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

Percentage Accurate: 100.0% → 100.0%

Time: 8.1s

Alternatives: 7

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: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y + -2}\\ t_1 := -1 - \frac{\left(2 - y\right) - y}{x}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+116}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-9}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-93}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ y -2.0))) (t_1 (- -1.0 (/ (- (- 2.0 y) y) x))))
   (if (<= y -3.1e+116)
     1.0
     (if (<= y -1.25e+61)
       t_1
       (if (<= y -2.9e-9)
         t_0
         (if (<= y -3.2e-44)
           t_1
           (if (<= y -2.1e-93)
             (* y -0.5)
             (if (<= y 5.2e-69) (/ x (- 2.0 x)) t_0))))))))

C

double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double t_1 = -1.0 - (((2.0 - y) - y) / x);
	double tmp;
	if (y <= -3.1e+116) {
		tmp = 1.0;
	} else if (y <= -1.25e+61) {
		tmp = t_1;
	} else if (y <= -2.9e-9) {
		tmp = t_0;
	} else if (y <= -3.2e-44) {
		tmp = t_1;
	} else if (y <= -2.1e-93) {
		tmp = y * -0.5;
	} else if (y <= 5.2e-69) {
		tmp = x / (2.0 - x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y / (y + (-2.0d0))
    t_1 = (-1.0d0) - (((2.0d0 - y) - y) / x)
    if (y <= (-3.1d+116)) then
        tmp = 1.0d0
    else if (y <= (-1.25d+61)) then
        tmp = t_1
    else if (y <= (-2.9d-9)) then
        tmp = t_0
    else if (y <= (-3.2d-44)) then
        tmp = t_1
    else if (y <= (-2.1d-93)) then
        tmp = y * (-0.5d0)
    else if (y <= 5.2d-69) then
        tmp = x / (2.0d0 - x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double t_1 = -1.0 - (((2.0 - y) - y) / x);
	double tmp;
	if (y <= -3.1e+116) {
		tmp = 1.0;
	} else if (y <= -1.25e+61) {
		tmp = t_1;
	} else if (y <= -2.9e-9) {
		tmp = t_0;
	} else if (y <= -3.2e-44) {
		tmp = t_1;
	} else if (y <= -2.1e-93) {
		tmp = y * -0.5;
	} else if (y <= 5.2e-69) {
		tmp = x / (2.0 - x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (y + -2.0)
	t_1 = -1.0 - (((2.0 - y) - y) / x)
	tmp = 0
	if y <= -3.1e+116:
		tmp = 1.0
	elif y <= -1.25e+61:
		tmp = t_1
	elif y <= -2.9e-9:
		tmp = t_0
	elif y <= -3.2e-44:
		tmp = t_1
	elif y <= -2.1e-93:
		tmp = y * -0.5
	elif y <= 5.2e-69:
		tmp = x / (2.0 - x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y + -2.0))
	t_1 = Float64(-1.0 - Float64(Float64(Float64(2.0 - y) - y) / x))
	tmp = 0.0
	if (y <= -3.1e+116)
		tmp = 1.0;
	elseif (y <= -1.25e+61)
		tmp = t_1;
	elseif (y <= -2.9e-9)
		tmp = t_0;
	elseif (y <= -3.2e-44)
		tmp = t_1;
	elseif (y <= -2.1e-93)
		tmp = Float64(y * -0.5);
	elseif (y <= 5.2e-69)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (y + -2.0);
	t_1 = -1.0 - (((2.0 - y) - y) / x);
	tmp = 0.0;
	if (y <= -3.1e+116)
		tmp = 1.0;
	elseif (y <= -1.25e+61)
		tmp = t_1;
	elseif (y <= -2.9e-9)
		tmp = t_0;
	elseif (y <= -3.2e-44)
		tmp = t_1;
	elseif (y <= -2.1e-93)
		tmp = y * -0.5;
	elseif (y <= 5.2e-69)
		tmp = x / (2.0 - x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-1.0 - N[(N[(N[(2.0 - y), $MachinePrecision] - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.1e+116], 1.0, If[LessEqual[y, -1.25e+61], t$95$1, If[LessEqual[y, -2.9e-9], t$95$0, If[LessEqual[y, -3.2e-44], t$95$1, If[LessEqual[y, -2.1e-93], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 5.2e-69], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.09999999999999996e116

   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 86.7%

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

   if -3.09999999999999996e116 < y < -1.25000000000000004e61 or -2.89999999999999991e-9 < y < -3.19999999999999995e-44

   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. div-sub 100.0%

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

      2. flip-- 67.5%

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

      3. associate-/r/ 67.4%

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

      4. associate-/r/ 67.5%

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

      5. flip-- 100.0%

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

      6. associate--l- 100.0%

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

      7. associate--l- 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. sub-div 100.0%

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

      2. clear-num 99.9%

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

   7. Applied egg-rr 99.9%

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

      1. associate--r+ 99.9%

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

      2. div-sub 99.9%

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

      3. sub-neg 99.9%

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

   9. Applied egg-rr 99.9%

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

       1. sub-neg 99.9%

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

   11. Simplified 99.9%

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

   12. Taylor expanded in x around -inf 81.0%

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

       1. sub-neg 81.0%

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

       2. metadata-eval 81.0%

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

       3. +-commutative 81.0%

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

       4. associate-*r/ 81.0%

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

   14. Simplified 81.0%

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

   if -1.25000000000000004e61 < y < -2.89999999999999991e-9 or 5.2000000000000004e-69 < 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 x around 0 75.8%

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

      1. associate-*r/ 75.8%

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

      2. neg-mul-1 75.8%

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

   6. Simplified 75.8%

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

      1. distribute-frac-neg 75.8%

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

      2. neg-sub0 75.8%

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

      3. div-inv 75.5%

         \[\leadsto 0 - \color{blue}{y \cdot \frac{1}{2 - y}} \]

      4. cancel-sign-sub-inv 75.5%

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

      5. div-inv 75.8%

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

      6. frac-2neg 75.8%

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

      7. remove-double-neg 75.8%

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

      8. sub-neg 75.8%

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

      9. distribute-neg-in 75.8%

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

      10. metadata-eval 75.8%

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

      11. remove-double-neg 75.8%

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

   8. Applied egg-rr 75.8%

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

      1. +-lft-identity 75.8%

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

      2. +-commutative 75.8%

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

   10. Simplified 75.8%

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

   if -3.19999999999999995e-44 < y < -2.1000000000000001e-93

   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 78.2%

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

      1. associate-*r/ 78.2%

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

      2. neg-mul-1 78.2%

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

   6. Simplified 78.2%

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

   7. Taylor expanded in y around 0 78.2%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   8. Step-by-step derivation

      1. *-commutative 78.2%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   9. Simplified 78.2%

      \[\leadsto \color{blue}{y \cdot -0.5} \]

   if -2.1000000000000001e-93 < y < 5.2000000000000004e-69

   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 89.7%

      \[\leadsto \color{blue}{\frac{x}{2 - x}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+116}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{+61}:\\ \;\;\;\;-1 - \frac{\left(2 - y\right) - y}{x}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-9}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-44}:\\ \;\;\;\;-1 - \frac{\left(2 - y\right) - y}{x}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-93}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]

Alternative 3: 62.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5000000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-44}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -3.55 \cdot 10^{-96}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-38}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+22}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5000000000000.0)
   1.0
   (if (<= y -1.95e-44)
     -1.0
     (if (<= y -3.55e-96)
       (* y -0.5)
       (if (<= y 2e-71)
         -1.0
         (if (<= y 7.2e-38) (* y -0.5) (if (<= y 1.4e+22) -1.0 1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5000000000000.0) {
		tmp = 1.0;
	} else if (y <= -1.95e-44) {
		tmp = -1.0;
	} else if (y <= -3.55e-96) {
		tmp = y * -0.5;
	} else if (y <= 2e-71) {
		tmp = -1.0;
	} else if (y <= 7.2e-38) {
		tmp = y * -0.5;
	} else if (y <= 1.4e+22) {
		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 <= (-5000000000000.0d0)) then
        tmp = 1.0d0
    else if (y <= (-1.95d-44)) then
        tmp = -1.0d0
    else if (y <= (-3.55d-96)) then
        tmp = y * (-0.5d0)
    else if (y <= 2d-71) then
        tmp = -1.0d0
    else if (y <= 7.2d-38) then
        tmp = y * (-0.5d0)
    else if (y <= 1.4d+22) 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 <= -5000000000000.0) {
		tmp = 1.0;
	} else if (y <= -1.95e-44) {
		tmp = -1.0;
	} else if (y <= -3.55e-96) {
		tmp = y * -0.5;
	} else if (y <= 2e-71) {
		tmp = -1.0;
	} else if (y <= 7.2e-38) {
		tmp = y * -0.5;
	} else if (y <= 1.4e+22) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5000000000000.0:
		tmp = 1.0
	elif y <= -1.95e-44:
		tmp = -1.0
	elif y <= -3.55e-96:
		tmp = y * -0.5
	elif y <= 2e-71:
		tmp = -1.0
	elif y <= 7.2e-38:
		tmp = y * -0.5
	elif y <= 1.4e+22:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5000000000000.0)
		tmp = 1.0;
	elseif (y <= -1.95e-44)
		tmp = -1.0;
	elseif (y <= -3.55e-96)
		tmp = Float64(y * -0.5);
	elseif (y <= 2e-71)
		tmp = -1.0;
	elseif (y <= 7.2e-38)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.4e+22)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5000000000000.0)
		tmp = 1.0;
	elseif (y <= -1.95e-44)
		tmp = -1.0;
	elseif (y <= -3.55e-96)
		tmp = y * -0.5;
	elseif (y <= 2e-71)
		tmp = -1.0;
	elseif (y <= 7.2e-38)
		tmp = y * -0.5;
	elseif (y <= 1.4e+22)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5000000000000.0], 1.0, If[LessEqual[y, -1.95e-44], -1.0, If[LessEqual[y, -3.55e-96], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 2e-71], -1.0, If[LessEqual[y, 7.2e-38], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.4e+22], -1.0, 1.0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5e12 or 1.4e22 < y

   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 79.7%

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

   if -5e12 < y < -1.9500000000000001e-44 or -3.55000000000000019e-96 < y < 1.9999999999999998e-71 or 7.2000000000000001e-38 < y < 1.4e22

   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 59.5%

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

   if -1.9500000000000001e-44 < y < -3.55000000000000019e-96 or 1.9999999999999998e-71 < y < 7.2000000000000001e-38

   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 80.4%

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

      1. associate-*r/ 80.4%

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

      2. neg-mul-1 80.4%

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

   6. Simplified 80.4%

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

   7. Taylor expanded in y around 0 80.4%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   8. Step-by-step derivation

      1. *-commutative 80.4%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   9. Simplified 80.4%

      \[\leadsto \color{blue}{y \cdot -0.5} \]
3. Recombined 3 regimes into one program.

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5000000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-44}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -3.55 \cdot 10^{-96}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-38}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+22}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -800000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-44}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-88}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-70}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-38}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+22}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= y -800000000000.0)
     1.0
     (if (<= y -9.5e-44)
       t_0
       (if (<= y -7.2e-88)
         (* y -0.5)
         (if (<= y 8.5e-70)
           t_0
           (if (<= y 4.6e-38) (* y -0.5) (if (<= y 1.45e+22) -1.0 1.0))))))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -800000000000.0) {
		tmp = 1.0;
	} else if (y <= -9.5e-44) {
		tmp = t_0;
	} else if (y <= -7.2e-88) {
		tmp = y * -0.5;
	} else if (y <= 8.5e-70) {
		tmp = t_0;
	} else if (y <= 4.6e-38) {
		tmp = y * -0.5;
	} else if (y <= 1.45e+22) {
		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) :: t_0
    real(8) :: tmp
    t_0 = x / (2.0d0 - x)
    if (y <= (-800000000000.0d0)) then
        tmp = 1.0d0
    else if (y <= (-9.5d-44)) then
        tmp = t_0
    else if (y <= (-7.2d-88)) then
        tmp = y * (-0.5d0)
    else if (y <= 8.5d-70) then
        tmp = t_0
    else if (y <= 4.6d-38) then
        tmp = y * (-0.5d0)
    else if (y <= 1.45d+22) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -800000000000.0) {
		tmp = 1.0;
	} else if (y <= -9.5e-44) {
		tmp = t_0;
	} else if (y <= -7.2e-88) {
		tmp = y * -0.5;
	} else if (y <= 8.5e-70) {
		tmp = t_0;
	} else if (y <= 4.6e-38) {
		tmp = y * -0.5;
	} else if (y <= 1.45e+22) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if y <= -800000000000.0:
		tmp = 1.0
	elif y <= -9.5e-44:
		tmp = t_0
	elif y <= -7.2e-88:
		tmp = y * -0.5
	elif y <= 8.5e-70:
		tmp = t_0
	elif y <= 4.6e-38:
		tmp = y * -0.5
	elif y <= 1.45e+22:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -800000000000.0)
		tmp = 1.0;
	elseif (y <= -9.5e-44)
		tmp = t_0;
	elseif (y <= -7.2e-88)
		tmp = Float64(y * -0.5);
	elseif (y <= 8.5e-70)
		tmp = t_0;
	elseif (y <= 4.6e-38)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.45e+22)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -800000000000.0)
		tmp = 1.0;
	elseif (y <= -9.5e-44)
		tmp = t_0;
	elseif (y <= -7.2e-88)
		tmp = y * -0.5;
	elseif (y <= 8.5e-70)
		tmp = t_0;
	elseif (y <= 4.6e-38)
		tmp = y * -0.5;
	elseif (y <= 1.45e+22)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -800000000000.0], 1.0, If[LessEqual[y, -9.5e-44], t$95$0, If[LessEqual[y, -7.2e-88], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 8.5e-70], t$95$0, If[LessEqual[y, 4.6e-38], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.45e+22], -1.0, 1.0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8e11 or 1.45e22 < y

   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 79.7%

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

   if -8e11 < y < -9.49999999999999924e-44 or -7.1999999999999999e-88 < y < 8.5000000000000002e-70

   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 87.1%

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

   if -9.49999999999999924e-44 < y < -7.1999999999999999e-88 or 8.5000000000000002e-70 < y < 4.60000000000000003e-38

   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 80.4%

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

      1. associate-*r/ 80.4%

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

      2. neg-mul-1 80.4%

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

   6. Simplified 80.4%

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

   7. Taylor expanded in y around 0 80.4%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   8. Step-by-step derivation

      1. *-commutative 80.4%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   9. Simplified 80.4%

      \[\leadsto \color{blue}{y \cdot -0.5} \]

   if 4.60000000000000003e-38 < y < 1.45e22

   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 68.0%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -800000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-88}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-38}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+22}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 74.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y + -2}\\ t_1 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -3 \cdot 10^{-7}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-88}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ y -2.0))) (t_1 (/ x (- 2.0 x))))
   (if (<= y -3e-7)
     t_0
     (if (<= y -1.8e-44)
       t_1
       (if (<= y -7.2e-88) (* y -0.5) (if (<= y 1.25e-70) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double t_1 = x / (2.0 - x);
	double tmp;
	if (y <= -3e-7) {
		tmp = t_0;
	} else if (y <= -1.8e-44) {
		tmp = t_1;
	} else if (y <= -7.2e-88) {
		tmp = y * -0.5;
	} else if (y <= 1.25e-70) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y / (y + (-2.0d0))
    t_1 = x / (2.0d0 - x)
    if (y <= (-3d-7)) then
        tmp = t_0
    else if (y <= (-1.8d-44)) then
        tmp = t_1
    else if (y <= (-7.2d-88)) then
        tmp = y * (-0.5d0)
    else if (y <= 1.25d-70) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double t_1 = x / (2.0 - x);
	double tmp;
	if (y <= -3e-7) {
		tmp = t_0;
	} else if (y <= -1.8e-44) {
		tmp = t_1;
	} else if (y <= -7.2e-88) {
		tmp = y * -0.5;
	} else if (y <= 1.25e-70) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (y + -2.0)
	t_1 = x / (2.0 - x)
	tmp = 0
	if y <= -3e-7:
		tmp = t_0
	elif y <= -1.8e-44:
		tmp = t_1
	elif y <= -7.2e-88:
		tmp = y * -0.5
	elif y <= 1.25e-70:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y + -2.0))
	t_1 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -3e-7)
		tmp = t_0;
	elseif (y <= -1.8e-44)
		tmp = t_1;
	elseif (y <= -7.2e-88)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.25e-70)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (y + -2.0);
	t_1 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -3e-7)
		tmp = t_0;
	elseif (y <= -1.8e-44)
		tmp = t_1;
	elseif (y <= -7.2e-88)
		tmp = y * -0.5;
	elseif (y <= 1.25e-70)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3e-7], t$95$0, If[LessEqual[y, -1.8e-44], t$95$1, If[LessEqual[y, -7.2e-88], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.25e-70], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9999999999999999e-7 or 1.25e-70 < 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 x around 0 75.7%

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

      1. associate-*r/ 75.7%

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

      2. neg-mul-1 75.7%

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

   6. Simplified 75.7%

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

      1. distribute-frac-neg 75.7%

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

      2. neg-sub0 75.7%

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

      3. div-inv 75.4%

         \[\leadsto 0 - \color{blue}{y \cdot \frac{1}{2 - y}} \]

      4. cancel-sign-sub-inv 75.4%

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

      5. div-inv 75.7%

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

      6. frac-2neg 75.7%

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

      7. remove-double-neg 75.7%

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

      8. sub-neg 75.7%

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

      9. distribute-neg-in 75.7%

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

      10. metadata-eval 75.7%

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

      11. remove-double-neg 75.7%

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

   8. Applied egg-rr 75.7%

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

      1. +-lft-identity 75.7%

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

      2. +-commutative 75.7%

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

   10. Simplified 75.7%

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

   if -2.9999999999999999e-7 < y < -1.7999999999999999e-44 or -7.1999999999999999e-88 < y < 1.25e-70

   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 89.4%

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

   if -1.7999999999999999e-44 < y < -7.1999999999999999e-88

   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 78.2%

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

      1. associate-*r/ 78.2%

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

      2. neg-mul-1 78.2%

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

   6. Simplified 78.2%

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

   7. Taylor expanded in y around 0 78.2%

      \[\leadsto \color{blue}{-0.5 \cdot y} \]
   8. Step-by-step derivation

      1. *-commutative 78.2%

         \[\leadsto \color{blue}{y \cdot -0.5} \]

   9. Simplified 78.2%

      \[\leadsto \color{blue}{y \cdot -0.5} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-88}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-70}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]

Alternative 6: 62.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1060000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+22}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1060000000000.0) 1.0 (if (<= y 1.4e+22) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1060000000000.0) {
		tmp = 1.0;
	} else if (y <= 1.4e+22) {
		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 <= (-1060000000000.0d0)) then
        tmp = 1.0d0
    else if (y <= 1.4d+22) 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 <= -1060000000000.0) {
		tmp = 1.0;
	} else if (y <= 1.4e+22) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1060000000000.0:
		tmp = 1.0
	elif y <= 1.4e+22:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1060000000000.0)
		tmp = 1.0;
	elseif (y <= 1.4e+22)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1060000000000.0)
		tmp = 1.0;
	elseif (y <= 1.4e+22)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1060000000000.0], 1.0, If[LessEqual[y, 1.4e+22], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.06e12 or 1.4e22 < y

   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 79.7%

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

   if -1.06e12 < y < 1.4e22

   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 54.4%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1060000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+22}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 37.2% 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 38.8%

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

5. Final simplification 38.8%

   \[\leadsto -1 \]

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 2023297 
(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))))