Data.Colour.RGB:hslsv from colour-2.3.3, C

Percentage Accurate: 100.0% → 99.9%

Time: 12.0s

Alternatives: 12

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{x \cdot -2 + \left(\left(x - y\right) + 2\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (+ (* x -2.0) (+ (- x y) 2.0))))

C

double code(double x, double y) {
	return (x - y) / ((x * -2.0) + ((x - y) + 2.0));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / ((x * (-2.0d0)) + ((x - y) + 2.0d0))
end function

Java

public static double code(double x, double y) {
	return (x - y) / ((x * -2.0) + ((x - y) + 2.0));
}

Python

def code(x, y):
	return (x - y) / ((x * -2.0) + ((x - y) + 2.0))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(Float64(x * -2.0) + Float64(Float64(x - y) + 2.0)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / ((x * -2.0) + ((x - y) + 2.0));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(N[(x * -2.0), $MachinePrecision] + N[(N[(x - y), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. sub-neg 100.0%

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

   2. flip-+ 56.4%

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

   3. metadata-eval 56.4%

      \[\leadsto \frac{x - y}{\frac{\color{blue}{4} - \left(-\left(x + y\right)\right) \cdot \left(-\left(x + y\right)\right)}{2 - \left(-\left(x + y\right)\right)}} \]

4. Applied egg-rr 56.4%

   \[\leadsto \frac{x - y}{\color{blue}{\frac{4 - \left(-\left(x + y\right)\right) \cdot \left(-\left(x + y\right)\right)}{2 - \left(-\left(x + y\right)\right)}}} \]

5. Taylor expanded in y around inf 100.0%

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

   1. neg-mul-1 100.0%

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

   2. associate--l+ 100.0%

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

   3. *-commutative 100.0%

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

   4. cancel-sign-sub-inv 100.0%

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

   5. metadata-eval 100.0%

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

   6. *-lft-identity 100.0%

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

   7. +-commutative 100.0%

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

   8. sub-neg 100.0%

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

   9. associate--l+ 100.0%

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

7. Simplified 100.0%

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

8. Final simplification 100.0%

   \[\leadsto \frac{x - y}{x \cdot -2 + \left(\left(x - y\right) + 2\right)} \]
9. Add Preprocessing

Alternative 2: 62.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+72}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+56}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -8000000000:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-80}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-31}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+40}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -3.8e+72)
     t_0
     (if (<= y -3e+56)
       -1.0
       (if (<= y -8000000000.0)
         (+ 1.0 (/ 2.0 y))
         (if (<= y 7.8e-80)
           -1.0
           (if (<= y 1.5e-31) (* y -0.5) (if (<= y 1.35e+40) -1.0 t_0))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -3.8e+72) {
		tmp = t_0;
	} else if (y <= -3e+56) {
		tmp = -1.0;
	} else if (y <= -8000000000.0) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= 7.8e-80) {
		tmp = -1.0;
	} else if (y <= 1.5e-31) {
		tmp = y * -0.5;
	} else if (y <= 1.35e+40) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    if (y <= (-3.8d+72)) then
        tmp = t_0
    else if (y <= (-3d+56)) then
        tmp = -1.0d0
    else if (y <= (-8000000000.0d0)) then
        tmp = 1.0d0 + (2.0d0 / y)
    else if (y <= 7.8d-80) then
        tmp = -1.0d0
    else if (y <= 1.5d-31) then
        tmp = y * (-0.5d0)
    else if (y <= 1.35d+40) then
        tmp = -1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -3.8e+72) {
		tmp = t_0;
	} else if (y <= -3e+56) {
		tmp = -1.0;
	} else if (y <= -8000000000.0) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= 7.8e-80) {
		tmp = -1.0;
	} else if (y <= 1.5e-31) {
		tmp = y * -0.5;
	} else if (y <= 1.35e+40) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -3.8e+72:
		tmp = t_0
	elif y <= -3e+56:
		tmp = -1.0
	elif y <= -8000000000.0:
		tmp = 1.0 + (2.0 / y)
	elif y <= 7.8e-80:
		tmp = -1.0
	elif y <= 1.5e-31:
		tmp = y * -0.5
	elif y <= 1.35e+40:
		tmp = -1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -3.8e+72)
		tmp = t_0;
	elseif (y <= -3e+56)
		tmp = -1.0;
	elseif (y <= -8000000000.0)
		tmp = Float64(1.0 + Float64(2.0 / y));
	elseif (y <= 7.8e-80)
		tmp = -1.0;
	elseif (y <= 1.5e-31)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.35e+40)
		tmp = -1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -3.8e+72)
		tmp = t_0;
	elseif (y <= -3e+56)
		tmp = -1.0;
	elseif (y <= -8000000000.0)
		tmp = 1.0 + (2.0 / y);
	elseif (y <= 7.8e-80)
		tmp = -1.0;
	elseif (y <= 1.5e-31)
		tmp = y * -0.5;
	elseif (y <= 1.35e+40)
		tmp = -1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+72], t$95$0, If[LessEqual[y, -3e+56], -1.0, If[LessEqual[y, -8000000000.0], N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e-80], -1.0, If[LessEqual[y, 1.5e-31], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.35e+40], -1.0, t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.80000000000000006e72 or 1.35000000000000005e40 < y

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.2%

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

      1. neg-mul-1 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in x around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. unsub-neg 81.2%

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

   8. Simplified 81.2%

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

   if -3.80000000000000006e72 < y < -3.00000000000000006e56 or -8e9 < y < 7.7999999999999995e-80 or 1.49999999999999991e-31 < y < 1.35000000000000005e40

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 56.4%

      \[\leadsto \color{blue}{-1} \]

   if -3.00000000000000006e56 < y < -8e9

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. flip-+ 78.5%

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

      3. metadata-eval 78.5%

         \[\leadsto \frac{x - y}{\frac{\color{blue}{4} - \left(-\left(x + y\right)\right) \cdot \left(-\left(x + y\right)\right)}{2 - \left(-\left(x + y\right)\right)}} \]

   4. Applied egg-rr 78.5%

      \[\leadsto \frac{x - y}{\color{blue}{\frac{4 - \left(-\left(x + y\right)\right) \cdot \left(-\left(x + y\right)\right)}{2 - \left(-\left(x + y\right)\right)}}} \]

   5. Taylor expanded in y around -inf 78.0%

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

      1. associate-*r/ 78.0%

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

      2. cancel-sign-sub-inv 78.0%

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

      3. metadata-eval 78.0%

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

      4. distribute-lft-in 78.0%

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

      5. distribute-rgt1-in 78.0%

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

      6. metadata-eval 78.0%

         \[\leadsto 1 + \frac{-1 \cdot \left(-1 \cdot \left(2 + \color{blue}{0} \cdot x\right)\right) + -1 \cdot \left(2 \cdot x\right)}{y} \]

      7. mul0-lft 78.0%

         \[\leadsto 1 + \frac{-1 \cdot \left(-1 \cdot \left(2 + \color{blue}{0}\right)\right) + -1 \cdot \left(2 \cdot x\right)}{y} \]

      8. metadata-eval 78.0%

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

      9. metadata-eval 78.0%

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

      10. metadata-eval 78.0%

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

      11. neg-mul-1 78.0%

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

      12. distribute-lft-neg-in 78.0%

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

      13. metadata-eval 78.0%

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

      14. *-commutative 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in x around 0 78.1%

      \[\leadsto \color{blue}{1 + 2 \cdot \frac{1}{y}} \]
   9. Step-by-step derivation

      1. associate-*r/ 78.1%

         \[\leadsto 1 + \color{blue}{\frac{2 \cdot 1}{y}} \]

      2. metadata-eval 78.1%

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

   10. Simplified 78.1%

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

   if 7.7999999999999995e-80 < y < 1.49999999999999991e-31

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 68.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   4. Step-by-step derivation

      1. associate-*r/ 68.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot y}{2 - y}} \]

      2. neg-mul-1 68.7%

         \[\leadsto \frac{\color{blue}{-y}}{2 - y} \]

   5. Simplified 68.7%

      \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   6. Taylor expanded in y around 0 68.7%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative 68.7%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   8. Simplified 68.7%

      \[\leadsto \color{blue}{y \cdot -0.5} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+72}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -3 \cdot 10^{+56}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -8000000000:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-80}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-31}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+40}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+72}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+55}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -22000000000:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-93}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-29}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.34 \cdot 10^{+39}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -2.6e+72)
     t_0
     (if (<= y -1.3e+55)
       -1.0
       (if (<= y -22000000000.0)
         (+ 1.0 (/ 2.0 y))
         (if (<= y 8.5e-93)
           (+ (/ y x) -1.0)
           (if (<= y 2.45e-29) (* y -0.5) (if (<= y 1.34e+39) -1.0 t_0))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -2.6e+72) {
		tmp = t_0;
	} else if (y <= -1.3e+55) {
		tmp = -1.0;
	} else if (y <= -22000000000.0) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= 8.5e-93) {
		tmp = (y / x) + -1.0;
	} else if (y <= 2.45e-29) {
		tmp = y * -0.5;
	} else if (y <= 1.34e+39) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    if (y <= (-2.6d+72)) then
        tmp = t_0
    else if (y <= (-1.3d+55)) then
        tmp = -1.0d0
    else if (y <= (-22000000000.0d0)) then
        tmp = 1.0d0 + (2.0d0 / y)
    else if (y <= 8.5d-93) then
        tmp = (y / x) + (-1.0d0)
    else if (y <= 2.45d-29) then
        tmp = y * (-0.5d0)
    else if (y <= 1.34d+39) then
        tmp = -1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -2.6e+72) {
		tmp = t_0;
	} else if (y <= -1.3e+55) {
		tmp = -1.0;
	} else if (y <= -22000000000.0) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= 8.5e-93) {
		tmp = (y / x) + -1.0;
	} else if (y <= 2.45e-29) {
		tmp = y * -0.5;
	} else if (y <= 1.34e+39) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -2.6e+72:
		tmp = t_0
	elif y <= -1.3e+55:
		tmp = -1.0
	elif y <= -22000000000.0:
		tmp = 1.0 + (2.0 / y)
	elif y <= 8.5e-93:
		tmp = (y / x) + -1.0
	elif y <= 2.45e-29:
		tmp = y * -0.5
	elif y <= 1.34e+39:
		tmp = -1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -2.6e+72)
		tmp = t_0;
	elseif (y <= -1.3e+55)
		tmp = -1.0;
	elseif (y <= -22000000000.0)
		tmp = Float64(1.0 + Float64(2.0 / y));
	elseif (y <= 8.5e-93)
		tmp = Float64(Float64(y / x) + -1.0);
	elseif (y <= 2.45e-29)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.34e+39)
		tmp = -1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -2.6e+72)
		tmp = t_0;
	elseif (y <= -1.3e+55)
		tmp = -1.0;
	elseif (y <= -22000000000.0)
		tmp = 1.0 + (2.0 / y);
	elseif (y <= 8.5e-93)
		tmp = (y / x) + -1.0;
	elseif (y <= 2.45e-29)
		tmp = y * -0.5;
	elseif (y <= 1.34e+39)
		tmp = -1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+72], t$95$0, If[LessEqual[y, -1.3e+55], -1.0, If[LessEqual[y, -22000000000.0], N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-93], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[y, 2.45e-29], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.34e+39], -1.0, t$95$0]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.59999999999999981e72 or 1.34000000000000005e39 < y

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.2%

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

      1. neg-mul-1 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in x around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. unsub-neg 81.2%

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

   8. Simplified 81.2%

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

   if -2.59999999999999981e72 < y < -1.3e55 or 2.4499999999999999e-29 < y < 1.34000000000000005e39

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 84.1%

      \[\leadsto \color{blue}{-1} \]

   if -1.3e55 < y < -2.2e10

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. flip-+ 78.5%

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

      3. metadata-eval 78.5%

         \[\leadsto \frac{x - y}{\frac{\color{blue}{4} - \left(-\left(x + y\right)\right) \cdot \left(-\left(x + y\right)\right)}{2 - \left(-\left(x + y\right)\right)}} \]

   4. Applied egg-rr 78.5%

      \[\leadsto \frac{x - y}{\color{blue}{\frac{4 - \left(-\left(x + y\right)\right) \cdot \left(-\left(x + y\right)\right)}{2 - \left(-\left(x + y\right)\right)}}} \]

   5. Taylor expanded in y around -inf 78.0%

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

      1. associate-*r/ 78.0%

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

      2. cancel-sign-sub-inv 78.0%

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

      3. metadata-eval 78.0%

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

      4. distribute-lft-in 78.0%

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

      5. distribute-rgt1-in 78.0%

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

      6. metadata-eval 78.0%

         \[\leadsto 1 + \frac{-1 \cdot \left(-1 \cdot \left(2 + \color{blue}{0} \cdot x\right)\right) + -1 \cdot \left(2 \cdot x\right)}{y} \]

      7. mul0-lft 78.0%

         \[\leadsto 1 + \frac{-1 \cdot \left(-1 \cdot \left(2 + \color{blue}{0}\right)\right) + -1 \cdot \left(2 \cdot x\right)}{y} \]

      8. metadata-eval 78.0%

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

      9. metadata-eval 78.0%

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

      10. metadata-eval 78.0%

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

      11. neg-mul-1 78.0%

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

      12. distribute-lft-neg-in 78.0%

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

      13. metadata-eval 78.0%

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

      14. *-commutative 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in x around 0 78.1%

      \[\leadsto \color{blue}{1 + 2 \cdot \frac{1}{y}} \]
   9. Step-by-step derivation

      1. associate-*r/ 78.1%

         \[\leadsto 1 + \color{blue}{\frac{2 \cdot 1}{y}} \]

      2. metadata-eval 78.1%

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

   10. Simplified 78.1%

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

   if -2.2e10 < y < 8.5000000000000007e-93

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 52.5%

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

      1. mul-1-neg 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in x around 0 52.5%

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

   if 8.5000000000000007e-93 < y < 2.4499999999999999e-29

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 63.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   4. Step-by-step derivation

      1. associate-*r/ 63.4%

         \[\leadsto \color{blue}{\frac{-1 \cdot y}{2 - y}} \]

      2. neg-mul-1 63.4%

         \[\leadsto \frac{\color{blue}{-y}}{2 - y} \]

   5. Simplified 63.4%

      \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   6. Taylor expanded in y around 0 63.4%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative 63.4%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   8. Simplified 63.4%

      \[\leadsto \color{blue}{y \cdot -0.5} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+72}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+55}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -22000000000:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-93}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-29}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.34 \cdot 10^{+39}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ t_1 := \frac{x}{-2 - x}\\ \mathbf{if}\;y \leq -3.15 \cdot 10^{+72}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+55}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -40000000000:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-28}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))) (t_1 (/ x (- -2.0 x))))
   (if (<= y -3.15e+72)
     t_0
     (if (<= y -4e+55)
       -1.0
       (if (<= y -40000000000.0)
         (+ 1.0 (/ 2.0 y))
         (if (<= y 1.1e-79)
           t_1
           (if (<= y 4.2e-28) (* y -0.5) (if (<= y 1.36e+42) t_1 t_0))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double t_1 = x / (-2.0 - x);
	double tmp;
	if (y <= -3.15e+72) {
		tmp = t_0;
	} else if (y <= -4e+55) {
		tmp = -1.0;
	} else if (y <= -40000000000.0) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= 1.1e-79) {
		tmp = t_1;
	} else if (y <= 4.2e-28) {
		tmp = y * -0.5;
	} else if (y <= 1.36e+42) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    t_1 = x / ((-2.0d0) - x)
    if (y <= (-3.15d+72)) then
        tmp = t_0
    else if (y <= (-4d+55)) then
        tmp = -1.0d0
    else if (y <= (-40000000000.0d0)) then
        tmp = 1.0d0 + (2.0d0 / y)
    else if (y <= 1.1d-79) then
        tmp = t_1
    else if (y <= 4.2d-28) then
        tmp = y * (-0.5d0)
    else if (y <= 1.36d+42) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double t_1 = x / (-2.0 - x);
	double tmp;
	if (y <= -3.15e+72) {
		tmp = t_0;
	} else if (y <= -4e+55) {
		tmp = -1.0;
	} else if (y <= -40000000000.0) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= 1.1e-79) {
		tmp = t_1;
	} else if (y <= 4.2e-28) {
		tmp = y * -0.5;
	} else if (y <= 1.36e+42) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	t_1 = x / (-2.0 - x)
	tmp = 0
	if y <= -3.15e+72:
		tmp = t_0
	elif y <= -4e+55:
		tmp = -1.0
	elif y <= -40000000000.0:
		tmp = 1.0 + (2.0 / y)
	elif y <= 1.1e-79:
		tmp = t_1
	elif y <= 4.2e-28:
		tmp = y * -0.5
	elif y <= 1.36e+42:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	t_1 = Float64(x / Float64(-2.0 - x))
	tmp = 0.0
	if (y <= -3.15e+72)
		tmp = t_0;
	elseif (y <= -4e+55)
		tmp = -1.0;
	elseif (y <= -40000000000.0)
		tmp = Float64(1.0 + Float64(2.0 / y));
	elseif (y <= 1.1e-79)
		tmp = t_1;
	elseif (y <= 4.2e-28)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.36e+42)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (x / y);
	t_1 = x / (-2.0 - x);
	tmp = 0.0;
	if (y <= -3.15e+72)
		tmp = t_0;
	elseif (y <= -4e+55)
		tmp = -1.0;
	elseif (y <= -40000000000.0)
		tmp = 1.0 + (2.0 / y);
	elseif (y <= 1.1e-79)
		tmp = t_1;
	elseif (y <= 4.2e-28)
		tmp = y * -0.5;
	elseif (y <= 1.36e+42)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(-2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.15e+72], t$95$0, If[LessEqual[y, -4e+55], -1.0, If[LessEqual[y, -40000000000.0], N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-79], t$95$1, If[LessEqual[y, 4.2e-28], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.36e+42], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.14999999999999981e72 or 1.35999999999999999e42 < y

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.2%

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

      1. neg-mul-1 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in x around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. unsub-neg 81.2%

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

   8. Simplified 81.2%

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

   if -3.14999999999999981e72 < y < -4.00000000000000004e55

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{-1} \]

   if -4.00000000000000004e55 < y < -4e10

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. flip-+ 78.5%

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

      3. metadata-eval 78.5%

         \[\leadsto \frac{x - y}{\frac{\color{blue}{4} - \left(-\left(x + y\right)\right) \cdot \left(-\left(x + y\right)\right)}{2 - \left(-\left(x + y\right)\right)}} \]

   4. Applied egg-rr 78.5%

      \[\leadsto \frac{x - y}{\color{blue}{\frac{4 - \left(-\left(x + y\right)\right) \cdot \left(-\left(x + y\right)\right)}{2 - \left(-\left(x + y\right)\right)}}} \]

   5. Taylor expanded in y around -inf 78.0%

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

      1. associate-*r/ 78.0%

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

      2. cancel-sign-sub-inv 78.0%

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

      3. metadata-eval 78.0%

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

      4. distribute-lft-in 78.0%

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

      5. distribute-rgt1-in 78.0%

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

      6. metadata-eval 78.0%

         \[\leadsto 1 + \frac{-1 \cdot \left(-1 \cdot \left(2 + \color{blue}{0} \cdot x\right)\right) + -1 \cdot \left(2 \cdot x\right)}{y} \]

      7. mul0-lft 78.0%

         \[\leadsto 1 + \frac{-1 \cdot \left(-1 \cdot \left(2 + \color{blue}{0}\right)\right) + -1 \cdot \left(2 \cdot x\right)}{y} \]

      8. metadata-eval 78.0%

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

      9. metadata-eval 78.0%

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

      10. metadata-eval 78.0%

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

      11. neg-mul-1 78.0%

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

      12. distribute-lft-neg-in 78.0%

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

      13. metadata-eval 78.0%

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

      14. *-commutative 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in x around 0 78.1%

      \[\leadsto \color{blue}{1 + 2 \cdot \frac{1}{y}} \]
   9. Step-by-step derivation

      1. associate-*r/ 78.1%

         \[\leadsto 1 + \color{blue}{\frac{2 \cdot 1}{y}} \]

      2. metadata-eval 78.1%

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

   10. Simplified 78.1%

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

   if -4e10 < y < 1.0999999999999999e-79 or 4.20000000000000013e-28 < y < 1.35999999999999999e42

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 76.3%

      \[\leadsto \color{blue}{\frac{x}{2 - x}} \]
   4. Step-by-step derivation

      1. frac-2neg 76.3%

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

      2. div-inv 76.1%

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

      3. add-sqr-sqrt 39.6%

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

      4. sqrt-unprod 23.0%

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

      5. sqr-neg 23.0%

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

      6. sqrt-unprod 1.5%

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

      7. add-sqr-sqrt 3.0%

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

      8. sub-neg 3.0%

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

      9. add-sqr-sqrt 1.5%

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

      10. sqrt-unprod 15.1%

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

      11. sqr-neg 15.1%

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

      12. sqrt-unprod 27.0%

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

      13. add-sqr-sqrt 54.8%

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

   5. Applied egg-rr 54.8%

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

      1. neg-mul-1 54.8%

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

      2. associate-*r/ 55.0%

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

      3. *-rgt-identity 55.0%

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

      4. neg-mul-1 55.0%

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

      5. distribute-neg-in 55.0%

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

      6. metadata-eval 55.0%

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

      7. unsub-neg 55.0%

         \[\leadsto \frac{x}{\color{blue}{-2 - x}} \]

   7. Simplified 55.0%

      \[\leadsto \color{blue}{\frac{x}{-2 - x}} \]

   if 1.0999999999999999e-79 < y < 4.20000000000000013e-28

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 68.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   4. Step-by-step derivation

      1. associate-*r/ 68.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot y}{2 - y}} \]

      2. neg-mul-1 68.7%

         \[\leadsto \frac{\color{blue}{-y}}{2 - y} \]

   5. Simplified 68.7%

      \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   6. Taylor expanded in y around 0 68.7%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative 68.7%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   8. Simplified 68.7%

      \[\leadsto \color{blue}{y \cdot -0.5} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+72}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+55}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -40000000000:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-79}:\\ \;\;\;\;\frac{x}{-2 - x}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-28}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{-2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+72}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+55}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -85000000000:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-80}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-29}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{-2 - x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= y -2.6e+72)
     t_0
     (if (<= y -1.2e+55)
       -1.0
       (if (<= y -85000000000.0)
         (+ 1.0 (/ 2.0 y))
         (if (<= y 6e-80)
           (/ x (- 2.0 x))
           (if (<= y 2.4e-29)
             (* y -0.5)
             (if (<= y 1.25e+42) (/ x (- -2.0 x)) t_0))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -2.6e+72) {
		tmp = t_0;
	} else if (y <= -1.2e+55) {
		tmp = -1.0;
	} else if (y <= -85000000000.0) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= 6e-80) {
		tmp = x / (2.0 - x);
	} else if (y <= 2.4e-29) {
		tmp = y * -0.5;
	} else if (y <= 1.25e+42) {
		tmp = x / (-2.0 - x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 - (x / y)
    if (y <= (-2.6d+72)) then
        tmp = t_0
    else if (y <= (-1.2d+55)) then
        tmp = -1.0d0
    else if (y <= (-85000000000.0d0)) then
        tmp = 1.0d0 + (2.0d0 / y)
    else if (y <= 6d-80) then
        tmp = x / (2.0d0 - x)
    else if (y <= 2.4d-29) then
        tmp = y * (-0.5d0)
    else if (y <= 1.25d+42) then
        tmp = x / ((-2.0d0) - x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (y <= -2.6e+72) {
		tmp = t_0;
	} else if (y <= -1.2e+55) {
		tmp = -1.0;
	} else if (y <= -85000000000.0) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= 6e-80) {
		tmp = x / (2.0 - x);
	} else if (y <= 2.4e-29) {
		tmp = y * -0.5;
	} else if (y <= 1.25e+42) {
		tmp = x / (-2.0 - x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if y <= -2.6e+72:
		tmp = t_0
	elif y <= -1.2e+55:
		tmp = -1.0
	elif y <= -85000000000.0:
		tmp = 1.0 + (2.0 / y)
	elif y <= 6e-80:
		tmp = x / (2.0 - x)
	elif y <= 2.4e-29:
		tmp = y * -0.5
	elif y <= 1.25e+42:
		tmp = x / (-2.0 - x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (y <= -2.6e+72)
		tmp = t_0;
	elseif (y <= -1.2e+55)
		tmp = -1.0;
	elseif (y <= -85000000000.0)
		tmp = Float64(1.0 + Float64(2.0 / y));
	elseif (y <= 6e-80)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (y <= 2.4e-29)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.25e+42)
		tmp = Float64(x / Float64(-2.0 - x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (y <= -2.6e+72)
		tmp = t_0;
	elseif (y <= -1.2e+55)
		tmp = -1.0;
	elseif (y <= -85000000000.0)
		tmp = 1.0 + (2.0 / y);
	elseif (y <= 6e-80)
		tmp = x / (2.0 - x);
	elseif (y <= 2.4e-29)
		tmp = y * -0.5;
	elseif (y <= 1.25e+42)
		tmp = x / (-2.0 - x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+72], t$95$0, If[LessEqual[y, -1.2e+55], -1.0, If[LessEqual[y, -85000000000.0], N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e-80], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-29], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.25e+42], N[(x / N[(-2.0 - x), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.59999999999999981e72 or 1.25000000000000002e42 < y

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 81.2%

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

      1. neg-mul-1 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in x around 0 81.2%

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

      1. mul-1-neg 81.2%

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

      2. unsub-neg 81.2%

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

   8. Simplified 81.2%

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

   if -2.59999999999999981e72 < y < -1.2e55

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{-1} \]

   if -1.2e55 < y < -8.5e10

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. flip-+ 78.5%

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

      3. metadata-eval 78.5%

         \[\leadsto \frac{x - y}{\frac{\color{blue}{4} - \left(-\left(x + y\right)\right) \cdot \left(-\left(x + y\right)\right)}{2 - \left(-\left(x + y\right)\right)}} \]

   4. Applied egg-rr 78.5%

      \[\leadsto \frac{x - y}{\color{blue}{\frac{4 - \left(-\left(x + y\right)\right) \cdot \left(-\left(x + y\right)\right)}{2 - \left(-\left(x + y\right)\right)}}} \]

   5. Taylor expanded in y around -inf 78.0%

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

      1. associate-*r/ 78.0%

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

      2. cancel-sign-sub-inv 78.0%

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

      3. metadata-eval 78.0%

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

      4. distribute-lft-in 78.0%

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

      5. distribute-rgt1-in 78.0%

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

      6. metadata-eval 78.0%

         \[\leadsto 1 + \frac{-1 \cdot \left(-1 \cdot \left(2 + \color{blue}{0} \cdot x\right)\right) + -1 \cdot \left(2 \cdot x\right)}{y} \]

      7. mul0-lft 78.0%

         \[\leadsto 1 + \frac{-1 \cdot \left(-1 \cdot \left(2 + \color{blue}{0}\right)\right) + -1 \cdot \left(2 \cdot x\right)}{y} \]

      8. metadata-eval 78.0%

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

      9. metadata-eval 78.0%

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

      10. metadata-eval 78.0%

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

      11. neg-mul-1 78.0%

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

      12. distribute-lft-neg-in 78.0%

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

      13. metadata-eval 78.0%

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

      14. *-commutative 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in x around 0 78.1%

      \[\leadsto \color{blue}{1 + 2 \cdot \frac{1}{y}} \]
   9. Step-by-step derivation

      1. associate-*r/ 78.1%

         \[\leadsto 1 + \color{blue}{\frac{2 \cdot 1}{y}} \]

      2. metadata-eval 78.1%

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

   10. Simplified 78.1%

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

   if -8.5e10 < y < 6.00000000000000014e-80

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 76.1%

      \[\leadsto \color{blue}{\frac{x}{2 - x}} \]

   if 6.00000000000000014e-80 < y < 2.39999999999999992e-29

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 68.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   4. Step-by-step derivation

      1. associate-*r/ 68.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot y}{2 - y}} \]

      2. neg-mul-1 68.7%

         \[\leadsto \frac{\color{blue}{-y}}{2 - y} \]

   5. Simplified 68.7%

      \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   6. Taylor expanded in y around 0 68.7%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative 68.7%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   8. Simplified 68.7%

      \[\leadsto \color{blue}{y \cdot -0.5} \]

   if 2.39999999999999992e-29 < y < 1.25000000000000002e42

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 77.5%

      \[\leadsto \color{blue}{\frac{x}{2 - x}} \]
   4. Step-by-step derivation

      1. frac-2neg 77.5%

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

      2. div-inv 77.4%

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

      3. add-sqr-sqrt 53.8%

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

      4. sqrt-unprod 25.1%

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

      5. sqr-neg 25.1%

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

      6. sqrt-unprod 1.1%

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

      7. add-sqr-sqrt 2.4%

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

      8. sub-neg 2.4%

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

      9. add-sqr-sqrt 1.3%

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

      10. sqrt-unprod 3.2%

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

      11. sqr-neg 3.2%

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

      12. sqrt-unprod 23.7%

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

      13. add-sqr-sqrt 78.0%

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

   5. Applied egg-rr 78.0%

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

      1. neg-mul-1 78.0%

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

      2. associate-*r/ 78.1%

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

      3. *-rgt-identity 78.1%

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

      4. neg-mul-1 78.1%

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

      5. distribute-neg-in 78.1%

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

      6. metadata-eval 78.1%

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

      7. unsub-neg 78.1%

         \[\leadsto \frac{x}{\color{blue}{-2 - x}} \]

   7. Simplified 78.1%

      \[\leadsto \color{blue}{\frac{x}{-2 - x}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+72}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{+55}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -85000000000:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-80}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-29}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{-2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+55}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -85000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-82}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-29}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+43}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7e+72)
   1.0
   (if (<= y -8e+55)
     -1.0
     (if (<= y -85000000000.0)
       1.0
       (if (<= y 2.05e-82)
         -1.0
         (if (<= y 1.8e-29) (* y -0.5) (if (<= y 3.1e+43) -1.0 1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7e+72) {
		tmp = 1.0;
	} else if (y <= -8e+55) {
		tmp = -1.0;
	} else if (y <= -85000000000.0) {
		tmp = 1.0;
	} else if (y <= 2.05e-82) {
		tmp = -1.0;
	} else if (y <= 1.8e-29) {
		tmp = y * -0.5;
	} else if (y <= 3.1e+43) {
		tmp = -1.0;
	} else {
		tmp = 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 <= (-7d+72)) then
        tmp = 1.0d0
    else if (y <= (-8d+55)) then
        tmp = -1.0d0
    else if (y <= (-85000000000.0d0)) then
        tmp = 1.0d0
    else if (y <= 2.05d-82) then
        tmp = -1.0d0
    else if (y <= 1.8d-29) then
        tmp = y * (-0.5d0)
    else if (y <= 3.1d+43) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -7e+72) {
		tmp = 1.0;
	} else if (y <= -8e+55) {
		tmp = -1.0;
	} else if (y <= -85000000000.0) {
		tmp = 1.0;
	} else if (y <= 2.05e-82) {
		tmp = -1.0;
	} else if (y <= 1.8e-29) {
		tmp = y * -0.5;
	} else if (y <= 3.1e+43) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7e+72:
		tmp = 1.0
	elif y <= -8e+55:
		tmp = -1.0
	elif y <= -85000000000.0:
		tmp = 1.0
	elif y <= 2.05e-82:
		tmp = -1.0
	elif y <= 1.8e-29:
		tmp = y * -0.5
	elif y <= 3.1e+43:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7e+72)
		tmp = 1.0;
	elseif (y <= -8e+55)
		tmp = -1.0;
	elseif (y <= -85000000000.0)
		tmp = 1.0;
	elseif (y <= 2.05e-82)
		tmp = -1.0;
	elseif (y <= 1.8e-29)
		tmp = Float64(y * -0.5);
	elseif (y <= 3.1e+43)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -7e+72)
		tmp = 1.0;
	elseif (y <= -8e+55)
		tmp = -1.0;
	elseif (y <= -85000000000.0)
		tmp = 1.0;
	elseif (y <= 2.05e-82)
		tmp = -1.0;
	elseif (y <= 1.8e-29)
		tmp = y * -0.5;
	elseif (y <= 3.1e+43)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7e+72], 1.0, If[LessEqual[y, -8e+55], -1.0, If[LessEqual[y, -85000000000.0], 1.0, If[LessEqual[y, 2.05e-82], -1.0, If[LessEqual[y, 1.8e-29], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 3.1e+43], -1.0, 1.0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.0000000000000002e72 or -8.00000000000000008e55 < y < -8.5e10 or 3.1000000000000002e43 < y

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 79.9%

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

   if -7.0000000000000002e72 < y < -8.00000000000000008e55 or -8.5e10 < y < 2.04999999999999998e-82 or 1.79999999999999987e-29 < y < 3.1000000000000002e43

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 56.4%

      \[\leadsto \color{blue}{-1} \]

   if 2.04999999999999998e-82 < y < 1.79999999999999987e-29

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 68.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   4. Step-by-step derivation

      1. associate-*r/ 68.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot y}{2 - y}} \]

      2. neg-mul-1 68.7%

         \[\leadsto \frac{\color{blue}{-y}}{2 - y} \]

   5. Simplified 68.7%

      \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   6. Taylor expanded in y around 0 68.7%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative 68.7%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   8. Simplified 68.7%

      \[\leadsto \color{blue}{y \cdot -0.5} \]
3. Recombined 3 regimes into one program.

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+55}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -85000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-82}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-29}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+43}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+56}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -22000000000:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-86}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-31}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+42}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.4e+72)
   1.0
   (if (<= y -2.8e+56)
     -1.0
     (if (<= y -22000000000.0)
       (+ 1.0 (/ 2.0 y))
       (if (<= y 2.9e-86)
         -1.0
         (if (<= y 2.6e-31) (* y -0.5) (if (<= y 1.95e+42) -1.0 1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.4e+72) {
		tmp = 1.0;
	} else if (y <= -2.8e+56) {
		tmp = -1.0;
	} else if (y <= -22000000000.0) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= 2.9e-86) {
		tmp = -1.0;
	} else if (y <= 2.6e-31) {
		tmp = y * -0.5;
	} else if (y <= 1.95e+42) {
		tmp = -1.0;
	} else {
		tmp = 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 <= (-4.4d+72)) then
        tmp = 1.0d0
    else if (y <= (-2.8d+56)) then
        tmp = -1.0d0
    else if (y <= (-22000000000.0d0)) then
        tmp = 1.0d0 + (2.0d0 / y)
    else if (y <= 2.9d-86) then
        tmp = -1.0d0
    else if (y <= 2.6d-31) then
        tmp = y * (-0.5d0)
    else if (y <= 1.95d+42) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.4e+72) {
		tmp = 1.0;
	} else if (y <= -2.8e+56) {
		tmp = -1.0;
	} else if (y <= -22000000000.0) {
		tmp = 1.0 + (2.0 / y);
	} else if (y <= 2.9e-86) {
		tmp = -1.0;
	} else if (y <= 2.6e-31) {
		tmp = y * -0.5;
	} else if (y <= 1.95e+42) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.4e+72:
		tmp = 1.0
	elif y <= -2.8e+56:
		tmp = -1.0
	elif y <= -22000000000.0:
		tmp = 1.0 + (2.0 / y)
	elif y <= 2.9e-86:
		tmp = -1.0
	elif y <= 2.6e-31:
		tmp = y * -0.5
	elif y <= 1.95e+42:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.4e+72)
		tmp = 1.0;
	elseif (y <= -2.8e+56)
		tmp = -1.0;
	elseif (y <= -22000000000.0)
		tmp = Float64(1.0 + Float64(2.0 / y));
	elseif (y <= 2.9e-86)
		tmp = -1.0;
	elseif (y <= 2.6e-31)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.95e+42)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.4e+72)
		tmp = 1.0;
	elseif (y <= -2.8e+56)
		tmp = -1.0;
	elseif (y <= -22000000000.0)
		tmp = 1.0 + (2.0 / y);
	elseif (y <= 2.9e-86)
		tmp = -1.0;
	elseif (y <= 2.6e-31)
		tmp = y * -0.5;
	elseif (y <= 1.95e+42)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.4e+72], 1.0, If[LessEqual[y, -2.8e+56], -1.0, If[LessEqual[y, -22000000000.0], N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-86], -1.0, If[LessEqual[y, 2.6e-31], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.95e+42], -1.0, 1.0]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.4e72 or 1.94999999999999985e42 < y

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.6%

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

   if -4.4e72 < y < -2.80000000000000008e56 or -2.2e10 < y < 2.8999999999999999e-86 or 2.59999999999999995e-31 < y < 1.94999999999999985e42

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 56.4%

      \[\leadsto \color{blue}{-1} \]

   if -2.80000000000000008e56 < y < -2.2e10

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. flip-+ 78.5%

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

      3. metadata-eval 78.5%

         \[\leadsto \frac{x - y}{\frac{\color{blue}{4} - \left(-\left(x + y\right)\right) \cdot \left(-\left(x + y\right)\right)}{2 - \left(-\left(x + y\right)\right)}} \]

   4. Applied egg-rr 78.5%

      \[\leadsto \frac{x - y}{\color{blue}{\frac{4 - \left(-\left(x + y\right)\right) \cdot \left(-\left(x + y\right)\right)}{2 - \left(-\left(x + y\right)\right)}}} \]

   5. Taylor expanded in y around -inf 78.0%

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

      1. associate-*r/ 78.0%

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

      2. cancel-sign-sub-inv 78.0%

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

      3. metadata-eval 78.0%

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

      4. distribute-lft-in 78.0%

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

      5. distribute-rgt1-in 78.0%

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

      6. metadata-eval 78.0%

         \[\leadsto 1 + \frac{-1 \cdot \left(-1 \cdot \left(2 + \color{blue}{0} \cdot x\right)\right) + -1 \cdot \left(2 \cdot x\right)}{y} \]

      7. mul0-lft 78.0%

         \[\leadsto 1 + \frac{-1 \cdot \left(-1 \cdot \left(2 + \color{blue}{0}\right)\right) + -1 \cdot \left(2 \cdot x\right)}{y} \]

      8. metadata-eval 78.0%

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

      9. metadata-eval 78.0%

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

      10. metadata-eval 78.0%

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

      11. neg-mul-1 78.0%

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

      12. distribute-lft-neg-in 78.0%

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

      13. metadata-eval 78.0%

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

      14. *-commutative 78.0%

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

   7. Simplified 78.0%

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

   8. Taylor expanded in x around 0 78.1%

      \[\leadsto \color{blue}{1 + 2 \cdot \frac{1}{y}} \]
   9. Step-by-step derivation

      1. associate-*r/ 78.1%

         \[\leadsto 1 + \color{blue}{\frac{2 \cdot 1}{y}} \]

      2. metadata-eval 78.1%

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

   10. Simplified 78.1%

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

   if 2.8999999999999999e-86 < y < 2.59999999999999995e-31

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 68.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   4. Step-by-step derivation

      1. associate-*r/ 68.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot y}{2 - y}} \]

      2. neg-mul-1 68.7%

         \[\leadsto \frac{\color{blue}{-y}}{2 - y} \]

   5. Simplified 68.7%

      \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]

   6. Taylor expanded in y around 0 68.7%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   7. Step-by-step derivation

      1. *-commutative 68.7%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   8. Simplified 68.7%

      \[\leadsto \color{blue}{y \cdot -0.5} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{+56}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -22000000000:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-86}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{-31}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+42}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;x \leq -5.1 \cdot 10^{-42}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+80}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= x -5.1e-42)
     t_0
     (if (<= x 1.45e-34)
       (/ y (+ y -2.0))
       (if (<= x 8.5e+48)
         t_0
         (if (<= x 8.2e+80) (+ 1.0 (/ 2.0 y)) (+ (/ y x) -1.0)))))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (x <= -5.1e-42) {
		tmp = t_0;
	} else if (x <= 1.45e-34) {
		tmp = y / (y + -2.0);
	} else if (x <= 8.5e+48) {
		tmp = t_0;
	} else if (x <= 8.2e+80) {
		tmp = 1.0 + (2.0 / y);
	} else {
		tmp = (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 / (2.0d0 - x)
    if (x <= (-5.1d-42)) then
        tmp = t_0
    else if (x <= 1.45d-34) then
        tmp = y / (y + (-2.0d0))
    else if (x <= 8.5d+48) then
        tmp = t_0
    else if (x <= 8.2d+80) then
        tmp = 1.0d0 + (2.0d0 / y)
    else
        tmp = (y / x) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (x <= -5.1e-42) {
		tmp = t_0;
	} else if (x <= 1.45e-34) {
		tmp = y / (y + -2.0);
	} else if (x <= 8.5e+48) {
		tmp = t_0;
	} else if (x <= 8.2e+80) {
		tmp = 1.0 + (2.0 / y);
	} else {
		tmp = (y / x) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if x <= -5.1e-42:
		tmp = t_0
	elif x <= 1.45e-34:
		tmp = y / (y + -2.0)
	elif x <= 8.5e+48:
		tmp = t_0
	elif x <= 8.2e+80:
		tmp = 1.0 + (2.0 / y)
	else:
		tmp = (y / x) + -1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (x <= -5.1e-42)
		tmp = t_0;
	elseif (x <= 1.45e-34)
		tmp = Float64(y / Float64(y + -2.0));
	elseif (x <= 8.5e+48)
		tmp = t_0;
	elseif (x <= 8.2e+80)
		tmp = Float64(1.0 + Float64(2.0 / y));
	else
		tmp = Float64(Float64(y / x) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - x);
	tmp = 0.0;
	if (x <= -5.1e-42)
		tmp = t_0;
	elseif (x <= 1.45e-34)
		tmp = y / (y + -2.0);
	elseif (x <= 8.5e+48)
		tmp = t_0;
	elseif (x <= 8.2e+80)
		tmp = 1.0 + (2.0 / y);
	else
		tmp = (y / x) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.1e-42], t$95$0, If[LessEqual[x, 1.45e-34], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e+48], t$95$0, If[LessEqual[x, 8.2e+80], N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.1e-42 or 1.4500000000000001e-34 < x < 8.5000000000000001e48

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 70.4%

      \[\leadsto \color{blue}{\frac{x}{2 - x}} \]

   if -5.1e-42 < x < 1.4500000000000001e-34

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 82.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{y}{2 - y}} \]
   4. Step-by-step derivation

      1. associate-*r/ 82.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot y}{2 - y}} \]

      2. neg-mul-1 82.1%

         \[\leadsto \frac{\color{blue}{-y}}{2 - y} \]

   5. Simplified 82.1%

      \[\leadsto \color{blue}{\frac{-y}{2 - y}} \]
   6. Step-by-step derivation

      1. frac-2neg 82.1%

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

      2. div-inv 82.0%

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

      3. remove-double-neg 82.0%

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

      4. sub-neg 82.0%

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

      5. distribute-neg-in 82.0%

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

      6. metadata-eval 82.0%

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

      7. remove-double-neg 82.0%

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

   7. Applied egg-rr 82.0%

      \[\leadsto \color{blue}{y \cdot \frac{1}{-2 + y}} \]
   8. Step-by-step derivation

      1. associate-*r/ 82.1%

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

      2. *-rgt-identity 82.1%

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

      3. +-commutative 82.1%

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

   9. Simplified 82.1%

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

   if 8.5000000000000001e48 < x < 8.20000000000000003e80

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. flip-+ 51.6%

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

      3. metadata-eval 51.6%

         \[\leadsto \frac{x - y}{\frac{\color{blue}{4} - \left(-\left(x + y\right)\right) \cdot \left(-\left(x + y\right)\right)}{2 - \left(-\left(x + y\right)\right)}} \]

   4. Applied egg-rr 51.6%

      \[\leadsto \frac{x - y}{\color{blue}{\frac{4 - \left(-\left(x + y\right)\right) \cdot \left(-\left(x + y\right)\right)}{2 - \left(-\left(x + y\right)\right)}}} \]

   5. Taylor expanded in y around -inf 67.3%

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

      1. associate-*r/ 67.3%

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

      2. cancel-sign-sub-inv 67.3%

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

      3. metadata-eval 67.3%

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

      4. distribute-lft-in 67.3%

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

      5. distribute-rgt1-in 67.3%

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

      6. metadata-eval 67.3%

         \[\leadsto 1 + \frac{-1 \cdot \left(-1 \cdot \left(2 + \color{blue}{0} \cdot x\right)\right) + -1 \cdot \left(2 \cdot x\right)}{y} \]

      7. mul0-lft 67.3%

         \[\leadsto 1 + \frac{-1 \cdot \left(-1 \cdot \left(2 + \color{blue}{0}\right)\right) + -1 \cdot \left(2 \cdot x\right)}{y} \]

      8. metadata-eval 67.3%

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

      9. metadata-eval 67.3%

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

      10. metadata-eval 67.3%

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

      11. neg-mul-1 67.3%

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

      12. distribute-lft-neg-in 67.3%

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

      13. metadata-eval 67.3%

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

      14. *-commutative 67.3%

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

   7. Simplified 67.3%

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

   8. Taylor expanded in x around 0 68.1%

      \[\leadsto \color{blue}{1 + 2 \cdot \frac{1}{y}} \]
   9. Step-by-step derivation

      1. associate-*r/ 68.1%

         \[\leadsto 1 + \color{blue}{\frac{2 \cdot 1}{y}} \]

      2. metadata-eval 68.1%

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

   10. Simplified 68.1%

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

   if 8.20000000000000003e80 < x

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.0%

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

      1. mul-1-neg 87.0%

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

   5. Simplified 87.0%

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

   6. Taylor expanded in x around 0 87.0%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.1 \cdot 10^{-42}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{+48}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+80}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} + -1\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+76}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 0.32:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+80}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ y x) -1.0)))
   (if (<= x -6.2e+76)
     t_0
     (if (<= x 0.32)
       (/ (- x y) (- 2.0 y))
       (if (<= x 3e+50)
         (/ x (- 2.0 x))
         (if (<= x 8e+80) (+ 1.0 (/ 2.0 y)) t_0))))))

C

double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double tmp;
	if (x <= -6.2e+76) {
		tmp = t_0;
	} else if (x <= 0.32) {
		tmp = (x - y) / (2.0 - y);
	} else if (x <= 3e+50) {
		tmp = x / (2.0 - x);
	} else if (x <= 8e+80) {
		tmp = 1.0 + (2.0 / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y / x) + (-1.0d0)
    if (x <= (-6.2d+76)) then
        tmp = t_0
    else if (x <= 0.32d0) then
        tmp = (x - y) / (2.0d0 - y)
    else if (x <= 3d+50) then
        tmp = x / (2.0d0 - x)
    else if (x <= 8d+80) then
        tmp = 1.0d0 + (2.0d0 / y)
    else
        tmp = 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 (x <= -6.2e+76) {
		tmp = t_0;
	} else if (x <= 0.32) {
		tmp = (x - y) / (2.0 - y);
	} else if (x <= 3e+50) {
		tmp = x / (2.0 - x);
	} else if (x <= 8e+80) {
		tmp = 1.0 + (2.0 / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / x) + -1.0
	tmp = 0
	if x <= -6.2e+76:
		tmp = t_0
	elif x <= 0.32:
		tmp = (x - y) / (2.0 - y)
	elif x <= 3e+50:
		tmp = x / (2.0 - x)
	elif x <= 8e+80:
		tmp = 1.0 + (2.0 / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y / x) + -1.0)
	tmp = 0.0
	if (x <= -6.2e+76)
		tmp = t_0;
	elseif (x <= 0.32)
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	elseif (x <= 3e+50)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (x <= 8e+80)
		tmp = Float64(1.0 + Float64(2.0 / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y / x) + -1.0;
	tmp = 0.0;
	if (x <= -6.2e+76)
		tmp = t_0;
	elseif (x <= 0.32)
		tmp = (x - y) / (2.0 - y);
	elseif (x <= 3e+50)
		tmp = x / (2.0 - x);
	elseif (x <= 8e+80)
		tmp = 1.0 + (2.0 / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision]}, If[LessEqual[x, -6.2e+76], t$95$0, If[LessEqual[x, 0.32], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e+50], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e+80], N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.20000000000000023e76 or 8e80 < x

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 78.9%

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

      1. mul-1-neg 78.9%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in x around 0 78.9%

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

   if -6.20000000000000023e76 < x < 0.320000000000000007

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 96.4%

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

   if 0.320000000000000007 < x < 2.9999999999999998e50

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 73.2%

      \[\leadsto \color{blue}{\frac{x}{2 - x}} \]

   if 2.9999999999999998e50 < x < 8e80

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. flip-+ 51.6%

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

      3. metadata-eval 51.6%

         \[\leadsto \frac{x - y}{\frac{\color{blue}{4} - \left(-\left(x + y\right)\right) \cdot \left(-\left(x + y\right)\right)}{2 - \left(-\left(x + y\right)\right)}} \]

   4. Applied egg-rr 51.6%

      \[\leadsto \frac{x - y}{\color{blue}{\frac{4 - \left(-\left(x + y\right)\right) \cdot \left(-\left(x + y\right)\right)}{2 - \left(-\left(x + y\right)\right)}}} \]

   5. Taylor expanded in y around -inf 67.3%

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

      1. associate-*r/ 67.3%

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

      2. cancel-sign-sub-inv 67.3%

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

      3. metadata-eval 67.3%

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

      4. distribute-lft-in 67.3%

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

      5. distribute-rgt1-in 67.3%

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

      6. metadata-eval 67.3%

         \[\leadsto 1 + \frac{-1 \cdot \left(-1 \cdot \left(2 + \color{blue}{0} \cdot x\right)\right) + -1 \cdot \left(2 \cdot x\right)}{y} \]

      7. mul0-lft 67.3%

         \[\leadsto 1 + \frac{-1 \cdot \left(-1 \cdot \left(2 + \color{blue}{0}\right)\right) + -1 \cdot \left(2 \cdot x\right)}{y} \]

      8. metadata-eval 67.3%

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

      9. metadata-eval 67.3%

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

      10. metadata-eval 67.3%

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

      11. neg-mul-1 67.3%

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

      12. distribute-lft-neg-in 67.3%

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

      13. metadata-eval 67.3%

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

      14. *-commutative 67.3%

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

   7. Simplified 67.3%

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

   8. Taylor expanded in x around 0 68.1%

      \[\leadsto \color{blue}{1 + 2 \cdot \frac{1}{y}} \]
   9. Step-by-step derivation

      1. associate-*r/ 68.1%

         \[\leadsto 1 + \color{blue}{\frac{2 \cdot 1}{y}} \]

      2. metadata-eval 68.1%

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

   10. Simplified 68.1%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+76}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 0.32:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+50}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+80}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+56}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -80000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+42}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5e+72)
   1.0
   (if (<= y -2e+56)
     -1.0
     (if (<= y -80000000000.0) 1.0 (if (<= y 5e+42) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5e+72) {
		tmp = 1.0;
	} else if (y <= -2e+56) {
		tmp = -1.0;
	} else if (y <= -80000000000.0) {
		tmp = 1.0;
	} else if (y <= 5e+42) {
		tmp = -1.0;
	} else {
		tmp = 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 <= (-5d+72)) then
        tmp = 1.0d0
    else if (y <= (-2d+56)) then
        tmp = -1.0d0
    else if (y <= (-80000000000.0d0)) then
        tmp = 1.0d0
    else if (y <= 5d+42) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5e+72) {
		tmp = 1.0;
	} else if (y <= -2e+56) {
		tmp = -1.0;
	} else if (y <= -80000000000.0) {
		tmp = 1.0;
	} else if (y <= 5e+42) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5e+72:
		tmp = 1.0
	elif y <= -2e+56:
		tmp = -1.0
	elif y <= -80000000000.0:
		tmp = 1.0
	elif y <= 5e+42:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5e+72)
		tmp = 1.0;
	elseif (y <= -2e+56)
		tmp = -1.0;
	elseif (y <= -80000000000.0)
		tmp = 1.0;
	elseif (y <= 5e+42)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5e+72)
		tmp = 1.0;
	elseif (y <= -2e+56)
		tmp = -1.0;
	elseif (y <= -80000000000.0)
		tmp = 1.0;
	elseif (y <= 5e+42)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5e+72], 1.0, If[LessEqual[y, -2e+56], -1.0, If[LessEqual[y, -80000000000.0], 1.0, If[LessEqual[y, 5e+42], -1.0, 1.0]]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999992e72 or -2.00000000000000018e56 < y < -8e10 or 5.00000000000000007e42 < y

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 79.9%

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

   if -4.99999999999999992e72 < y < -2.00000000000000018e56 or -8e10 < y < 5.00000000000000007e42

   1. Initial program 100.0%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 54.1%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{+56}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -80000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+42}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{2 - \left(x + y\right)} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) (- 2.0 (+ x y))))

C

double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / (2.0d0 - (x + y))
end function

Java

public static double code(double x, double y) {
	return (x - y) / (2.0 - (x + y));
}

Python

def code(x, y):
	return (x - y) / (2.0 - (x + y))

Julia

function code(x, y)
	return Float64(Float64(x - y) / Float64(2.0 - Float64(x + y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / (2.0 - (x + y));
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{2 - \left(x + y\right)} \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto \frac{x - y}{2 - \left(x + y\right)} \]
4. Add Preprocessing

Alternative 12: 38.6% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

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

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{2 - \left(x + y\right)} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 38.3%

   \[\leadsto \color{blue}{-1} \]

4. Final simplification 38.3%

   \[\leadsto -1 \]
5. Add Preprocessing

Developer target: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 - \left(x + y\right)\\ \frac{x}{t_0} - \frac{y}{t_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 2.0 (+ x y)))) (- (/ x t_0) (/ y t_0))))

C

double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = 2.0d0 - (x + y)
    code = (x / t_0) - (y / t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = 2.0 - (x + y);
	return (x / t_0) - (y / t_0);
}

Python

def code(x, y):
	t_0 = 2.0 - (x + y)
	return (x / t_0) - (y / t_0)

Julia

function code(x, y)
	t_0 = Float64(2.0 - Float64(x + y))
	return Float64(Float64(x / t_0) - Float64(y / t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = 2.0 - (x + y);
	tmp = (x / t_0) - (y / t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(2.0 - N[(x + y), $MachinePrecision]), $MachinePrecision]}, N[(N[(x / t$95$0), $MachinePrecision] - N[(y / t$95$0), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024019 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2.0 (+ x y))) (/ y (- 2.0 (+ x y))))

  (/ (- x y) (- 2.0 (+ x y))))