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

Percentage Accurate: 100.0% → 100.0%

Time: 6.9s

Alternatives: 9

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: 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. Final simplification 100.0%

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

Alternative 2: 74.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{-x}\\ \mathbf{if}\;x \leq -8.8 \cdot 10^{+51}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+66}:\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- x))))
   (if (<= x -8.8e+51)
     t_0
     (if (<= x 9e-24)
       (/ y (+ y -2.0))
       (if (<= x 5e+45)
         (/ x (- 2.0 x))
         (if (<= x 7e+66) (+ 1.0 (/ (* x -2.0) y)) t_0))))))

C

double code(double x, double y) {
	double t_0 = (x - y) / -x;
	double tmp;
	if (x <= -8.8e+51) {
		tmp = t_0;
	} else if (x <= 9e-24) {
		tmp = y / (y + -2.0);
	} else if (x <= 5e+45) {
		tmp = x / (2.0 - x);
	} else if (x <= 7e+66) {
		tmp = 1.0 + ((x * -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 = (x - y) / -x
    if (x <= (-8.8d+51)) then
        tmp = t_0
    else if (x <= 9d-24) then
        tmp = y / (y + (-2.0d0))
    else if (x <= 5d+45) then
        tmp = x / (2.0d0 - x)
    else if (x <= 7d+66) then
        tmp = 1.0d0 + ((x * (-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 = (x - y) / -x;
	double tmp;
	if (x <= -8.8e+51) {
		tmp = t_0;
	} else if (x <= 9e-24) {
		tmp = y / (y + -2.0);
	} else if (x <= 5e+45) {
		tmp = x / (2.0 - x);
	} else if (x <= 7e+66) {
		tmp = 1.0 + ((x * -2.0) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) / -x
	tmp = 0
	if x <= -8.8e+51:
		tmp = t_0
	elif x <= 9e-24:
		tmp = y / (y + -2.0)
	elif x <= 5e+45:
		tmp = x / (2.0 - x)
	elif x <= 7e+66:
		tmp = 1.0 + ((x * -2.0) / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / Float64(-x))
	tmp = 0.0
	if (x <= -8.8e+51)
		tmp = t_0;
	elseif (x <= 9e-24)
		tmp = Float64(y / Float64(y + -2.0));
	elseif (x <= 5e+45)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (x <= 7e+66)
		tmp = Float64(1.0 + Float64(Float64(x * -2.0) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) / -x;
	tmp = 0.0;
	if (x <= -8.8e+51)
		tmp = t_0;
	elseif (x <= 9e-24)
		tmp = y / (y + -2.0);
	elseif (x <= 5e+45)
		tmp = x / (2.0 - x);
	elseif (x <= 7e+66)
		tmp = 1.0 + ((x * -2.0) / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / (-x)), $MachinePrecision]}, If[LessEqual[x, -8.8e+51], t$95$0, If[LessEqual[x, 9e-24], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+45], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e+66], N[(1.0 + N[(N[(x * -2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.79999999999999967e51 or 6.9999999999999994e66 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

      1. flip-- 35.6%

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

      2. associate-/r/ 35.4%

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

      3. pow2 35.4%

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

      4. +-commutative 35.4%

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

   5. Applied egg-rr 35.4%

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

      1. associate-*l/ 33.9%

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

      2. associate-/l* 35.6%

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

   7. Simplified 35.6%

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

   8. Taylor expanded in x around inf 85.5%

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

      1. mul-1-neg 85.5%

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

   10. Simplified 85.5%

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

   if -8.79999999999999967e51 < x < 8.9999999999999995e-24

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. distribute-neg-frac 84.6%

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

   6. Simplified 84.6%

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

      1. add-log-exp 62.2%

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

      2. *-un-lft-identity 62.2%

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

      3. log-prod 62.2%

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

      4. metadata-eval 62.2%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{-y}{2 - y}}\right) \]

      5. add-log-exp 84.6%

         \[\leadsto 0 + \color{blue}{\frac{-y}{2 - y}} \]

      6. frac-2neg 84.6%

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

      7. remove-double-neg 84.6%

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

      8. sub-neg 84.6%

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

      9. distribute-neg-in 84.6%

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

      10. metadata-eval 84.6%

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

      11. remove-double-neg 84.6%

          \[\leadsto 0 + \frac{y}{-2 + \color{blue}{y}} \]

   8. Applied egg-rr 84.6%

      \[\leadsto \color{blue}{0 + \frac{y}{-2 + y}} \]
   9. Step-by-step derivation

      1. +-lft-identity 84.6%

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

      2. +-commutative 84.6%

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

   10. Simplified 84.6%

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

   if 8.9999999999999995e-24 < x < 5e45

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 80.9%

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

   if 5e45 < x < 6.9999999999999994e66

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 86.6%

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

      1. associate--l+ 86.9%

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

      2. associate-*r/ 86.9%

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

      3. associate-*r/ 86.9%

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

      4. div-sub 86.9%

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

      5. cancel-sign-sub-inv 86.9%

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

      6. metadata-eval 86.9%

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

      7. *-lft-identity 86.9%

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

      8. +-commutative 86.9%

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

      9. mul-1-neg 86.9%

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

      10. unsub-neg 86.9%

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

   6. Simplified 86.9%

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

   7. Taylor expanded in x around inf 86.9%

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

      1. *-commutative 86.9%

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

   9. Simplified 86.9%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+51}:\\ \;\;\;\;\frac{x - y}{-x}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+66}:\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{-x}\\ \end{array} \]

Alternative 3: 74.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{-x}\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-22}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+66}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- x))))
   (if (<= x -1.9e+52)
     t_0
     (if (<= x 1.05e-22)
       (/ y (+ y -2.0))
       (if (<= x 2.35e+44) (/ x (- 2.0 x)) (if (<= x 3.6e+66) 1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = (x - y) / -x;
	double tmp;
	if (x <= -1.9e+52) {
		tmp = t_0;
	} else if (x <= 1.05e-22) {
		tmp = y / (y + -2.0);
	} else if (x <= 2.35e+44) {
		tmp = x / (2.0 - x);
	} else if (x <= 3.6e+66) {
		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 = (x - y) / -x
    if (x <= (-1.9d+52)) then
        tmp = t_0
    else if (x <= 1.05d-22) then
        tmp = y / (y + (-2.0d0))
    else if (x <= 2.35d+44) then
        tmp = x / (2.0d0 - x)
    else if (x <= 3.6d+66) 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 = (x - y) / -x;
	double tmp;
	if (x <= -1.9e+52) {
		tmp = t_0;
	} else if (x <= 1.05e-22) {
		tmp = y / (y + -2.0);
	} else if (x <= 2.35e+44) {
		tmp = x / (2.0 - x);
	} else if (x <= 3.6e+66) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) / -x
	tmp = 0
	if x <= -1.9e+52:
		tmp = t_0
	elif x <= 1.05e-22:
		tmp = y / (y + -2.0)
	elif x <= 2.35e+44:
		tmp = x / (2.0 - x)
	elif x <= 3.6e+66:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / Float64(-x))
	tmp = 0.0
	if (x <= -1.9e+52)
		tmp = t_0;
	elseif (x <= 1.05e-22)
		tmp = Float64(y / Float64(y + -2.0));
	elseif (x <= 2.35e+44)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (x <= 3.6e+66)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) / -x;
	tmp = 0.0;
	if (x <= -1.9e+52)
		tmp = t_0;
	elseif (x <= 1.05e-22)
		tmp = y / (y + -2.0);
	elseif (x <= 2.35e+44)
		tmp = x / (2.0 - x);
	elseif (x <= 3.6e+66)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / (-x)), $MachinePrecision]}, If[LessEqual[x, -1.9e+52], t$95$0, If[LessEqual[x, 1.05e-22], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.35e+44], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.6e+66], 1.0, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.9e52 or 3.6e66 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

      1. flip-- 35.6%

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

      2. associate-/r/ 35.4%

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

      3. pow2 35.4%

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

      4. +-commutative 35.4%

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

   5. Applied egg-rr 35.4%

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

      1. associate-*l/ 33.9%

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

      2. associate-/l* 35.6%

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

   7. Simplified 35.6%

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

   8. Taylor expanded in x around inf 85.5%

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

      1. mul-1-neg 85.5%

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

   10. Simplified 85.5%

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

   if -1.9e52 < x < 1.05000000000000004e-22

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. distribute-neg-frac 84.6%

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

   6. Simplified 84.6%

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

      1. add-log-exp 62.2%

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

      2. *-un-lft-identity 62.2%

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

      3. log-prod 62.2%

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

      4. metadata-eval 62.2%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{-y}{2 - y}}\right) \]

      5. add-log-exp 84.6%

         \[\leadsto 0 + \color{blue}{\frac{-y}{2 - y}} \]

      6. frac-2neg 84.6%

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

      7. remove-double-neg 84.6%

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

      8. sub-neg 84.6%

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

      9. distribute-neg-in 84.6%

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

      10. metadata-eval 84.6%

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

      11. remove-double-neg 84.6%

          \[\leadsto 0 + \frac{y}{-2 + \color{blue}{y}} \]

   8. Applied egg-rr 84.6%

      \[\leadsto \color{blue}{0 + \frac{y}{-2 + y}} \]
   9. Step-by-step derivation

      1. +-lft-identity 84.6%

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

      2. +-commutative 84.6%

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

   10. Simplified 84.6%

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

   if 1.05000000000000004e-22 < x < 2.35000000000000009e44

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 80.9%

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

   if 2.35000000000000009e44 < x < 3.6e66

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 84.0%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+52}:\\ \;\;\;\;\frac{x - y}{-x}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-22}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+66}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{-x}\\ \end{array} \]

Alternative 4: 74.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{-x}\\ \mathbf{if}\;x \leq -2 \cdot 10^{+52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-22}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+66}:\\ \;\;\;\;\frac{x - y}{-y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) (- x))))
   (if (<= x -2e+52)
     t_0
     (if (<= x 1.05e-22)
       (/ y (+ y -2.0))
       (if (<= x 2.5e+45)
         (/ x (- 2.0 x))
         (if (<= x 1.1e+66) (/ (- x y) (- y)) t_0))))))

C

double code(double x, double y) {
	double t_0 = (x - y) / -x;
	double tmp;
	if (x <= -2e+52) {
		tmp = t_0;
	} else if (x <= 1.05e-22) {
		tmp = y / (y + -2.0);
	} else if (x <= 2.5e+45) {
		tmp = x / (2.0 - x);
	} else if (x <= 1.1e+66) {
		tmp = (x - y) / -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 = (x - y) / -x
    if (x <= (-2d+52)) then
        tmp = t_0
    else if (x <= 1.05d-22) then
        tmp = y / (y + (-2.0d0))
    else if (x <= 2.5d+45) then
        tmp = x / (2.0d0 - x)
    else if (x <= 1.1d+66) then
        tmp = (x - y) / -y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x - y) / -x;
	double tmp;
	if (x <= -2e+52) {
		tmp = t_0;
	} else if (x <= 1.05e-22) {
		tmp = y / (y + -2.0);
	} else if (x <= 2.5e+45) {
		tmp = x / (2.0 - x);
	} else if (x <= 1.1e+66) {
		tmp = (x - y) / -y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) / -x
	tmp = 0
	if x <= -2e+52:
		tmp = t_0
	elif x <= 1.05e-22:
		tmp = y / (y + -2.0)
	elif x <= 2.5e+45:
		tmp = x / (2.0 - x)
	elif x <= 1.1e+66:
		tmp = (x - y) / -y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / Float64(-x))
	tmp = 0.0
	if (x <= -2e+52)
		tmp = t_0;
	elseif (x <= 1.05e-22)
		tmp = Float64(y / Float64(y + -2.0));
	elseif (x <= 2.5e+45)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (x <= 1.1e+66)
		tmp = Float64(Float64(x - y) / Float64(-y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) / -x;
	tmp = 0.0;
	if (x <= -2e+52)
		tmp = t_0;
	elseif (x <= 1.05e-22)
		tmp = y / (y + -2.0);
	elseif (x <= 2.5e+45)
		tmp = x / (2.0 - x);
	elseif (x <= 1.1e+66)
		tmp = (x - y) / -y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / (-x)), $MachinePrecision]}, If[LessEqual[x, -2e+52], t$95$0, If[LessEqual[x, 1.05e-22], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e+45], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+66], N[(N[(x - y), $MachinePrecision] / (-y)), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2e52 or 1.0999999999999999e66 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

      1. flip-- 35.6%

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

      2. associate-/r/ 35.4%

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

      3. pow2 35.4%

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

      4. +-commutative 35.4%

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

   5. Applied egg-rr 35.4%

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

      1. associate-*l/ 33.9%

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

      2. associate-/l* 35.6%

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

   7. Simplified 35.6%

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

   8. Taylor expanded in x around inf 85.5%

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

      1. mul-1-neg 85.5%

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

   10. Simplified 85.5%

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

   if -2e52 < x < 1.05000000000000004e-22

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. distribute-neg-frac 84.6%

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

   6. Simplified 84.6%

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

      1. add-log-exp 62.2%

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

      2. *-un-lft-identity 62.2%

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

      3. log-prod 62.2%

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

      4. metadata-eval 62.2%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{-y}{2 - y}}\right) \]

      5. add-log-exp 84.6%

         \[\leadsto 0 + \color{blue}{\frac{-y}{2 - y}} \]

      6. frac-2neg 84.6%

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

      7. remove-double-neg 84.6%

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

      8. sub-neg 84.6%

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

      9. distribute-neg-in 84.6%

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

      10. metadata-eval 84.6%

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

      11. remove-double-neg 84.6%

          \[\leadsto 0 + \frac{y}{-2 + \color{blue}{y}} \]

   8. Applied egg-rr 84.6%

      \[\leadsto \color{blue}{0 + \frac{y}{-2 + y}} \]
   9. Step-by-step derivation

      1. +-lft-identity 84.6%

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

      2. +-commutative 84.6%

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

   10. Simplified 84.6%

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

   if 1.05000000000000004e-22 < x < 2.5e45

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 80.9%

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

   if 2.5e45 < x < 1.0999999999999999e66

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

      1. flip-- 44.4%

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

      2. associate-/r/ 44.2%

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

      3. pow2 44.2%

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

      4. +-commutative 44.2%

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

   5. Applied egg-rr 44.2%

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

      1. associate-*l/ 42.9%

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

      2. associate-/l* 44.4%

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

   7. Simplified 44.4%

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

   8. Taylor expanded in y around inf 85.2%

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

      1. neg-mul-1 85.2%

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

   10. Simplified 85.2%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+52}:\\ \;\;\;\;\frac{x - y}{-x}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-22}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+66}:\\ \;\;\;\;\frac{x - y}{-y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{-x}\\ \end{array} \]

Alternative 5: 74.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+90}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+64} \lor \neg \left(y \leq -3.2 \cdot 10^{+31}\right) \land y \leq 3 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6e+90)
   1.0
   (if (or (<= y -2.3e+64) (and (not (<= y -3.2e+31)) (<= y 3e+15)))
     (/ x (- 2.0 x))
     1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6e+90) {
		tmp = 1.0;
	} else if ((y <= -2.3e+64) || (!(y <= -3.2e+31) && (y <= 3e+15))) {
		tmp = x / (2.0 - x);
	} 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 <= (-6d+90)) then
        tmp = 1.0d0
    else if ((y <= (-2.3d+64)) .or. (.not. (y <= (-3.2d+31))) .and. (y <= 3d+15)) then
        tmp = x / (2.0d0 - x)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6e+90) {
		tmp = 1.0;
	} else if ((y <= -2.3e+64) || (!(y <= -3.2e+31) && (y <= 3e+15))) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6e+90:
		tmp = 1.0
	elif (y <= -2.3e+64) or (not (y <= -3.2e+31) and (y <= 3e+15)):
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6e+90)
		tmp = 1.0;
	elseif ((y <= -2.3e+64) || (!(y <= -3.2e+31) && (y <= 3e+15)))
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6e+90)
		tmp = 1.0;
	elseif ((y <= -2.3e+64) || (~((y <= -3.2e+31)) && (y <= 3e+15)))
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6e+90], 1.0, If[Or[LessEqual[y, -2.3e+64], And[N[Not[LessEqual[y, -3.2e+31]], $MachinePrecision], LessEqual[y, 3e+15]]], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -5.99999999999999957e90 or -2.3e64 < y < -3.2000000000000001e31 or 3e15 < y

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 78.3%

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

   if -5.99999999999999957e90 < y < -2.3e64 or -3.2000000000000001e31 < y < 3e15

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 72.5%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+90}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+64} \lor \neg \left(y \leq -3.2 \cdot 10^{+31}\right) \land y \leq 3 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y + -2}\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+52}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-24}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+72}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ y -2.0))))
   (if (<= x -2.8e+52)
     -1.0
     (if (<= x 9e-24)
       t_0
       (if (<= x 5.3e+45) (/ x (- 2.0 x)) (if (<= x 1.25e+72) t_0 -1.0))))))

C

double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double tmp;
	if (x <= -2.8e+52) {
		tmp = -1.0;
	} else if (x <= 9e-24) {
		tmp = t_0;
	} else if (x <= 5.3e+45) {
		tmp = x / (2.0 - x);
	} else if (x <= 1.25e+72) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = y / (y + (-2.0d0))
    if (x <= (-2.8d+52)) then
        tmp = -1.0d0
    else if (x <= 9d-24) then
        tmp = t_0
    else if (x <= 5.3d+45) then
        tmp = x / (2.0d0 - x)
    else if (x <= 1.25d+72) then
        tmp = t_0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double tmp;
	if (x <= -2.8e+52) {
		tmp = -1.0;
	} else if (x <= 9e-24) {
		tmp = t_0;
	} else if (x <= 5.3e+45) {
		tmp = x / (2.0 - x);
	} else if (x <= 1.25e+72) {
		tmp = t_0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (y + -2.0)
	tmp = 0
	if x <= -2.8e+52:
		tmp = -1.0
	elif x <= 9e-24:
		tmp = t_0
	elif x <= 5.3e+45:
		tmp = x / (2.0 - x)
	elif x <= 1.25e+72:
		tmp = t_0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y + -2.0))
	tmp = 0.0
	if (x <= -2.8e+52)
		tmp = -1.0;
	elseif (x <= 9e-24)
		tmp = t_0;
	elseif (x <= 5.3e+45)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (x <= 1.25e+72)
		tmp = t_0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (y + -2.0);
	tmp = 0.0;
	if (x <= -2.8e+52)
		tmp = -1.0;
	elseif (x <= 9e-24)
		tmp = t_0;
	elseif (x <= 5.3e+45)
		tmp = x / (2.0 - x);
	elseif (x <= 1.25e+72)
		tmp = t_0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.8e+52], -1.0, If[LessEqual[x, 9e-24], t$95$0, If[LessEqual[x, 5.3e+45], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e+72], t$95$0, -1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.8e52 or 1.24999999999999998e72 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 85.6%

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

   if -2.8e52 < x < 8.9999999999999995e-24 or 5.29999999999999991e45 < x < 1.24999999999999998e72

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 84.1%

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

      1. mul-1-neg 84.1%

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

      2. distribute-neg-frac 84.1%

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

   6. Simplified 84.1%

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

      1. add-log-exp 63.2%

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

      2. *-un-lft-identity 63.2%

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

      3. log-prod 63.2%

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

      4. metadata-eval 63.2%

         \[\leadsto \color{blue}{0} + \log \left(e^{\frac{-y}{2 - y}}\right) \]

      5. add-log-exp 84.1%

         \[\leadsto 0 + \color{blue}{\frac{-y}{2 - y}} \]

      6. frac-2neg 84.1%

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

      7. remove-double-neg 84.1%

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

      8. sub-neg 84.1%

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

      9. distribute-neg-in 84.1%

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

      10. metadata-eval 84.1%

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

      11. remove-double-neg 84.1%

          \[\leadsto 0 + \frac{y}{-2 + \color{blue}{y}} \]

   8. Applied egg-rr 84.1%

      \[\leadsto \color{blue}{0 + \frac{y}{-2 + y}} \]
   9. Step-by-step derivation

      1. +-lft-identity 84.1%

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

      2. +-commutative 84.1%

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

   10. Simplified 84.1%

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

   if 8.9999999999999995e-24 < x < 5.29999999999999991e45

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 80.9%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+52}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-24}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+72}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 7: 87.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+31}:\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+16}:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{-y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4e+31)
   (+ 1.0 (/ (* x -2.0) y))
   (if (<= y 1.45e+16) (/ (- x y) (- 2.0 x)) (/ (- x y) (- y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4e+31) {
		tmp = 1.0 + ((x * -2.0) / y);
	} else if (y <= 1.45e+16) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = (x - y) / -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 <= (-4d+31)) then
        tmp = 1.0d0 + ((x * (-2.0d0)) / y)
    else if (y <= 1.45d+16) then
        tmp = (x - y) / (2.0d0 - x)
    else
        tmp = (x - y) / -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4e+31) {
		tmp = 1.0 + ((x * -2.0) / y);
	} else if (y <= 1.45e+16) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = (x - y) / -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4e+31:
		tmp = 1.0 + ((x * -2.0) / y)
	elif y <= 1.45e+16:
		tmp = (x - y) / (2.0 - x)
	else:
		tmp = (x - y) / -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4e+31)
		tmp = Float64(1.0 + Float64(Float64(x * -2.0) / y));
	elseif (y <= 1.45e+16)
		tmp = Float64(Float64(x - y) / Float64(2.0 - x));
	else
		tmp = Float64(Float64(x - y) / Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4e+31)
		tmp = 1.0 + ((x * -2.0) / y);
	elseif (y <= 1.45e+16)
		tmp = (x - y) / (2.0 - x);
	else
		tmp = (x - y) / -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4e+31], N[(1.0 + N[(N[(x * -2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.45e+16], N[(N[(x - y), $MachinePrecision] / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.9999999999999999e31

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 74.4%

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

      1. associate--l+ 74.4%

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

      2. associate-*r/ 74.4%

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

      3. associate-*r/ 74.4%

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

      4. div-sub 74.4%

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

      5. cancel-sign-sub-inv 74.4%

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

      6. metadata-eval 74.4%

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

      7. *-lft-identity 74.4%

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

      8. +-commutative 74.4%

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

      9. mul-1-neg 74.4%

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

      10. unsub-neg 74.4%

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

   6. Simplified 74.4%

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

   7. Taylor expanded in x around inf 74.4%

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

      1. *-commutative 74.4%

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

   9. Simplified 74.4%

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

   if -3.9999999999999999e31 < y < 1.45e16

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

      1. flip-- 68.9%

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

      2. associate-/r/ 68.8%

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

      3. pow2 68.8%

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

      4. +-commutative 68.8%

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

   5. Applied egg-rr 68.8%

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

      1. associate-*l/ 67.9%

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

      2. associate-/l* 68.9%

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

   7. Simplified 68.9%

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

   8. Taylor expanded in y around 0 96.5%

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

   if 1.45e16 < y

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

      1. flip-- 49.0%

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

      2. associate-/r/ 48.8%

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

      3. pow2 48.8%

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

      4. +-commutative 48.8%

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

   5. Applied egg-rr 48.8%

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

      1. associate-*l/ 47.8%

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

      2. associate-/l* 49.0%

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

   7. Simplified 49.0%

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

   8. Taylor expanded in y around inf 77.1%

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

      1. neg-mul-1 77.1%

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

   10. Simplified 77.1%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+31}:\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+16}:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{-y}\\ \end{array} \]

Alternative 8: 62.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+52}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1860000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 10^{+45}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+58}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4e+52)
   -1.0
   (if (<= x 1860000.0)
     1.0
     (if (<= x 1e+45) -1.0 (if (<= x 6e+58) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4e+52) {
		tmp = -1.0;
	} else if (x <= 1860000.0) {
		tmp = 1.0;
	} else if (x <= 1e+45) {
		tmp = -1.0;
	} else if (x <= 6e+58) {
		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 (x <= (-4d+52)) then
        tmp = -1.0d0
    else if (x <= 1860000.0d0) then
        tmp = 1.0d0
    else if (x <= 1d+45) then
        tmp = -1.0d0
    else if (x <= 6d+58) 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 (x <= -4e+52) {
		tmp = -1.0;
	} else if (x <= 1860000.0) {
		tmp = 1.0;
	} else if (x <= 1e+45) {
		tmp = -1.0;
	} else if (x <= 6e+58) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4e+52:
		tmp = -1.0
	elif x <= 1860000.0:
		tmp = 1.0
	elif x <= 1e+45:
		tmp = -1.0
	elif x <= 6e+58:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4e+52)
		tmp = -1.0;
	elseif (x <= 1860000.0)
		tmp = 1.0;
	elseif (x <= 1e+45)
		tmp = -1.0;
	elseif (x <= 6e+58)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4e+52)
		tmp = -1.0;
	elseif (x <= 1860000.0)
		tmp = 1.0;
	elseif (x <= 1e+45)
		tmp = -1.0;
	elseif (x <= 6e+58)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4e+52], -1.0, If[LessEqual[x, 1860000.0], 1.0, If[LessEqual[x, 1e+45], -1.0, If[LessEqual[x, 6e+58], 1.0, -1.0]]]]

Derivation

1. Split input into 2 regimes

2. if x < -4e52 or 1.86e6 < x < 9.9999999999999993e44 or 6.0000000000000005e58 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 82.9%

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

   if -4e52 < x < 1.86e6 or 9.9999999999999993e44 < x < 6.0000000000000005e58

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 60.9%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+52}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1860000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 10^{+45}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+58}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 9: 39.0% 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. Step-by-step derivation

   1. associate--r+ 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in x around inf 41.0%

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

5. Final simplification 41.0%

   \[\leadsto -1 \]

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 2023227 
(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))))