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

Percentage Accurate: 100.0% → 100.0%

Time: 7.8s

Alternatives: 11

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, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. remove-double-neg 100.0%

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

   2. +-commutative 100.0%

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

   3. distribute-neg-frac2 100.0%

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

   4. distribute-frac-neg 100.0%

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

   5. sub-neg 100.0%

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

   6. distribute-neg-in 100.0%

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

   7. remove-double-neg 100.0%

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

   8. +-commutative 100.0%

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

   9. sub-neg 100.0%

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

   10. neg-sub0 100.0%

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

   11. associate--r- 100.0%

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

   12. metadata-eval 100.0%

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

   13. metadata-eval 100.0%

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

   14. +-commutative 100.0%

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

   15. +-commutative 100.0%

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

   16. associate-+r+ 100.0%

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

   17. metadata-eval 100.0%

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

3. Simplified 100.0%

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

   1. expm1-log1p-u 35.4%

      \[\leadsto \frac{y - x}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x + \left(y + -2\right)\right)\right)}} \]

   2. expm1-undefine 35.4%

      \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(x + \left(y + -2\right)\right)} - 1}} \]

   3. +-commutative 35.4%

      \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(\color{blue}{\left(y + -2\right) + x}\right)} - 1} \]

   4. associate-+l+ 35.4%

      \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(\color{blue}{y + \left(-2 + x\right)}\right)} - 1} \]

6. Applied egg-rr 35.4%

   \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} - 1}} \]
7. Step-by-step derivation

   1. sub-neg 35.4%

      \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} + \left(-1\right)}} \]

   2. metadata-eval 35.4%

      \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} + \color{blue}{-1}} \]

   3. +-commutative 35.4%

      \[\leadsto \frac{y - x}{\color{blue}{-1 + e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)}}} \]

   4. log1p-undefine 35.4%

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

   5. rem-exp-log 100.0%

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

   6. associate-+r+ 100.0%

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

   7. associate-+r+ 100.0%

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

   8. +-commutative 100.0%

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

   9. associate-+r+ 100.0%

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

   10. metadata-eval 100.0%

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

8. Simplified 100.0%

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

9. Final simplification 100.0%

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

Alternative 2: 61.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+34}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.28 \cdot 10^{-200}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-271}:\\ \;\;\;\;\frac{x}{2}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+21}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.1e+34)
   1.0
   (if (<= y -1.28e-200)
     -1.0
     (if (<= y 7e-271) (/ x 2.0) (if (<= y 3.2e+21) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.1e+34) {
		tmp = 1.0;
	} else if (y <= -1.28e-200) {
		tmp = -1.0;
	} else if (y <= 7e-271) {
		tmp = x / 2.0;
	} else if (y <= 3.2e+21) {
		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 <= (-1.1d+34)) then
        tmp = 1.0d0
    else if (y <= (-1.28d-200)) then
        tmp = -1.0d0
    else if (y <= 7d-271) then
        tmp = x / 2.0d0
    else if (y <= 3.2d+21) 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 <= -1.1e+34) {
		tmp = 1.0;
	} else if (y <= -1.28e-200) {
		tmp = -1.0;
	} else if (y <= 7e-271) {
		tmp = x / 2.0;
	} else if (y <= 3.2e+21) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.1e+34:
		tmp = 1.0
	elif y <= -1.28e-200:
		tmp = -1.0
	elif y <= 7e-271:
		tmp = x / 2.0
	elif y <= 3.2e+21:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.1e+34)
		tmp = 1.0;
	elseif (y <= -1.28e-200)
		tmp = -1.0;
	elseif (y <= 7e-271)
		tmp = Float64(x / 2.0);
	elseif (y <= 3.2e+21)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.1e+34)
		tmp = 1.0;
	elseif (y <= -1.28e-200)
		tmp = -1.0;
	elseif (y <= 7e-271)
		tmp = x / 2.0;
	elseif (y <= 3.2e+21)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.1e+34], 1.0, If[LessEqual[y, -1.28e-200], -1.0, If[LessEqual[y, 7e-271], N[(x / 2.0), $MachinePrecision], If[LessEqual[y, 3.2e+21], -1.0, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1000000000000001e34 or 3.2e21 < y

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-frac2 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. sub-neg 99.9%

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

      6. distribute-neg-in 99.9%

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

      7. remove-double-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. neg-sub0 99.9%

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

      11. associate--r- 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

      14. +-commutative 99.9%

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

      15. +-commutative 99.9%

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

      16. associate-+r+ 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 78.7%

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

   if -1.1000000000000001e34 < y < -1.28e-200 or 6.9999999999999999e-271 < y < 3.2e21

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 61.5%

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

   if -1.28e-200 < y < 6.9999999999999999e-271

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 93.7%

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

      1. mul-1-neg 93.7%

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

      2. distribute-neg-frac2 93.7%

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

      3. neg-sub0 93.7%

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

      4. associate-+l- 93.7%

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

      5. neg-sub0 93.7%

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

      6. +-commutative 93.7%

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

      7. unsub-neg 93.7%

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

   7. Simplified 93.7%

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

   8. Taylor expanded in x around 0 61.8%

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

Alternative 3: 86.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+35} \lor \neg \left(y \leq 2.1 \cdot 10^{+19}\right):\\ \;\;\;\;1 + \frac{\left(2 - x\right) - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{x - 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.5e+35) (not (<= y 2.1e+19)))
   (+ 1.0 (/ (- (- 2.0 x) x) y))
   (/ (- y x) (- x 2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.5e+35) || !(y <= 2.1e+19)) {
		tmp = 1.0 + (((2.0 - x) - x) / y);
	} else {
		tmp = (y - x) / (x - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2.5d+35)) .or. (.not. (y <= 2.1d+19))) then
        tmp = 1.0d0 + (((2.0d0 - x) - x) / y)
    else
        tmp = (y - x) / (x - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.5e+35) || !(y <= 2.1e+19)) {
		tmp = 1.0 + (((2.0 - x) - x) / y);
	} else {
		tmp = (y - x) / (x - 2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.5e+35) or not (y <= 2.1e+19):
		tmp = 1.0 + (((2.0 - x) - x) / y)
	else:
		tmp = (y - x) / (x - 2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.5e+35) || !(y <= 2.1e+19))
		tmp = Float64(1.0 + Float64(Float64(Float64(2.0 - x) - x) / y));
	else
		tmp = Float64(Float64(y - x) / Float64(x - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.5e+35) || ~((y <= 2.1e+19)))
		tmp = 1.0 + (((2.0 - x) - x) / y);
	else
		tmp = (y - x) / (x - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.5e+35], N[Not[LessEqual[y, 2.1e+19]], $MachinePrecision]], N[(1.0 + N[(N[(N[(2.0 - x), $MachinePrecision] - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] / N[(x - 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.50000000000000011e35 or 2.1e19 < y

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-frac2 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. sub-neg 99.9%

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

      6. distribute-neg-in 99.9%

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

      7. remove-double-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. neg-sub0 99.9%

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

      11. associate--r- 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

      14. +-commutative 99.9%

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

      15. +-commutative 99.9%

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

      16. associate-+r+ 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 80.2%

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

      1. associate--l+ 80.2%

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

      2. +-commutative 80.2%

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

      3. mul-1-neg 80.2%

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

      4. unsub-neg 80.2%

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

      5. associate-*r/ 80.2%

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

      6. metadata-eval 80.2%

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

      7. div-sub 80.2%

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

      8. unsub-neg 80.2%

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

      9. +-commutative 80.2%

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

      10. neg-sub0 80.2%

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

      11. associate-+l- 80.2%

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

      12. neg-sub0 80.2%

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

      13. mul-1-neg 80.2%

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

      14. +-rgt-identity 80.2%

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

      15. div-sub 80.2%

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

      16. +-rgt-identity 80.2%

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

      17. mul-1-neg 80.2%

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

      18. neg-sub0 80.2%

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

      19. associate-+l- 80.2%

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

      20. neg-sub0 80.2%

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

      21. +-commutative 80.2%

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

      22. unsub-neg 80.2%

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

   7. Simplified 80.2%

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

   if -2.50000000000000011e35 < y < 2.1e19

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.7%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+35} \lor \neg \left(y \leq 2.1 \cdot 10^{+19}\right):\\ \;\;\;\;1 + \frac{\left(2 - x\right) - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{x - 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+34}:\\ \;\;\;\;-1 + \left(2 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+19}:\\ \;\;\;\;\frac{y - x}{x - 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.2e+34)
   (+ -1.0 (- 2.0 (/ x y)))
   (if (<= y 1.15e+19) (/ (- y x) (- x 2.0)) (/ (- y x) y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.2e+34) {
		tmp = -1.0 + (2.0 - (x / y));
	} else if (y <= 1.15e+19) {
		tmp = (y - x) / (x - 2.0);
	} else {
		tmp = (y - x) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.2d+34)) then
        tmp = (-1.0d0) + (2.0d0 - (x / y))
    else if (y <= 1.15d+19) then
        tmp = (y - x) / (x - 2.0d0)
    else
        tmp = (y - x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.2e+34) {
		tmp = -1.0 + (2.0 - (x / y));
	} else if (y <= 1.15e+19) {
		tmp = (y - x) / (x - 2.0);
	} else {
		tmp = (y - x) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.2e+34:
		tmp = -1.0 + (2.0 - (x / y))
	elif y <= 1.15e+19:
		tmp = (y - x) / (x - 2.0)
	else:
		tmp = (y - x) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.2e+34)
		tmp = Float64(-1.0 + Float64(2.0 - Float64(x / y)));
	elseif (y <= 1.15e+19)
		tmp = Float64(Float64(y - x) / Float64(x - 2.0));
	else
		tmp = Float64(Float64(y - x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.2e+34)
		tmp = -1.0 + (2.0 - (x / y));
	elseif (y <= 1.15e+19)
		tmp = (y - x) / (x - 2.0);
	else
		tmp = (y - x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.2e+34], N[(-1.0 + N[(2.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+19], N[(N[(y - x), $MachinePrecision] / N[(x - 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.19999999999999993e34

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-frac2 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. sub-neg 99.9%

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

      6. distribute-neg-in 99.9%

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

      7. remove-double-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. neg-sub0 99.9%

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

      11. associate--r- 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

      14. +-commutative 99.9%

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

      15. +-commutative 99.9%

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

      16. associate-+r+ 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. expm1-log1p-u 7.7%

         \[\leadsto \frac{y - x}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x + \left(y + -2\right)\right)\right)}} \]

      2. expm1-undefine 7.7%

         \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(x + \left(y + -2\right)\right)} - 1}} \]

      3. +-commutative 7.7%

         \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(\color{blue}{\left(y + -2\right) + x}\right)} - 1} \]

      4. associate-+l+ 7.7%

         \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(\color{blue}{y + \left(-2 + x\right)}\right)} - 1} \]

   6. Applied egg-rr 7.7%

      \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} - 1}} \]
   7. Step-by-step derivation

      1. sub-neg 7.7%

         \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} + \left(-1\right)}} \]

      2. metadata-eval 7.7%

         \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} + \color{blue}{-1}} \]

      3. +-commutative 7.7%

         \[\leadsto \frac{y - x}{\color{blue}{-1 + e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)}}} \]

      4. log1p-undefine 7.7%

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

      5. rem-exp-log 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+r+ 99.9%

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

      8. +-commutative 99.9%

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

      9. associate-+r+ 99.9%

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

      10. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in y around inf 78.4%

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

       1. expm1-log1p-u 77.5%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y - x}{y}\right)\right)} \]

       2. expm1-undefine 77.5%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y - x}{y}\right)} - 1} \]

       3. div-sub 77.5%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{y} - \frac{x}{y}}\right)} - 1 \]

       4. *-inverses 77.5%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{1} - \frac{x}{y}\right)} - 1 \]

   11. Applied egg-rr 77.5%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(1 - \frac{x}{y}\right)} - 1} \]
   12. Step-by-step derivation

       1. sub-neg 77.5%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(1 - \frac{x}{y}\right)} + \left(-1\right)} \]

       2. log1p-undefine 77.5%

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

       3. rem-exp-log 78.4%

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

       4. associate-+r- 78.4%

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

       5. metadata-eval 78.4%

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

       6. metadata-eval 78.4%

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

   13. Simplified 78.4%

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

   if -1.19999999999999993e34 < y < 1.15e19

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.7%

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

   if 1.15e19 < y

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. expm1-log1p-u 83.7%

         \[\leadsto \frac{y - x}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x + \left(y + -2\right)\right)\right)}} \]

      2. expm1-undefine 83.7%

         \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(x + \left(y + -2\right)\right)} - 1}} \]

      3. +-commutative 83.7%

         \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(\color{blue}{\left(y + -2\right) + x}\right)} - 1} \]

      4. associate-+l+ 83.7%

         \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(\color{blue}{y + \left(-2 + x\right)}\right)} - 1} \]

   6. Applied egg-rr 83.7%

      \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} - 1}} \]
   7. Step-by-step derivation

      1. sub-neg 83.7%

         \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} + \left(-1\right)}} \]

      2. metadata-eval 83.7%

         \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} + \color{blue}{-1}} \]

      3. +-commutative 83.7%

         \[\leadsto \frac{y - x}{\color{blue}{-1 + e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)}}} \]

      4. log1p-undefine 83.7%

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

      5. rem-exp-log 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+r+ 100.0%

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

      8. +-commutative 100.0%

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

      9. associate-+r+ 100.0%

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

      10. metadata-eval 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in y around inf 80.5%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+34}:\\ \;\;\;\;-1 + \left(2 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+19}:\\ \;\;\;\;\frac{y - x}{x - 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+33} \lor \neg \left(y \leq 1.3 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.05e+33) (not (<= y 1.3e+39))) (/ (- y x) y) (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.05e+33) || !(y <= 1.3e+39)) {
		tmp = (y - x) / y;
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.05d+33)) .or. (.not. (y <= 1.3d+39))) then
        tmp = (y - x) / y
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.05e+33) || !(y <= 1.3e+39)) {
		tmp = (y - x) / y;
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.05e+33) or not (y <= 1.3e+39):
		tmp = (y - x) / y
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.05e+33) || !(y <= 1.3e+39))
		tmp = Float64(Float64(y - x) / y);
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.05e+33) || ~((y <= 1.3e+39)))
		tmp = (y - x) / y;
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.05e+33], N[Not[LessEqual[y, 1.3e+39]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e33 or 1.3e39 < y

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-frac2 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. sub-neg 99.9%

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

      6. distribute-neg-in 99.9%

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

      7. remove-double-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. neg-sub0 99.9%

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

      11. associate--r- 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

      14. +-commutative 99.9%

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

      15. +-commutative 99.9%

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

      16. associate-+r+ 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. expm1-log1p-u 43.8%

         \[\leadsto \frac{y - x}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x + \left(y + -2\right)\right)\right)}} \]

      2. expm1-undefine 43.8%

         \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(x + \left(y + -2\right)\right)} - 1}} \]

      3. +-commutative 43.8%

         \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(\color{blue}{\left(y + -2\right) + x}\right)} - 1} \]

      4. associate-+l+ 43.8%

         \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(\color{blue}{y + \left(-2 + x\right)}\right)} - 1} \]

   6. Applied egg-rr 43.8%

      \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} - 1}} \]
   7. Step-by-step derivation

      1. sub-neg 43.8%

         \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} + \left(-1\right)}} \]

      2. metadata-eval 43.8%

         \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} + \color{blue}{-1}} \]

      3. +-commutative 43.8%

         \[\leadsto \frac{y - x}{\color{blue}{-1 + e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)}}} \]

      4. log1p-undefine 43.8%

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

      5. rem-exp-log 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+r+ 99.9%

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

      8. +-commutative 99.9%

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

      9. associate-+r+ 99.9%

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

      10. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in y around inf 80.5%

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

   if -1.05e33 < y < 1.3e39

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. distribute-neg-frac2 78.1%

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

      3. neg-sub0 78.1%

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

      4. associate-+l- 78.1%

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

      5. neg-sub0 78.1%

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

      6. +-commutative 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 2 regimes into one program.

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+33} \lor \neg \left(y \leq 1.3 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{y - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+36}:\\ \;\;\;\;-1 + \left(2 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.7e+36)
   (+ -1.0 (- 2.0 (/ x y)))
   (if (<= y 3.6e+37) (/ x (- 2.0 x)) (/ (- y x) y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.7e+36) {
		tmp = -1.0 + (2.0 - (x / y));
	} else if (y <= 3.6e+37) {
		tmp = x / (2.0 - x);
	} else {
		tmp = (y - x) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-4.7d+36)) then
        tmp = (-1.0d0) + (2.0d0 - (x / y))
    else if (y <= 3.6d+37) then
        tmp = x / (2.0d0 - x)
    else
        tmp = (y - x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.7e+36) {
		tmp = -1.0 + (2.0 - (x / y));
	} else if (y <= 3.6e+37) {
		tmp = x / (2.0 - x);
	} else {
		tmp = (y - x) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.7e+36:
		tmp = -1.0 + (2.0 - (x / y))
	elif y <= 3.6e+37:
		tmp = x / (2.0 - x)
	else:
		tmp = (y - x) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.7e+36)
		tmp = Float64(-1.0 + Float64(2.0 - Float64(x / y)));
	elseif (y <= 3.6e+37)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = Float64(Float64(y - x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.7e+36)
		tmp = -1.0 + (2.0 - (x / y));
	elseif (y <= 3.6e+37)
		tmp = x / (2.0 - x);
	else
		tmp = (y - x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.7e+36], N[(-1.0 + N[(2.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+37], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.69999999999999989e36

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-frac2 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. sub-neg 99.9%

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

      6. distribute-neg-in 99.9%

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

      7. remove-double-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. neg-sub0 99.9%

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

      11. associate--r- 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

      14. +-commutative 99.9%

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

      15. +-commutative 99.9%

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

      16. associate-+r+ 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. expm1-log1p-u 7.7%

         \[\leadsto \frac{y - x}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x + \left(y + -2\right)\right)\right)}} \]

      2. expm1-undefine 7.7%

         \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(x + \left(y + -2\right)\right)} - 1}} \]

      3. +-commutative 7.7%

         \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(\color{blue}{\left(y + -2\right) + x}\right)} - 1} \]

      4. associate-+l+ 7.7%

         \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(\color{blue}{y + \left(-2 + x\right)}\right)} - 1} \]

   6. Applied egg-rr 7.7%

      \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} - 1}} \]
   7. Step-by-step derivation

      1. sub-neg 7.7%

         \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} + \left(-1\right)}} \]

      2. metadata-eval 7.7%

         \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} + \color{blue}{-1}} \]

      3. +-commutative 7.7%

         \[\leadsto \frac{y - x}{\color{blue}{-1 + e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)}}} \]

      4. log1p-undefine 7.7%

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

      5. rem-exp-log 99.9%

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

      6. associate-+r+ 99.9%

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

      7. associate-+r+ 99.9%

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

      8. +-commutative 99.9%

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

      9. associate-+r+ 99.9%

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

      10. metadata-eval 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in y around inf 78.4%

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

       1. expm1-log1p-u 77.5%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y - x}{y}\right)\right)} \]

       2. expm1-undefine 77.5%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{y - x}{y}\right)} - 1} \]

       3. div-sub 77.5%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{y}{y} - \frac{x}{y}}\right)} - 1 \]

       4. *-inverses 77.5%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{1} - \frac{x}{y}\right)} - 1 \]

   11. Applied egg-rr 77.5%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(1 - \frac{x}{y}\right)} - 1} \]
   12. Step-by-step derivation

       1. sub-neg 77.5%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(1 - \frac{x}{y}\right)} + \left(-1\right)} \]

       2. log1p-undefine 77.5%

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

       3. rem-exp-log 78.4%

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

       4. associate-+r- 78.4%

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

       5. metadata-eval 78.4%

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

       6. metadata-eval 78.4%

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

   13. Simplified 78.4%

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

   if -4.69999999999999989e36 < y < 3.59999999999999998e37

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. distribute-neg-frac2 78.1%

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

      3. neg-sub0 78.1%

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

      4. associate-+l- 78.1%

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

      5. neg-sub0 78.1%

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

      6. +-commutative 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%

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

   if 3.59999999999999998e37 < y

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. expm1-log1p-u 84.9%

         \[\leadsto \frac{y - x}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(x + \left(y + -2\right)\right)\right)}} \]

      2. expm1-undefine 84.9%

         \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(x + \left(y + -2\right)\right)} - 1}} \]

      3. +-commutative 84.9%

         \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(\color{blue}{\left(y + -2\right) + x}\right)} - 1} \]

      4. associate-+l+ 84.9%

         \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(\color{blue}{y + \left(-2 + x\right)}\right)} - 1} \]

   6. Applied egg-rr 84.9%

      \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} - 1}} \]
   7. Step-by-step derivation

      1. sub-neg 84.9%

         \[\leadsto \frac{y - x}{\color{blue}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} + \left(-1\right)}} \]

      2. metadata-eval 84.9%

         \[\leadsto \frac{y - x}{e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)} + \color{blue}{-1}} \]

      3. +-commutative 84.9%

         \[\leadsto \frac{y - x}{\color{blue}{-1 + e^{\mathsf{log1p}\left(y + \left(-2 + x\right)\right)}}} \]

      4. log1p-undefine 84.9%

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

      5. rem-exp-log 100.0%

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

      6. associate-+r+ 100.0%

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

      7. associate-+r+ 100.0%

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

      8. +-commutative 100.0%

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

      9. associate-+r+ 100.0%

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

      10. metadata-eval 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in y around inf 82.8%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+36}:\\ \;\;\;\;-1 + \left(2 - \frac{x}{y}\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+35}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y - 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.3e+35) 1.0 (if (<= y 4.3e+44) (/ x (- 2.0 x)) (/ y (- y 2.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.3e+35) {
		tmp = 1.0;
	} else if (y <= 4.3e+44) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (y - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-5.3d+35)) then
        tmp = 1.0d0
    else if (y <= 4.3d+44) then
        tmp = x / (2.0d0 - x)
    else
        tmp = y / (y - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5.3e+35) {
		tmp = 1.0;
	} else if (y <= 4.3e+44) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (y - 2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.3e+35:
		tmp = 1.0
	elif y <= 4.3e+44:
		tmp = x / (2.0 - x)
	else:
		tmp = y / (y - 2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.3e+35)
		tmp = 1.0;
	elseif (y <= 4.3e+44)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = Float64(y / Float64(y - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.3e+35)
		tmp = 1.0;
	elseif (y <= 4.3e+44)
		tmp = x / (2.0 - x);
	else
		tmp = y / (y - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.3e+35], 1.0, If[LessEqual[y, 4.3e+44], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(y / N[(y - 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.30000000000000009e35

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-frac2 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. sub-neg 99.9%

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

      6. distribute-neg-in 99.9%

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

      7. remove-double-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. neg-sub0 99.9%

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

      11. associate--r- 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

      14. +-commutative 99.9%

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

      15. +-commutative 99.9%

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

      16. associate-+r+ 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 77.7%

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

   if -5.30000000000000009e35 < y < 4.29999999999999982e44

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. distribute-neg-frac2 78.1%

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

      3. neg-sub0 78.1%

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

      4. associate-+l- 78.1%

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

      5. neg-sub0 78.1%

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

      6. +-commutative 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%

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

   if 4.29999999999999982e44 < y

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 82.0%

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

Alternative 8: 74.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+33}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+42}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -9e+33) 1.0 (if (<= y 4.9e+42) (/ x (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -9e+33) {
		tmp = 1.0;
	} else if (y <= 4.9e+42) {
		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 <= (-9d+33)) then
        tmp = 1.0d0
    else if (y <= 4.9d+42) 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 <= -9e+33) {
		tmp = 1.0;
	} else if (y <= 4.9e+42) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -9e+33:
		tmp = 1.0
	elif y <= 4.9e+42:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -9e+33)
		tmp = 1.0;
	elseif (y <= 4.9e+42)
		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 <= -9e+33)
		tmp = 1.0;
	elseif (y <= 4.9e+42)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -9e+33], 1.0, If[LessEqual[y, 4.9e+42], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -9.0000000000000001e33 or 4.9000000000000002e42 < y

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-frac2 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. sub-neg 99.9%

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

      6. distribute-neg-in 99.9%

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

      7. remove-double-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. neg-sub0 99.9%

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

      11. associate--r- 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

      14. +-commutative 99.9%

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

      15. +-commutative 99.9%

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

      16. associate-+r+ 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 79.7%

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

   if -9.0000000000000001e33 < y < 4.9000000000000002e42

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. distribute-neg-frac2 78.1%

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

      3. neg-sub0 78.1%

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

      4. associate-+l- 78.1%

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

      5. neg-sub0 78.1%

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

      6. +-commutative 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 2 regimes into one program.
4. Add Preprocessing

Alternative 9: 63.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+22}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+14}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.3e+22) 1.0 (if (<= y 4e+14) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.3e+22) {
		tmp = 1.0;
	} else if (y <= 4e+14) {
		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 <= (-3.3d+22)) then
        tmp = 1.0d0
    else if (y <= 4d+14) 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 <= -3.3e+22) {
		tmp = 1.0;
	} else if (y <= 4e+14) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.3e+22:
		tmp = 1.0
	elif y <= 4e+14:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.3e+22)
		tmp = 1.0;
	elseif (y <= 4e+14)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.3e+22)
		tmp = 1.0;
	elseif (y <= 4e+14)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.3e+22], 1.0, If[LessEqual[y, 4e+14], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.2999999999999998e22 or 4e14 < y

   1. Initial program 99.9%

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

      1. remove-double-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. distribute-neg-frac2 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. sub-neg 99.9%

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

      6. distribute-neg-in 99.9%

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

      7. remove-double-neg 99.9%

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

      8. +-commutative 99.9%

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

      9. sub-neg 99.9%

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

      10. neg-sub0 99.9%

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

      11. associate--r- 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

      14. +-commutative 99.9%

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

      15. +-commutative 99.9%

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

      16. associate-+r+ 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 78.2%

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

   if -3.2999999999999998e22 < y < 4e14

   1. Initial program 100.0%

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

      1. remove-double-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. distribute-neg-frac2 100.0%

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

      4. distribute-frac-neg 100.0%

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

      5. sub-neg 100.0%

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

      6. distribute-neg-in 100.0%

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

      7. remove-double-neg 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. neg-sub0 100.0%

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

      11. associate--r- 100.0%

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

      12. metadata-eval 100.0%

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

      13. metadata-eval 100.0%

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

      14. +-commutative 100.0%

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

      15. +-commutative 100.0%

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

      16. associate-+r+ 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 55.6%

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

Alternative 10: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 11: 38.7% 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. remove-double-neg 100.0%

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

   2. +-commutative 100.0%

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

   3. distribute-neg-frac2 100.0%

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

   4. distribute-frac-neg 100.0%

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

   5. sub-neg 100.0%

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

   6. distribute-neg-in 100.0%

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

   7. remove-double-neg 100.0%

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

   8. +-commutative 100.0%

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

   9. sub-neg 100.0%

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

   10. neg-sub0 100.0%

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

   11. associate--r- 100.0%

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

   12. metadata-eval 100.0%

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

   13. metadata-eval 100.0%

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

   14. +-commutative 100.0%

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

   15. +-commutative 100.0%

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

   16. associate-+r+ 100.0%

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

   17. metadata-eval 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in x around inf 40.3%

   \[\leadsto \color{blue}{-1} \]
6. Add Preprocessing

Developer Target 1: 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 2024157 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ x (- 2 (+ x y))) (/ y (- 2 (+ x y)))))

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