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

Percentage Accurate: 100.0% → 100.0%

Time: 9.1s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+63}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.5e-100)
   (/ x (- 2.0 x))
   (if (<= x 7e+63) (/ y (+ y -2.0)) (* (- x y) (/ -1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.5e-100) {
		tmp = x / (2.0 - x);
	} else if (x <= 7e+63) {
		tmp = y / (y + -2.0);
	} else {
		tmp = (x - y) * (-1.0 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-6.5d-100)) then
        tmp = x / (2.0d0 - x)
    else if (x <= 7d+63) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = (x - y) * ((-1.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.5e-100) {
		tmp = x / (2.0 - x);
	} else if (x <= 7e+63) {
		tmp = y / (y + -2.0);
	} else {
		tmp = (x - y) * (-1.0 / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.5e-100:
		tmp = x / (2.0 - x)
	elif x <= 7e+63:
		tmp = y / (y + -2.0)
	else:
		tmp = (x - y) * (-1.0 / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.5e-100)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (x <= 7e+63)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = Float64(Float64(x - y) * Float64(-1.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.5e-100)
		tmp = x / (2.0 - x);
	elseif (x <= 7e+63)
		tmp = y / (y + -2.0);
	else
		tmp = (x - y) * (-1.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.5e-100], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e+63], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] * N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.50000000000000013e-100

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 75.5%

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

   if -6.50000000000000013e-100 < x < 7.00000000000000059e63

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. distribute-neg-frac 77.5%

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

   4. Simplified 77.5%

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

      1. frac-2neg 77.5%

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

      2. div-inv 77.4%

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

      3. remove-double-neg 77.4%

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

      4. sub-neg 77.4%

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

      5. distribute-neg-in 77.4%

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

      6. metadata-eval 77.4%

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

      7. remove-double-neg 77.4%

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

   6. Applied egg-rr 77.4%

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

      1. associate-*r/ 77.5%

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

      2. *-rgt-identity 77.5%

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

      3. +-commutative 77.5%

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

   8. Simplified 77.5%

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

   if 7.00000000000000059e63 < x

   1. Initial program 100.0%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around inf 78.8%

      \[\leadsto \color{blue}{\frac{-1}{x}} \cdot \left(x - y\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+63}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{-1}{x}\\ \end{array} \]

Alternative 3: 73.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -240:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - 2 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -240.0)
   (/ y (+ y -2.0))
   (if (<= y 1.8e+59) (/ x (- 2.0 x)) (- 1.0 (* 2.0 (/ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -240.0) {
		tmp = y / (y + -2.0);
	} else if (y <= 1.8e+59) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0 - (2.0 * (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 <= (-240.0d0)) then
        tmp = y / (y + (-2.0d0))
    else if (y <= 1.8d+59) then
        tmp = x / (2.0d0 - x)
    else
        tmp = 1.0d0 - (2.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -240.0) {
		tmp = y / (y + -2.0);
	} else if (y <= 1.8e+59) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0 - (2.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -240.0:
		tmp = y / (y + -2.0)
	elif y <= 1.8e+59:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0 - (2.0 * (x / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -240.0)
		tmp = Float64(y / Float64(y + -2.0));
	elseif (y <= 1.8e+59)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = Float64(1.0 - Float64(2.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -240.0)
		tmp = y / (y + -2.0);
	elseif (y <= 1.8e+59)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0 - (2.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -240.0], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+59], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -240

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.6%

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

      1. mul-1-neg 72.6%

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

      2. distribute-neg-frac 72.6%

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

   4. Simplified 72.6%

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

      1. frac-2neg 72.6%

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

      2. div-inv 72.3%

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

      3. remove-double-neg 72.3%

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

      4. sub-neg 72.3%

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

      5. distribute-neg-in 72.3%

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

      6. metadata-eval 72.3%

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

      7. remove-double-neg 72.3%

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

   6. Applied egg-rr 72.3%

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

      1. associate-*r/ 72.6%

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

      2. *-rgt-identity 72.6%

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

      3. +-commutative 72.6%

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

   8. Simplified 72.6%

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

   if -240 < y < 1.7999999999999999e59

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.7%

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

   if 1.7999999999999999e59 < y

   1. Initial program 99.9%

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

      1. flip-- 30.1%

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

      2. associate-/r/ 30.0%

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

      3. metadata-eval 30.0%

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

      4. pow2 30.0%

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

   3. Applied egg-rr 30.0%

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

      1. associate-*l/ 27.8%

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

      2. associate-+r+ 27.8%

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

      3. +-commutative 27.8%

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

   5. Simplified 27.8%

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

   6. Taylor expanded in y around -inf 78.7%

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

      1. mul-1-neg 78.7%

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

      2. unsub-neg 78.7%

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

      3. cancel-sign-sub-inv 78.7%

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

      4. distribute-rgt1-in 78.7%

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

      5. metadata-eval 78.7%

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

      6. mul0-lft 78.7%

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

      7. metadata-eval 78.7%

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

      8. metadata-eval 78.7%

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

      9. metadata-eval 78.7%

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

   8. Simplified 78.7%

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

   9. Taylor expanded in x around inf 78.7%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -240:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - 2 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 4: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -26000:\\ \;\;\;\;1 - \frac{-2 + x \cdot 2}{y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - 2 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -26000.0)
   (- 1.0 (/ (+ -2.0 (* x 2.0)) y))
   (if (<= y 2.3e+56) (/ x (- 2.0 x)) (- 1.0 (* 2.0 (/ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -26000.0) {
		tmp = 1.0 - ((-2.0 + (x * 2.0)) / y);
	} else if (y <= 2.3e+56) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0 - (2.0 * (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 <= (-26000.0d0)) then
        tmp = 1.0d0 - (((-2.0d0) + (x * 2.0d0)) / y)
    else if (y <= 2.3d+56) then
        tmp = x / (2.0d0 - x)
    else
        tmp = 1.0d0 - (2.0d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -26000.0) {
		tmp = 1.0 - ((-2.0 + (x * 2.0)) / y);
	} else if (y <= 2.3e+56) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0 - (2.0 * (x / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -26000.0:
		tmp = 1.0 - ((-2.0 + (x * 2.0)) / y)
	elif y <= 2.3e+56:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0 - (2.0 * (x / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -26000.0)
		tmp = Float64(1.0 - Float64(Float64(-2.0 + Float64(x * 2.0)) / y));
	elseif (y <= 2.3e+56)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = Float64(1.0 - Float64(2.0 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -26000.0)
		tmp = 1.0 - ((-2.0 + (x * 2.0)) / y);
	elseif (y <= 2.3e+56)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0 - (2.0 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -26000.0], N[(1.0 - N[(N[(-2.0 + N[(x * 2.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+56], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -26000

   1. Initial program 100.0%

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

      1. flip-- 50.7%

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

      2. associate-/r/ 50.5%

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

      3. metadata-eval 50.5%

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

      4. pow2 50.5%

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

   3. Applied egg-rr 50.5%

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

      1. associate-*l/ 49.2%

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

      2. associate-+r+ 49.2%

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

      3. +-commutative 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in y around -inf 73.5%

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

      1. mul-1-neg 73.5%

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

      2. unsub-neg 73.5%

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

      3. cancel-sign-sub-inv 73.5%

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

      4. distribute-rgt1-in 73.5%

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

      5. metadata-eval 73.5%

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

      6. mul0-lft 73.5%

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

      7. metadata-eval 73.5%

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

      8. metadata-eval 73.5%

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

      9. metadata-eval 73.5%

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

   8. Simplified 73.5%

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

   if -26000 < y < 2.30000000000000015e56

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.7%

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

   if 2.30000000000000015e56 < y

   1. Initial program 99.9%

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

      1. flip-- 30.1%

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

      2. associate-/r/ 30.0%

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

      3. metadata-eval 30.0%

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

      4. pow2 30.0%

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

   3. Applied egg-rr 30.0%

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

      1. associate-*l/ 27.8%

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

      2. associate-+r+ 27.8%

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

      3. +-commutative 27.8%

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

   5. Simplified 27.8%

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

   6. Taylor expanded in y around -inf 78.7%

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

      1. mul-1-neg 78.7%

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

      2. unsub-neg 78.7%

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

      3. cancel-sign-sub-inv 78.7%

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

      4. distribute-rgt1-in 78.7%

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

      5. metadata-eval 78.7%

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

      6. mul0-lft 78.7%

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

      7. metadata-eval 78.7%

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

      8. metadata-eval 78.7%

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

      9. metadata-eval 78.7%

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

   8. Simplified 78.7%

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

   9. Taylor expanded in x around inf 78.7%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -26000:\\ \;\;\;\;1 - \frac{-2 + x \cdot 2}{y}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - 2 \cdot \frac{x}{y}\\ \end{array} \]

Alternative 5: 62.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -59000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+64}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -59000000.0) -1.0 (if (<= x 1.75e+64) (- 1.0 (/ x y)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -59000000.0) {
		tmp = -1.0;
	} else if (x <= 1.75e+64) {
		tmp = 1.0 - (x / y);
	} 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 <= (-59000000.0d0)) then
        tmp = -1.0d0
    else if (x <= 1.75d+64) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -59000000.0) {
		tmp = -1.0;
	} else if (x <= 1.75e+64) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -59000000.0:
		tmp = -1.0
	elif x <= 1.75e+64:
		tmp = 1.0 - (x / y)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -59000000.0)
		tmp = -1.0;
	elseif (x <= 1.75e+64)
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -59000000.0)
		tmp = -1.0;
	elseif (x <= 1.75e+64)
		tmp = 1.0 - (x / y);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -59000000.0], -1.0, If[LessEqual[x, 1.75e+64], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9e7 or 1.7499999999999999e64 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 78.5%

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

   if -5.9e7 < x < 1.7499999999999999e64

   1. Initial program 100.0%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in y around inf 52.9%

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

   5. Taylor expanded in y around 0 53.0%

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

      1. mul-1-neg 53.0%

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

      2. unsub-neg 53.0%

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

   7. Simplified 53.0%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -59000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+64}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6: 73.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -210000:\\ \;\;\;\;1 - \frac{-2}{y}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -210000.0)
   (- 1.0 (/ -2.0 y))
   (if (<= y 5.2e+56) (/ x (- 2.0 x)) (- 1.0 (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -210000.0) {
		tmp = 1.0 - (-2.0 / y);
	} else if (y <= 5.2e+56) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0 - (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 <= (-210000.0d0)) then
        tmp = 1.0d0 - ((-2.0d0) / y)
    else if (y <= 5.2d+56) then
        tmp = x / (2.0d0 - x)
    else
        tmp = 1.0d0 - (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -210000.0) {
		tmp = 1.0 - (-2.0 / y);
	} else if (y <= 5.2e+56) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -210000.0:
		tmp = 1.0 - (-2.0 / y)
	elif y <= 5.2e+56:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0 - (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -210000.0)
		tmp = Float64(1.0 - Float64(-2.0 / y));
	elseif (y <= 5.2e+56)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = Float64(1.0 - Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -210000.0)
		tmp = 1.0 - (-2.0 / y);
	elseif (y <= 5.2e+56)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0 - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -210000.0], N[(1.0 - N[(-2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.2e+56], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.1e5

   1. Initial program 100.0%

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

      1. flip-- 50.7%

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

      2. associate-/r/ 50.5%

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

      3. metadata-eval 50.5%

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

      4. pow2 50.5%

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

   3. Applied egg-rr 50.5%

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

      1. associate-*l/ 49.2%

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

      2. associate-+r+ 49.2%

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

      3. +-commutative 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in y around -inf 73.5%

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

      1. mul-1-neg 73.5%

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

      2. unsub-neg 73.5%

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

      3. cancel-sign-sub-inv 73.5%

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

      4. distribute-rgt1-in 73.5%

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

      5. metadata-eval 73.5%

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

      6. mul0-lft 73.5%

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

      7. metadata-eval 73.5%

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

      8. metadata-eval 73.5%

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

      9. metadata-eval 73.5%

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

   8. Simplified 73.5%

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

   9. Taylor expanded in x around 0 71.9%

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

   if -2.1e5 < y < 5.20000000000000022e56

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.7%

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

   if 5.20000000000000022e56 < y

   1. Initial program 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in y around inf 77.4%

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

   5. Taylor expanded in y around 0 77.6%

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

      1. mul-1-neg 77.6%

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

      2. unsub-neg 77.6%

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

   7. Simplified 77.6%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -210000:\\ \;\;\;\;1 - \frac{-2}{y}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+56}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]

Alternative 7: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -8e-100) (/ x (- 2.0 x)) (if (<= x 5.5e+63) (/ y (+ y -2.0)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -8e-100) {
		tmp = x / (2.0 - x);
	} else if (x <= 5.5e+63) {
		tmp = y / (y + -2.0);
	} 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 <= (-8d-100)) then
        tmp = x / (2.0d0 - x)
    else if (x <= 5.5d+63) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -8e-100) {
		tmp = x / (2.0 - x);
	} else if (x <= 5.5e+63) {
		tmp = y / (y + -2.0);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -8e-100:
		tmp = x / (2.0 - x)
	elif x <= 5.5e+63:
		tmp = y / (y + -2.0)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -8e-100)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (x <= 5.5e+63)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -8e-100)
		tmp = x / (2.0 - x);
	elseif (x <= 5.5e+63)
		tmp = y / (y + -2.0);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -8e-100], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.5e+63], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -8.0000000000000002e-100

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 75.5%

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

   if -8.0000000000000002e-100 < x < 5.50000000000000004e63

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. distribute-neg-frac 77.5%

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

   4. Simplified 77.5%

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

      1. frac-2neg 77.5%

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

      2. div-inv 77.4%

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

      3. remove-double-neg 77.4%

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

      4. sub-neg 77.4%

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

      5. distribute-neg-in 77.4%

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

      6. metadata-eval 77.4%

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

      7. remove-double-neg 77.4%

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

   6. Applied egg-rr 77.4%

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

      1. associate-*r/ 77.5%

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

      2. *-rgt-identity 77.5%

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

      3. +-commutative 77.5%

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

   8. Simplified 77.5%

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

   if 5.50000000000000004e63 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 78.2%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-100}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{+63}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8: 62.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2300000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2300000.0) -1.0 (if (<= x 1.4e+64) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2300000.0) {
		tmp = -1.0;
	} else if (x <= 1.4e+64) {
		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 <= (-2300000.0d0)) then
        tmp = -1.0d0
    else if (x <= 1.4d+64) 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 <= -2300000.0) {
		tmp = -1.0;
	} else if (x <= 1.4e+64) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2300000.0:
		tmp = -1.0
	elif x <= 1.4e+64:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2300000.0)
		tmp = -1.0;
	elseif (x <= 1.4e+64)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2300000.0)
		tmp = -1.0;
	elseif (x <= 1.4e+64)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2300000.0], -1.0, If[LessEqual[x, 1.4e+64], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.3e6 or 1.40000000000000012e64 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 78.5%

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

   if -2.3e6 < x < 1.40000000000000012e64

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 53.0%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2300000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+64}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 9: 38.4% 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. Taylor expanded in x around inf 38.6%

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

3. Final simplification 38.6%

   \[\leadsto -1 \]

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 2023340 
(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))))