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

Percentage Accurate: 100.0% → 100.0%

Time: 5.7s

Alternatives: 10

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: 98.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -10200 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;\frac{x - y}{\left(-x\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -10200.0) (not (<= x 2.0)))
   (/ (- x y) (- (- x) y))
   (/ (- x y) (- 2.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -10200.0) || !(x <= 2.0)) {
		tmp = (x - y) / (-x - y);
	} else {
		tmp = (x - y) / (2.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-10200.0d0)) .or. (.not. (x <= 2.0d0))) then
        tmp = (x - y) / (-x - y)
    else
        tmp = (x - y) / (2.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -10200.0) || !(x <= 2.0)) {
		tmp = (x - y) / (-x - y);
	} else {
		tmp = (x - y) / (2.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -10200.0) or not (x <= 2.0):
		tmp = (x - y) / (-x - y)
	else:
		tmp = (x - y) / (2.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -10200.0) || !(x <= 2.0))
		tmp = Float64(Float64(x - y) / Float64(Float64(-x) - y));
	else
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -10200.0) || ~((x <= 2.0)))
		tmp = (x - y) / (-x - y);
	else
		tmp = (x - y) / (2.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -10200.0], N[Not[LessEqual[x, 2.0]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] / N[((-x) - y), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -10200 or 2 < x

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

      1. flip-- 46.7%

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

      2. div-inv 46.5%

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

      3. fma-neg 46.5%

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

      4. metadata-eval 46.5%

         \[\leadsto \frac{x - y}{\mathsf{fma}\left(\color{blue}{4} - x \cdot x, \frac{1}{2 + x}, -y\right)} \]

      5. +-commutative 46.5%

         \[\leadsto \frac{x - y}{\mathsf{fma}\left(4 - x \cdot x, \frac{1}{\color{blue}{x + 2}}, -y\right)} \]

   5. Applied egg-rr 46.5%

      \[\leadsto \frac{x - y}{\color{blue}{\mathsf{fma}\left(4 - x \cdot x, \frac{1}{x + 2}, -y\right)}} \]
   6. Step-by-step derivation

      1. fma-neg 46.5%

         \[\leadsto \frac{x - y}{\color{blue}{\left(4 - x \cdot x\right) \cdot \frac{1}{x + 2} - y}} \]

      2. associate-*r/ 46.7%

         \[\leadsto \frac{x - y}{\color{blue}{\frac{\left(4 - x \cdot x\right) \cdot 1}{x + 2}} - y} \]

      3. *-rgt-identity 46.7%

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

      4. +-commutative 46.7%

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

   7. Simplified 46.7%

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

   8. Taylor expanded in x around inf 98.9%

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

      1. neg-mul-1 98.9%

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

   10. Simplified 98.9%

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

   if -10200 < x < 2

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 98.7%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -10200 \lor \neg \left(x \leq 2\right):\\ \;\;\;\;\frac{x - y}{\left(-x\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \end{array} \]

Alternative 3: 74.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+67} \lor \neg \left(x \leq 1.16 \cdot 10^{+58}\right):\\ \;\;\;\;2 \cdot \frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5.4e+67) (not (<= x 1.16e+58)))
   (+ (* 2.0 (/ y x)) -1.0)
   (/ y (+ y -2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5.4e+67) || !(x <= 1.16e+58)) {
		tmp = (2.0 * (y / x)) + -1.0;
	} 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 ((x <= (-5.4d+67)) .or. (.not. (x <= 1.16d+58))) then
        tmp = (2.0d0 * (y / x)) + (-1.0d0)
    else
        tmp = y / (y + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -5.4e+67) || !(x <= 1.16e+58)) {
		tmp = (2.0 * (y / x)) + -1.0;
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5.4e+67) or not (x <= 1.16e+58):
		tmp = (2.0 * (y / x)) + -1.0
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5.4e+67) || !(x <= 1.16e+58))
		tmp = Float64(Float64(2.0 * Float64(y / x)) + -1.0);
	else
		tmp = Float64(y / Float64(y + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -5.4e+67) || ~((x <= 1.16e+58)))
		tmp = (2.0 * (y / x)) + -1.0;
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5.4e+67], N[Not[LessEqual[x, 1.16e+58]], $MachinePrecision]], N[(N[(2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.3999999999999998e67 or 1.1600000000000001e58 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

      1. flip-- 36.3%

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

      2. div-inv 36.2%

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

      3. fma-neg 36.2%

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

      4. metadata-eval 36.2%

         \[\leadsto \frac{x - y}{\mathsf{fma}\left(\color{blue}{4} - x \cdot x, \frac{1}{2 + x}, -y\right)} \]

      5. +-commutative 36.2%

         \[\leadsto \frac{x - y}{\mathsf{fma}\left(4 - x \cdot x, \frac{1}{\color{blue}{x + 2}}, -y\right)} \]

   5. Applied egg-rr 36.2%

      \[\leadsto \frac{x - y}{\color{blue}{\mathsf{fma}\left(4 - x \cdot x, \frac{1}{x + 2}, -y\right)}} \]
   6. Step-by-step derivation

      1. fma-neg 36.2%

         \[\leadsto \frac{x - y}{\color{blue}{\left(4 - x \cdot x\right) \cdot \frac{1}{x + 2} - y}} \]

      2. associate-*r/ 36.3%

         \[\leadsto \frac{x - y}{\color{blue}{\frac{\left(4 - x \cdot x\right) \cdot 1}{x + 2}} - y} \]

      3. *-rgt-identity 36.3%

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

      4. +-commutative 36.3%

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

   7. Simplified 36.3%

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

   8. Taylor expanded in x around inf 99.9%

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

      1. neg-mul-1 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in y around 0 84.9%

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

   if -5.3999999999999998e67 < x < 1.1600000000000001e58

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 79.4%

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

      1. associate-*r/ 79.4%

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

      2. neg-mul-1 79.4%

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

   6. Simplified 79.4%

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

      1. frac-2neg 79.4%

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

      2. div-inv 79.2%

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

      3. remove-double-neg 79.2%

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

      4. sub-neg 79.2%

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

      5. distribute-neg-in 79.2%

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

      6. metadata-eval 79.2%

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

      7. remove-double-neg 79.2%

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

   8. Applied egg-rr 79.2%

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

      1. associate-*r/ 79.4%

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

      2. *-rgt-identity 79.4%

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

   10. Simplified 79.4%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+67} \lor \neg \left(x \leq 1.16 \cdot 10^{+58}\right):\\ \;\;\;\;2 \cdot \frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]

Alternative 4: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+68} \lor \neg \left(x \leq 2.35 \cdot 10^{+59}\right):\\ \;\;\;\;2 \cdot \frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5.8e+68) (not (<= x 2.35e+59)))
   (+ (* 2.0 (/ y x)) -1.0)
   (/ (- x y) (- 2.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5.8e+68) || !(x <= 2.35e+59)) {
		tmp = (2.0 * (y / x)) + -1.0;
	} else {
		tmp = (x - y) / (2.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-5.8d+68)) .or. (.not. (x <= 2.35d+59))) then
        tmp = (2.0d0 * (y / x)) + (-1.0d0)
    else
        tmp = (x - y) / (2.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -5.8e+68) || !(x <= 2.35e+59)) {
		tmp = (2.0 * (y / x)) + -1.0;
	} else {
		tmp = (x - y) / (2.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5.8e+68) or not (x <= 2.35e+59):
		tmp = (2.0 * (y / x)) + -1.0
	else:
		tmp = (x - y) / (2.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5.8e+68) || !(x <= 2.35e+59))
		tmp = Float64(Float64(2.0 * Float64(y / x)) + -1.0);
	else
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -5.8e+68) || ~((x <= 2.35e+59)))
		tmp = (2.0 * (y / x)) + -1.0;
	else
		tmp = (x - y) / (2.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5.8e+68], N[Not[LessEqual[x, 2.35e+59]], $MachinePrecision]], N[(N[(2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.80000000000000023e68 or 2.35e59 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

      1. flip-- 36.3%

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

      2. div-inv 36.2%

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

      3. fma-neg 36.2%

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

      4. metadata-eval 36.2%

         \[\leadsto \frac{x - y}{\mathsf{fma}\left(\color{blue}{4} - x \cdot x, \frac{1}{2 + x}, -y\right)} \]

      5. +-commutative 36.2%

         \[\leadsto \frac{x - y}{\mathsf{fma}\left(4 - x \cdot x, \frac{1}{\color{blue}{x + 2}}, -y\right)} \]

   5. Applied egg-rr 36.2%

      \[\leadsto \frac{x - y}{\color{blue}{\mathsf{fma}\left(4 - x \cdot x, \frac{1}{x + 2}, -y\right)}} \]
   6. Step-by-step derivation

      1. fma-neg 36.2%

         \[\leadsto \frac{x - y}{\color{blue}{\left(4 - x \cdot x\right) \cdot \frac{1}{x + 2} - y}} \]

      2. associate-*r/ 36.3%

         \[\leadsto \frac{x - y}{\color{blue}{\frac{\left(4 - x \cdot x\right) \cdot 1}{x + 2}} - y} \]

      3. *-rgt-identity 36.3%

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

      4. +-commutative 36.3%

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

   7. Simplified 36.3%

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

   8. Taylor expanded in x around inf 99.9%

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

      1. neg-mul-1 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in y around 0 84.9%

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

   if -5.80000000000000023e68 < x < 2.35e59

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 93.4%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+68} \lor \neg \left(x \leq 2.35 \cdot 10^{+59}\right):\\ \;\;\;\;2 \cdot \frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \end{array} \]

Alternative 5: 74.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+68}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 10^{+58}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{-x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.7e+68)
   (+ (/ y x) -1.0)
   (if (<= x 1e+58) (/ y (+ y -2.0)) (/ (- x y) (- x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.7e+68) {
		tmp = (y / x) + -1.0;
	} else if (x <= 1e+58) {
		tmp = y / (y + -2.0);
	} else {
		tmp = (x - y) / -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.7d+68)) then
        tmp = (y / x) + (-1.0d0)
    else if (x <= 1d+58) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = (x - y) / -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.7e+68) {
		tmp = (y / x) + -1.0;
	} else if (x <= 1e+58) {
		tmp = y / (y + -2.0);
	} else {
		tmp = (x - y) / -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.7e+68:
		tmp = (y / x) + -1.0
	elif x <= 1e+58:
		tmp = y / (y + -2.0)
	else:
		tmp = (x - y) / -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.7e+68)
		tmp = Float64(Float64(y / x) + -1.0);
	elseif (x <= 1e+58)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = Float64(Float64(x - y) / Float64(-x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.7e+68)
		tmp = (y / x) + -1.0;
	elseif (x <= 1e+58)
		tmp = y / (y + -2.0);
	else
		tmp = (x - y) / -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.7e+68], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[x, 1e+58], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / (-x)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.69999999999999998e68

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 85.6%

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

      1. neg-mul-1 85.6%

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

   6. Simplified 85.6%

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

   7. Taylor expanded in x around 0 85.6%

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

   if -3.69999999999999998e68 < x < 9.99999999999999944e57

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 79.4%

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

      1. associate-*r/ 79.4%

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

      2. neg-mul-1 79.4%

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

   6. Simplified 79.4%

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

      1. frac-2neg 79.4%

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

      2. div-inv 79.2%

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

      3. remove-double-neg 79.2%

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

      4. sub-neg 79.2%

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

      5. distribute-neg-in 79.2%

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

      6. metadata-eval 79.2%

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

      7. remove-double-neg 79.2%

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

   8. Applied egg-rr 79.2%

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

      1. associate-*r/ 79.4%

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

      2. *-rgt-identity 79.4%

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

   10. Simplified 79.4%

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

   if 9.99999999999999944e57 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 82.4%

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

      1. neg-mul-1 82.4%

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

   6. Simplified 82.4%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+68}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 10^{+58}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{-x}\\ \end{array} \]

Alternative 6: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+67} \lor \neg \left(x \leq 2.75 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5.2e+67) (not (<= x 2.75e+60))) (+ (/ y x) -1.0) 1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5.2e+67) || !(x <= 2.75e+60)) {
		tmp = (y / x) + -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-5.2d+67)) .or. (.not. (x <= 2.75d+60))) then
        tmp = (y / x) + (-1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -5.2e+67) || !(x <= 2.75e+60)) {
		tmp = (y / x) + -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5.2e+67) or not (x <= 2.75e+60):
		tmp = (y / x) + -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5.2e+67) || !(x <= 2.75e+60))
		tmp = Float64(Float64(y / x) + -1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -5.2e+67) || ~((x <= 2.75e+60)))
		tmp = (y / x) + -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5.2e+67], N[Not[LessEqual[x, 2.75e+60]], $MachinePrecision]], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -5.2000000000000001e67 or 2.75e60 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 84.0%

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

      1. neg-mul-1 84.0%

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

   6. Simplified 84.0%

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

   7. Taylor expanded in x around 0 84.0%

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

   if -5.2000000000000001e67 < x < 2.75e60

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 57.4%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.2 \cdot 10^{+67} \lor \neg \left(x \leq 2.75 \cdot 10^{+60}\right):\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 75.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+37} \lor \neg \left(y \leq 6200000000000\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -8.2e+37) (not (<= y 6200000000000.0)))
   (- 1.0 (/ x y))
   (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -8.2e+37) || !(y <= 6200000000000.0)) {
		tmp = 1.0 - (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 <= (-8.2d+37)) .or. (.not. (y <= 6200000000000.0d0))) then
        tmp = 1.0d0 - (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 <= -8.2e+37) || !(y <= 6200000000000.0)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -8.2e+37) or not (y <= 6200000000000.0):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -8.2e+37) || !(y <= 6200000000000.0))
		tmp = Float64(1.0 - Float64(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 <= -8.2e+37) || ~((y <= 6200000000000.0)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -8.2e+37], N[Not[LessEqual[y, 6200000000000.0]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.1999999999999996e37 or 6.2e12 < y

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 76.3%

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

      1. neg-mul-1 76.3%

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

   6. Simplified 76.3%

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

   7. Taylor expanded in x around 0 76.3%

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

      1. neg-mul-1 76.3%

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

      2. unsub-neg 76.3%

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

   9. Simplified 76.3%

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

   if -8.1999999999999996e37 < y < 6.2e12

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 72.7%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+37} \lor \neg \left(y \leq 6200000000000\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 8: 74.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+68} \lor \neg \left(x \leq 1.4 \cdot 10^{+58}\right):\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.6e+68) (not (<= x 1.4e+58)))
   (+ (/ y x) -1.0)
   (/ y (+ y -2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.6e+68) || !(x <= 1.4e+58)) {
		tmp = (y / x) + -1.0;
	} 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 ((x <= (-1.6d+68)) .or. (.not. (x <= 1.4d+58))) then
        tmp = (y / x) + (-1.0d0)
    else
        tmp = y / (y + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.6e+68) || !(x <= 1.4e+58)) {
		tmp = (y / x) + -1.0;
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.6e+68) or not (x <= 1.4e+58):
		tmp = (y / x) + -1.0
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.6e+68) || !(x <= 1.4e+58))
		tmp = Float64(Float64(y / x) + -1.0);
	else
		tmp = Float64(y / Float64(y + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.6e+68) || ~((x <= 1.4e+58)))
		tmp = (y / x) + -1.0;
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.6e+68], N[Not[LessEqual[x, 1.4e+58]], $MachinePrecision]], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.59999999999999997e68 or 1.3999999999999999e58 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 84.0%

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

      1. neg-mul-1 84.0%

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

   6. Simplified 84.0%

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

   7. Taylor expanded in x around 0 84.0%

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

   if -1.59999999999999997e68 < x < 1.3999999999999999e58

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 79.4%

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

      1. associate-*r/ 79.4%

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

      2. neg-mul-1 79.4%

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

   6. Simplified 79.4%

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

      1. frac-2neg 79.4%

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

      2. div-inv 79.2%

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

      3. remove-double-neg 79.2%

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

      4. sub-neg 79.2%

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

      5. distribute-neg-in 79.2%

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

      6. metadata-eval 79.2%

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

      7. remove-double-neg 79.2%

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

   8. Applied egg-rr 79.2%

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

      1. associate-*r/ 79.4%

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

      2. *-rgt-identity 79.4%

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

   10. Simplified 79.4%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+68} \lor \neg \left(x \leq 1.4 \cdot 10^{+58}\right):\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]

Alternative 9: 62.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+61}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+58}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.2e+61) -1.0 (if (<= x 5e+58) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.2e+61) {
		tmp = -1.0;
	} else if (x <= 5e+58) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-9.2d+61)) then
        tmp = -1.0d0
    else if (x <= 5d+58) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -9.2e+61) {
		tmp = -1.0;
	} else if (x <= 5e+58) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.2e+61:
		tmp = -1.0
	elif x <= 5e+58:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.2e+61)
		tmp = -1.0;
	elseif (x <= 5e+58)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9.2e+61)
		tmp = -1.0;
	elseif (x <= 5e+58)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.2e+61], -1.0, If[LessEqual[x, 5e+58], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -9.1999999999999998e61 or 4.99999999999999986e58 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 82.8%

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

   if -9.1999999999999998e61 < x < 4.99999999999999986e58

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 57.5%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+61}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+58}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 10: 38.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

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

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 100.0%

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

   1. associate--r+ 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in x around inf 39.2%

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

5. Final simplification 39.2%

   \[\leadsto -1 \]

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 2023293 
(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))))