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

Percentage Accurate: 100.0% → 100.0%

Time: 6.9s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+19} \lor \neg \left(y \leq 3.05 \cdot 10^{+50}\right):\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.5e+19) (not (<= y 3.05e+50)))
   (+ 1.0 (/ (* x -2.0) y))
   (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.5e+19) || !(y <= 3.05e+50)) {
		tmp = 1.0 + ((x * -2.0) / 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 <= (-4.5d+19)) .or. (.not. (y <= 3.05d+50))) then
        tmp = 1.0d0 + ((x * (-2.0d0)) / 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 <= -4.5e+19) || !(y <= 3.05e+50)) {
		tmp = 1.0 + ((x * -2.0) / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.5e+19) or not (y <= 3.05e+50):
		tmp = 1.0 + ((x * -2.0) / y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.5e+19) || !(y <= 3.05e+50))
		tmp = Float64(1.0 + Float64(Float64(x * -2.0) / 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 <= -4.5e+19) || ~((y <= 3.05e+50)))
		tmp = 1.0 + ((x * -2.0) / y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.5e+19], N[Not[LessEqual[y, 3.05e+50]], $MachinePrecision]], N[(1.0 + N[(N[(x * -2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5e19 or 3.05000000000000013e50 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in y around inf 81.8%

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

      1. associate--l+ 81.8%

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

      2. +-commutative 81.8%

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

      3. mul-1-neg 81.8%

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

      4. unsub-neg 81.8%

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

      5. associate-*r/ 81.8%

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

      6. metadata-eval 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in x around inf 81.8%

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

      1. associate-*r/ 81.8%

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

      2. *-commutative 81.8%

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

   9. Simplified 81.8%

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

   if -4.5e19 < y < 3.05000000000000013e50

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Step-by-step derivation

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. sub-neg 76.6%

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

      3. metadata-eval 76.6%

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

   8. Simplified 76.6%

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

      1. unpow-1 76.6%

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

      2. distribute-neg-frac 76.6%

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

      3. associate-/r/ 76.5%

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

      4. +-commutative 76.5%

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

      5. distribute-neg-in 76.5%

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

      6. metadata-eval 76.5%

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

   10. Applied egg-rr 76.5%

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

       1. associate-*l/ 76.7%

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

       2. *-lft-identity 76.7%

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

       3. unsub-neg 76.7%

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

   12. Simplified 76.7%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+19} \lor \neg \left(y \leq 3.05 \cdot 10^{+50}\right):\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 3: 61.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+52}:\\ \;\;\;\;-1 + \frac{-2}{x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.75e+19) 1.0 (if (<= y 8.2e+52) (+ -1.0 (/ -2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.75e+19) {
		tmp = 1.0;
	} else if (y <= 8.2e+52) {
		tmp = -1.0 + (-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 <= (-2.75d+19)) then
        tmp = 1.0d0
    else if (y <= 8.2d+52) then
        tmp = (-1.0d0) + ((-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 <= -2.75e+19) {
		tmp = 1.0;
	} else if (y <= 8.2e+52) {
		tmp = -1.0 + (-2.0 / x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.75e+19:
		tmp = 1.0
	elif y <= 8.2e+52:
		tmp = -1.0 + (-2.0 / x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.75e+19)
		tmp = 1.0;
	elseif (y <= 8.2e+52)
		tmp = Float64(-1.0 + Float64(-2.0 / x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.75e+19)
		tmp = 1.0;
	elseif (y <= 8.2e+52)
		tmp = -1.0 + (-2.0 / x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.75e+19], 1.0, If[LessEqual[y, 8.2e+52], N[(-1.0 + N[(-2.0 / x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.75e19 or 8.1999999999999999e52 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in y around inf 79.8%

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

   if -2.75e19 < y < 8.1999999999999999e52

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in y around 0 76.7%

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

      1. associate-*r/ 76.7%

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

      2. mul-1-neg 76.7%

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

      3. sub-neg 76.7%

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

      4. metadata-eval 76.7%

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

   6. Simplified 76.7%

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

   7. Taylor expanded in x around inf 57.4%

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

      1. distribute-neg-in 57.4%

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

      2. metadata-eval 57.4%

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

      3. associate-*r/ 57.4%

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

      4. metadata-eval 57.4%

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

      5. distribute-neg-frac 57.4%

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

      6. metadata-eval 57.4%

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

   9. Simplified 57.4%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+52}:\\ \;\;\;\;-1 + \frac{-2}{x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.5e+19) 1.0 (if (<= y 2e+52) (/ x (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.5e+19) {
		tmp = 1.0;
	} else if (y <= 2e+52) {
		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 <= (-2.5d+19)) then
        tmp = 1.0d0
    else if (y <= 2d+52) 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 <= -2.5e+19) {
		tmp = 1.0;
	} else if (y <= 2e+52) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.5e+19:
		tmp = 1.0
	elif y <= 2e+52:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.5e+19)
		tmp = 1.0;
	elseif (y <= 2e+52)
		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 <= -2.5e+19)
		tmp = 1.0;
	elseif (y <= 2e+52)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.5e+19], 1.0, If[LessEqual[y, 2e+52], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.5e19 or 2e52 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in y around inf 79.8%

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

   if -2.5e19 < y < 2e52

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Step-by-step derivation

      1. clear-num 99.9%

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

      2. inv-pow 99.9%

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

      3. +-commutative 99.9%

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

      4. associate-+l+ 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around 0 76.6%

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

      1. mul-1-neg 76.6%

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

      2. sub-neg 76.6%

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

      3. metadata-eval 76.6%

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

   8. Simplified 76.6%

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

      1. unpow-1 76.6%

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

      2. distribute-neg-frac 76.6%

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

      3. associate-/r/ 76.5%

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

      4. +-commutative 76.5%

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

      5. distribute-neg-in 76.5%

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

      6. metadata-eval 76.5%

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

   10. Applied egg-rr 76.5%

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

       1. associate-*l/ 76.7%

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

       2. *-lft-identity 76.7%

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

       3. unsub-neg 76.7%

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

   12. Simplified 76.7%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 62.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+50}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2e+19) 1.0 (if (<= y 4e+50) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2e+19) {
		tmp = 1.0;
	} else if (y <= 4e+50) {
		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 <= (-2d+19)) then
        tmp = 1.0d0
    else if (y <= 4d+50) 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 <= -2e+19) {
		tmp = 1.0;
	} else if (y <= 4e+50) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2e+19:
		tmp = 1.0
	elif y <= 4e+50:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2e+19)
		tmp = 1.0;
	elseif (y <= 4e+50)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2e+19)
		tmp = 1.0;
	elseif (y <= 4e+50)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2e+19], 1.0, If[LessEqual[y, 4e+50], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2e19 or 4.0000000000000003e50 < y

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in y around inf 79.8%

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

   if -2e19 < y < 4.0000000000000003e50

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. neg-mul-1 100.0%

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

      6. *-commutative 100.0%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. sub-neg 100.0%

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

      10. div-sub 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. sub-neg 100.0%

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

      14. distribute-frac-neg 100.0%

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

      15. neg-mul-1 100.0%

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

      16. *-commutative 100.0%

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

      17. associate-/l* 100.0%

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

      18. metadata-eval 100.0%

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

      19. /-rgt-identity 100.0%

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

      20. +-commutative 100.0%

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

      21. +-commutative 100.0%

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

      22. associate-+r+ 100.0%

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

      23. 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. Taylor expanded in x around inf 57.2%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+19}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+50}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 38.5% 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. +-commutative 100.0%

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

   2. remove-double-neg 100.0%

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

   3. unsub-neg 100.0%

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

   4. distribute-neg-in 100.0%

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

   5. neg-mul-1 100.0%

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

   6. *-commutative 100.0%

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

   7. associate-/l* 100.0%

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

   8. +-commutative 100.0%

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

   9. sub-neg 100.0%

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

   10. div-sub 100.0%

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

   11. metadata-eval 100.0%

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

   12. metadata-eval 100.0%

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

   13. sub-neg 100.0%

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

   14. distribute-frac-neg 100.0%

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

   15. neg-mul-1 100.0%

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

   16. *-commutative 100.0%

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

   17. associate-/l* 100.0%

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

   18. metadata-eval 100.0%

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

   19. /-rgt-identity 100.0%

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

   20. +-commutative 100.0%

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

   21. +-commutative 100.0%

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

   22. associate-+r+ 100.0%

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

   23. 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. Taylor expanded in x around inf 40.4%

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

5. Final simplification 40.4%

   \[\leadsto -1 \]

Developer target: 100.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023302 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

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

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