

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

   4. times-frac 99.8%

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

   5. +-commutative 99.8%

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

   6. +-commutative 99.8%

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

8. Applied egg-rr 99.8%

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

9. Taylor expanded in x around inf 48.9%

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

10. Taylor expanded in y around inf 4.4%

    \[\leadsto \color{blue}{\frac{1}{y}} \]
11. Add Preprocessing

Alternative 15: 3.6% accurate, 8.5× 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 Float64(-y)
end

MATLAB

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

Wolfram

code[x_, y_] := (-y)

Derivation

1. Initial program 65.0%

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

   1. associate-/l* 83.6%

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

   2. associate-+l+ 83.6%

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

3. Simplified 83.6%

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

5. Taylor expanded in y around 0 47.0%

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

   1. associate-/r* 44.8%

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

   2. +-commutative 44.8%

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

7. Simplified 44.8%

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

8. Taylor expanded in x around 0 12.5%

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

   1. associate-*r* 12.5%

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

   2. mul-1-neg 12.5%

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

10. Simplified 12.5%

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

11. Taylor expanded in x around inf 3.7%

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

    1. neg-mul-1 3.7%

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

13. Simplified 3.7%

    \[\leadsto \color{blue}{-y} \]
14. Add Preprocessing

Developer target: 99.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{\frac{x}{\left(y + 1\right) + x}}{y + x}}{\frac{1}{\frac{y}{y + x}}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024091 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteBetaApprox from math-functions-0.1.5.2, A"
  :precision binary64

  :alt
  (/ (/ (/ x (+ (+ y 1.0) x)) (+ y x)) (/ 1.0 (/ y (+ y x))))

  (/ (* x y) (* (* (+ x y) (+ x y)) (+ (+ x y) 1.0))))