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

Percentage Accurate: 100.0% → 100.0%

Time: 8.3s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.6× 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]]

Derivation

1. Initial program 100.0%

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

   1. div-sub 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 60.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} + -1\\ t_1 := 1 - \frac{x}{y}\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+50}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-125}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-269}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-168}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 480000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ y x) -1.0)) (t_1 (- 1.0 (/ x y))))
   (if (<= x -6.2e+50)
     t_0
     (if (<= x -1.45e-13)
       t_1
       (if (<= x -4.6e-125)
         (* x 0.5)
         (if (<= x 2.45e-269)
           t_1
           (if (<= x 1.1e-168) (* y -0.5) (if (<= x 480000.0) 1.0 t_0))))))))

C

double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double t_1 = 1.0 - (x / y);
	double tmp;
	if (x <= -6.2e+50) {
		tmp = t_0;
	} else if (x <= -1.45e-13) {
		tmp = t_1;
	} else if (x <= -4.6e-125) {
		tmp = x * 0.5;
	} else if (x <= 2.45e-269) {
		tmp = t_1;
	} else if (x <= 1.1e-168) {
		tmp = y * -0.5;
	} else if (x <= 480000.0) {
		tmp = 1.0;
	} 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 / x) + (-1.0d0)
    t_1 = 1.0d0 - (x / y)
    if (x <= (-6.2d+50)) then
        tmp = t_0
    else if (x <= (-1.45d-13)) then
        tmp = t_1
    else if (x <= (-4.6d-125)) then
        tmp = x * 0.5d0
    else if (x <= 2.45d-269) then
        tmp = t_1
    else if (x <= 1.1d-168) then
        tmp = y * (-0.5d0)
    else if (x <= 480000.0d0) then
        tmp = 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double t_1 = 1.0 - (x / y);
	double tmp;
	if (x <= -6.2e+50) {
		tmp = t_0;
	} else if (x <= -1.45e-13) {
		tmp = t_1;
	} else if (x <= -4.6e-125) {
		tmp = x * 0.5;
	} else if (x <= 2.45e-269) {
		tmp = t_1;
	} else if (x <= 1.1e-168) {
		tmp = y * -0.5;
	} else if (x <= 480000.0) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / x) + -1.0
	t_1 = 1.0 - (x / y)
	tmp = 0
	if x <= -6.2e+50:
		tmp = t_0
	elif x <= -1.45e-13:
		tmp = t_1
	elif x <= -4.6e-125:
		tmp = x * 0.5
	elif x <= 2.45e-269:
		tmp = t_1
	elif x <= 1.1e-168:
		tmp = y * -0.5
	elif x <= 480000.0:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y / x) + -1.0)
	t_1 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (x <= -6.2e+50)
		tmp = t_0;
	elseif (x <= -1.45e-13)
		tmp = t_1;
	elseif (x <= -4.6e-125)
		tmp = Float64(x * 0.5);
	elseif (x <= 2.45e-269)
		tmp = t_1;
	elseif (x <= 1.1e-168)
		tmp = Float64(y * -0.5);
	elseif (x <= 480000.0)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y / x) + -1.0;
	t_1 = 1.0 - (x / y);
	tmp = 0.0;
	if (x <= -6.2e+50)
		tmp = t_0;
	elseif (x <= -1.45e-13)
		tmp = t_1;
	elseif (x <= -4.6e-125)
		tmp = x * 0.5;
	elseif (x <= 2.45e-269)
		tmp = t_1;
	elseif (x <= 1.1e-168)
		tmp = y * -0.5;
	elseif (x <= 480000.0)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+50], t$95$0, If[LessEqual[x, -1.45e-13], t$95$1, If[LessEqual[x, -4.6e-125], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 2.45e-269], t$95$1, If[LessEqual[x, 1.1e-168], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 480000.0], 1.0, t$95$0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -6.20000000000000006e50 or 4.8e5 < 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 75.7%

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

   5. Taylor expanded in x around 0 75.9%

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

   if -6.20000000000000006e50 < x < -1.4499999999999999e-13 or -4.5999999999999998e-125 < x < 2.45e-269

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   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 57.1%

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

   5. Taylor expanded in y around 0 57.3%

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

      1. mul-1-neg 57.3%

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

      2. unsub-neg 57.3%

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

   7. Simplified 57.3%

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

   if -1.4499999999999999e-13 < x < -4.5999999999999998e-125

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 57.9%

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

   3. Taylor expanded in x around 0 57.9%

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

      1. *-commutative 57.9%

         \[\leadsto \color{blue}{x \cdot 0.5} \]

   5. Simplified 57.9%

      \[\leadsto \color{blue}{x \cdot 0.5} \]

   if 2.45e-269 < x < 1.0999999999999999e-168

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 82.9%

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

      1. mul-1-neg 82.9%

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

      2. distribute-neg-frac 82.9%

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

   4. Simplified 82.9%

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

   5. Taylor expanded in y around 0 57.8%

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

      1. *-commutative 57.8%

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

   7. Simplified 57.8%

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

   if 1.0999999999999999e-168 < x < 4.8e5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 78.6%

      \[\leadsto \color{blue}{1} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+50}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-13}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-125}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-269}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-168}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 480000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]

Alternative 3: 60.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+52}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-14}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-125}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-269}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-168}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 600000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9e+52)
   -1.0
   (if (<= x -2.3e-14)
     1.0
     (if (<= x -1.8e-125)
       (* x 0.5)
       (if (<= x 3.4e-269)
         1.0
         (if (<= x 1.1e-168) (* y -0.5) (if (<= x 600000.0) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9e+52) {
		tmp = -1.0;
	} else if (x <= -2.3e-14) {
		tmp = 1.0;
	} else if (x <= -1.8e-125) {
		tmp = x * 0.5;
	} else if (x <= 3.4e-269) {
		tmp = 1.0;
	} else if (x <= 1.1e-168) {
		tmp = y * -0.5;
	} else if (x <= 600000.0) {
		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 <= (-9d+52)) then
        tmp = -1.0d0
    else if (x <= (-2.3d-14)) then
        tmp = 1.0d0
    else if (x <= (-1.8d-125)) then
        tmp = x * 0.5d0
    else if (x <= 3.4d-269) then
        tmp = 1.0d0
    else if (x <= 1.1d-168) then
        tmp = y * (-0.5d0)
    else if (x <= 600000.0d0) 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 <= -9e+52) {
		tmp = -1.0;
	} else if (x <= -2.3e-14) {
		tmp = 1.0;
	} else if (x <= -1.8e-125) {
		tmp = x * 0.5;
	} else if (x <= 3.4e-269) {
		tmp = 1.0;
	} else if (x <= 1.1e-168) {
		tmp = y * -0.5;
	} else if (x <= 600000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9e+52:
		tmp = -1.0
	elif x <= -2.3e-14:
		tmp = 1.0
	elif x <= -1.8e-125:
		tmp = x * 0.5
	elif x <= 3.4e-269:
		tmp = 1.0
	elif x <= 1.1e-168:
		tmp = y * -0.5
	elif x <= 600000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9e+52)
		tmp = -1.0;
	elseif (x <= -2.3e-14)
		tmp = 1.0;
	elseif (x <= -1.8e-125)
		tmp = Float64(x * 0.5);
	elseif (x <= 3.4e-269)
		tmp = 1.0;
	elseif (x <= 1.1e-168)
		tmp = Float64(y * -0.5);
	elseif (x <= 600000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9e+52)
		tmp = -1.0;
	elseif (x <= -2.3e-14)
		tmp = 1.0;
	elseif (x <= -1.8e-125)
		tmp = x * 0.5;
	elseif (x <= 3.4e-269)
		tmp = 1.0;
	elseif (x <= 1.1e-168)
		tmp = y * -0.5;
	elseif (x <= 600000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9e+52], -1.0, If[LessEqual[x, -2.3e-14], 1.0, If[LessEqual[x, -1.8e-125], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 3.4e-269], 1.0, If[LessEqual[x, 1.1e-168], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 600000.0], 1.0, -1.0]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -8.9999999999999999e52 or 6e5 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 75.2%

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

   if -8.9999999999999999e52 < x < -2.29999999999999998e-14 or -1.8000000000000001e-125 < x < 3.3999999999999997e-269 or 1.0999999999999999e-168 < x < 6e5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 61.7%

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

   if -2.29999999999999998e-14 < x < -1.8000000000000001e-125

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 57.9%

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

   3. Taylor expanded in x around 0 57.9%

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

      1. *-commutative 57.9%

         \[\leadsto \color{blue}{x \cdot 0.5} \]

   5. Simplified 57.9%

      \[\leadsto \color{blue}{x \cdot 0.5} \]

   if 3.3999999999999997e-269 < x < 1.0999999999999999e-168

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 82.9%

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

      1. mul-1-neg 82.9%

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

      2. distribute-neg-frac 82.9%

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

   4. Simplified 82.9%

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

   5. Taylor expanded in y around 0 57.8%

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

      1. *-commutative 57.8%

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

   7. Simplified 57.8%

      \[\leadsto \color{blue}{y \cdot -0.5} \]
3. Recombined 4 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+52}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-14}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-125}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-269}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-168}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 600000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4: 60.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{x}{y}\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+48}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-128}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-269}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-165}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 550000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ x y))))
   (if (<= x -2.2e+48)
     -1.0
     (if (<= x -4.5e-16)
       t_0
       (if (<= x -4.8e-128)
         (* x 0.5)
         (if (<= x 1.4e-269)
           t_0
           (if (<= x 1.7e-165) (* y -0.5) (if (<= x 550000.0) 1.0 -1.0))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 - (x / y);
	double tmp;
	if (x <= -2.2e+48) {
		tmp = -1.0;
	} else if (x <= -4.5e-16) {
		tmp = t_0;
	} else if (x <= -4.8e-128) {
		tmp = x * 0.5;
	} else if (x <= 1.4e-269) {
		tmp = t_0;
	} else if (x <= 1.7e-165) {
		tmp = y * -0.5;
	} else if (x <= 550000.0) {
		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 = 1.0d0 - (x / y)
    if (x <= (-2.2d+48)) then
        tmp = -1.0d0
    else if (x <= (-4.5d-16)) then
        tmp = t_0
    else if (x <= (-4.8d-128)) then
        tmp = x * 0.5d0
    else if (x <= 1.4d-269) then
        tmp = t_0
    else if (x <= 1.7d-165) then
        tmp = y * (-0.5d0)
    else if (x <= 550000.0d0) 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 = 1.0 - (x / y);
	double tmp;
	if (x <= -2.2e+48) {
		tmp = -1.0;
	} else if (x <= -4.5e-16) {
		tmp = t_0;
	} else if (x <= -4.8e-128) {
		tmp = x * 0.5;
	} else if (x <= 1.4e-269) {
		tmp = t_0;
	} else if (x <= 1.7e-165) {
		tmp = y * -0.5;
	} else if (x <= 550000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - (x / y)
	tmp = 0
	if x <= -2.2e+48:
		tmp = -1.0
	elif x <= -4.5e-16:
		tmp = t_0
	elif x <= -4.8e-128:
		tmp = x * 0.5
	elif x <= 1.4e-269:
		tmp = t_0
	elif x <= 1.7e-165:
		tmp = y * -0.5
	elif x <= 550000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(x / y))
	tmp = 0.0
	if (x <= -2.2e+48)
		tmp = -1.0;
	elseif (x <= -4.5e-16)
		tmp = t_0;
	elseif (x <= -4.8e-128)
		tmp = Float64(x * 0.5);
	elseif (x <= 1.4e-269)
		tmp = t_0;
	elseif (x <= 1.7e-165)
		tmp = Float64(y * -0.5);
	elseif (x <= 550000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - (x / y);
	tmp = 0.0;
	if (x <= -2.2e+48)
		tmp = -1.0;
	elseif (x <= -4.5e-16)
		tmp = t_0;
	elseif (x <= -4.8e-128)
		tmp = x * 0.5;
	elseif (x <= 1.4e-269)
		tmp = t_0;
	elseif (x <= 1.7e-165)
		tmp = y * -0.5;
	elseif (x <= 550000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.2e+48], -1.0, If[LessEqual[x, -4.5e-16], t$95$0, If[LessEqual[x, -4.8e-128], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 1.4e-269], t$95$0, If[LessEqual[x, 1.7e-165], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 550000.0], 1.0, -1.0]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.1999999999999999e48 or 5.5e5 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 75.2%

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

   if -2.1999999999999999e48 < x < -4.5000000000000002e-16 or -4.7999999999999996e-128 < x < 1.39999999999999997e-269

   1. Initial program 99.9%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   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 57.1%

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

   5. Taylor expanded in y around 0 57.3%

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

      1. mul-1-neg 57.3%

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

      2. unsub-neg 57.3%

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

   7. Simplified 57.3%

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

   if -4.5000000000000002e-16 < x < -4.7999999999999996e-128

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 57.9%

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

   3. Taylor expanded in x around 0 57.9%

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

      1. *-commutative 57.9%

         \[\leadsto \color{blue}{x \cdot 0.5} \]

   5. Simplified 57.9%

      \[\leadsto \color{blue}{x \cdot 0.5} \]

   if 1.39999999999999997e-269 < x < 1.7e-165

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 82.9%

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

      1. mul-1-neg 82.9%

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

      2. distribute-neg-frac 82.9%

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

   4. Simplified 82.9%

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

   5. Taylor expanded in y around 0 57.8%

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

      1. *-commutative 57.8%

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

   7. Simplified 57.8%

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

   if 1.7e-165 < x < 5.5e5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 78.6%

      \[\leadsto \color{blue}{1} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+48}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-16}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-128}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-269}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-165}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 550000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5: 74.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+48}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-17}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-31}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.1e+48)
   (+ (/ y x) -1.0)
   (if (<= x -8.6e-17)
     (- 1.0 (/ x y))
     (if (<= x -1.9e-31)
       (* x 0.5)
       (if (<= x 4.3e-10) (/ y (+ y -2.0)) (/ x (- 2.0 x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.1e+48) {
		tmp = (y / x) + -1.0;
	} else if (x <= -8.6e-17) {
		tmp = 1.0 - (x / y);
	} else if (x <= -1.9e-31) {
		tmp = x * 0.5;
	} else if (x <= 4.3e-10) {
		tmp = y / (y + -2.0);
	} 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 (x <= (-2.1d+48)) then
        tmp = (y / x) + (-1.0d0)
    else if (x <= (-8.6d-17)) then
        tmp = 1.0d0 - (x / y)
    else if (x <= (-1.9d-31)) then
        tmp = x * 0.5d0
    else if (x <= 4.3d-10) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.1e+48) {
		tmp = (y / x) + -1.0;
	} else if (x <= -8.6e-17) {
		tmp = 1.0 - (x / y);
	} else if (x <= -1.9e-31) {
		tmp = x * 0.5;
	} else if (x <= 4.3e-10) {
		tmp = y / (y + -2.0);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.1e+48:
		tmp = (y / x) + -1.0
	elif x <= -8.6e-17:
		tmp = 1.0 - (x / y)
	elif x <= -1.9e-31:
		tmp = x * 0.5
	elif x <= 4.3e-10:
		tmp = y / (y + -2.0)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.1e+48)
		tmp = Float64(Float64(y / x) + -1.0);
	elseif (x <= -8.6e-17)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (x <= -1.9e-31)
		tmp = Float64(x * 0.5);
	elseif (x <= 4.3e-10)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.1e+48)
		tmp = (y / x) + -1.0;
	elseif (x <= -8.6e-17)
		tmp = 1.0 - (x / y);
	elseif (x <= -1.9e-31)
		tmp = x * 0.5;
	elseif (x <= 4.3e-10)
		tmp = y / (y + -2.0);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.1e+48], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[x, -8.6e-17], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.9e-31], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 4.3e-10], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.0999999999999998e48

   1. Initial program 100.0%

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

      1. clear-num 100.0%

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

      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 81.2%

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

   5. Taylor expanded in x around 0 81.5%

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

   if -2.0999999999999998e48 < x < -8.60000000000000046e-17

   1. Initial program 99.8%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   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 y around inf 63.3%

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

   5. Taylor expanded in y around 0 63.5%

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

      1. mul-1-neg 63.5%

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

      2. unsub-neg 63.5%

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

   7. Simplified 63.5%

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

   if -8.60000000000000046e-17 < x < -1.9e-31

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.6%

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

   3. Taylor expanded in x around 0 79.6%

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

      1. *-commutative 79.6%

         \[\leadsto \color{blue}{x \cdot 0.5} \]

   5. Simplified 79.6%

      \[\leadsto \color{blue}{x \cdot 0.5} \]

   if -1.9e-31 < x < 4.30000000000000014e-10

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. distribute-neg-frac 82.2%

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

   4. Simplified 82.2%

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

      1. frac-2neg 82.2%

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

      2. div-inv 82.1%

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

      3. remove-double-neg 82.1%

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

      4. sub-neg 82.1%

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

      5. distribute-neg-in 82.1%

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

      6. metadata-eval 82.1%

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

      7. remove-double-neg 82.1%

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

   6. Applied egg-rr 82.1%

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

      1. associate-*r/ 82.2%

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

      2. *-rgt-identity 82.2%

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

      3. +-commutative 82.2%

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

   8. Simplified 82.2%

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

   if 4.30000000000000014e-10 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 71.1%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+48}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-17}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-31}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 4.3 \cdot 10^{-10}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 6: 74.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+48}:\\ \;\;\;\;\frac{x - y}{-x}\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-16}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-31}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-10}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.1e+48)
   (/ (- x y) (- x))
   (if (<= x -3.3e-16)
     (- 1.0 (/ x y))
     (if (<= x -1.1e-31)
       (* x 0.5)
       (if (<= x 3e-10) (/ y (+ y -2.0)) (/ x (- 2.0 x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.1e+48) {
		tmp = (x - y) / -x;
	} else if (x <= -3.3e-16) {
		tmp = 1.0 - (x / y);
	} else if (x <= -1.1e-31) {
		tmp = x * 0.5;
	} else if (x <= 3e-10) {
		tmp = y / (y + -2.0);
	} 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 (x <= (-2.1d+48)) then
        tmp = (x - y) / -x
    else if (x <= (-3.3d-16)) then
        tmp = 1.0d0 - (x / y)
    else if (x <= (-1.1d-31)) then
        tmp = x * 0.5d0
    else if (x <= 3d-10) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.1e+48) {
		tmp = (x - y) / -x;
	} else if (x <= -3.3e-16) {
		tmp = 1.0 - (x / y);
	} else if (x <= -1.1e-31) {
		tmp = x * 0.5;
	} else if (x <= 3e-10) {
		tmp = y / (y + -2.0);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.1e+48:
		tmp = (x - y) / -x
	elif x <= -3.3e-16:
		tmp = 1.0 - (x / y)
	elif x <= -1.1e-31:
		tmp = x * 0.5
	elif x <= 3e-10:
		tmp = y / (y + -2.0)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.1e+48)
		tmp = Float64(Float64(x - y) / Float64(-x));
	elseif (x <= -3.3e-16)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (x <= -1.1e-31)
		tmp = Float64(x * 0.5);
	elseif (x <= 3e-10)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.1e+48)
		tmp = (x - y) / -x;
	elseif (x <= -3.3e-16)
		tmp = 1.0 - (x / y);
	elseif (x <= -1.1e-31)
		tmp = x * 0.5;
	elseif (x <= 3e-10)
		tmp = y / (y + -2.0);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.1e+48], N[(N[(x - y), $MachinePrecision] / (-x)), $MachinePrecision], If[LessEqual[x, -3.3e-16], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.1e-31], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 3e-10], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.0999999999999998e48

   1. Initial program 100.0%

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

      1. clear-num 100.0%

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

      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 81.2%

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

      1. sub-neg 81.2%

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

      2. distribute-lft-in 81.2%

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

   6. Applied egg-rr 81.2%

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

      1. distribute-lft-out 81.2%

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

      2. sub-neg 81.2%

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

      3. associate-*l/ 81.5%

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

      4. remove-double-neg 81.5%

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

      5. neg-mul-1 81.5%

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

      6. associate-*r* 81.5%

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

      7. metadata-eval 81.5%

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

      8. associate-*l/ 81.2%

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

      9. *-rgt-identity 81.2%

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

      10. *-commutative 81.2%

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

      11. associate-*l* 81.2%

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

      12. metadata-eval 81.2%

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

      13. associate-*l/ 81.5%

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

      14. metadata-eval 81.5%

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

      15. distribute-lft-neg-in 81.5%

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

      16. neg-mul-1 81.5%

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

      17. remove-double-neg 81.5%

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

      18. times-frac 81.5%

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

      19. neg-mul-1 81.5%

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

      20. remove-double-neg 81.5%

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

      21. neg-mul-1 81.5%

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

   8. Simplified 81.5%

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

   if -2.0999999999999998e48 < x < -3.29999999999999988e-16

   1. Initial program 99.8%

      \[\frac{x - y}{2 - \left(x + y\right)} \]
   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 y around inf 63.3%

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

   5. Taylor expanded in y around 0 63.5%

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

      1. mul-1-neg 63.5%

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

      2. unsub-neg 63.5%

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

   7. Simplified 63.5%

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

   if -3.29999999999999988e-16 < x < -1.10000000000000005e-31

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.6%

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

   3. Taylor expanded in x around 0 79.6%

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

      1. *-commutative 79.6%

         \[\leadsto \color{blue}{x \cdot 0.5} \]

   5. Simplified 79.6%

      \[\leadsto \color{blue}{x \cdot 0.5} \]

   if -1.10000000000000005e-31 < x < 3e-10

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. distribute-neg-frac 82.2%

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

   4. Simplified 82.2%

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

      1. frac-2neg 82.2%

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

      2. div-inv 82.1%

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

      3. remove-double-neg 82.1%

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

      4. sub-neg 82.1%

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

      5. distribute-neg-in 82.1%

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

      6. metadata-eval 82.1%

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

      7. remove-double-neg 82.1%

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

   6. Applied egg-rr 82.1%

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

      1. associate-*r/ 82.2%

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

      2. *-rgt-identity 82.2%

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

      3. +-commutative 82.2%

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

   8. Simplified 82.2%

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

   if 3e-10 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 71.1%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+48}:\\ \;\;\;\;\frac{x - y}{-x}\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-16}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-31}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-10}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 7: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+59}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-16}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-127}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 600000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2e+59)
   -1.0
   (if (<= x -2e-16)
     1.0
     (if (<= x -7e-127) (* x 0.5) (if (<= x 600000.0) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2e+59) {
		tmp = -1.0;
	} else if (x <= -2e-16) {
		tmp = 1.0;
	} else if (x <= -7e-127) {
		tmp = x * 0.5;
	} else if (x <= 600000.0) {
		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 <= (-2d+59)) then
        tmp = -1.0d0
    else if (x <= (-2d-16)) then
        tmp = 1.0d0
    else if (x <= (-7d-127)) then
        tmp = x * 0.5d0
    else if (x <= 600000.0d0) 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 <= -2e+59) {
		tmp = -1.0;
	} else if (x <= -2e-16) {
		tmp = 1.0;
	} else if (x <= -7e-127) {
		tmp = x * 0.5;
	} else if (x <= 600000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2e+59:
		tmp = -1.0
	elif x <= -2e-16:
		tmp = 1.0
	elif x <= -7e-127:
		tmp = x * 0.5
	elif x <= 600000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2e+59)
		tmp = -1.0;
	elseif (x <= -2e-16)
		tmp = 1.0;
	elseif (x <= -7e-127)
		tmp = Float64(x * 0.5);
	elseif (x <= 600000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2e+59)
		tmp = -1.0;
	elseif (x <= -2e-16)
		tmp = 1.0;
	elseif (x <= -7e-127)
		tmp = x * 0.5;
	elseif (x <= 600000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2e+59], -1.0, If[LessEqual[x, -2e-16], 1.0, If[LessEqual[x, -7e-127], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 600000.0], 1.0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.99999999999999994e59 or 6e5 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 75.2%

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

   if -1.99999999999999994e59 < x < -2e-16 or -6.99999999999999979e-127 < x < 6e5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 56.9%

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

   if -2e-16 < x < -6.99999999999999979e-127

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 57.9%

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

   3. Taylor expanded in x around 0 57.9%

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

      1. *-commutative 57.9%

         \[\leadsto \color{blue}{x \cdot 0.5} \]

   5. Simplified 57.9%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+59}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-16}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-127}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 600000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 8: 75.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+17} \lor \neg \left(y \leq 1.65 \cdot 10^{+30}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5.1e+17) (not (<= y 1.65e+30)))
   (- 1.0 (/ x y))
   (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5.1e+17) || !(y <= 1.65e+30)) {
		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 <= (-5.1d+17)) .or. (.not. (y <= 1.65d+30))) 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 <= -5.1e+17) || !(y <= 1.65e+30)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5.1e+17) or not (y <= 1.65e+30):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5.1e+17) || !(y <= 1.65e+30))
		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 <= -5.1e+17) || ~((y <= 1.65e+30)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5.1e+17], N[Not[LessEqual[y, 1.65e+30]], $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 < -5.1e17 or 1.65000000000000013e30 < y

   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/ 99.8%

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

   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 78.4%

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

   5. Taylor expanded in y around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. unsub-neg 78.5%

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

   7. Simplified 78.5%

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

   if -5.1e17 < y < 1.65000000000000013e30

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 69.5%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+17} \lor \neg \left(y \leq 1.65 \cdot 10^{+30}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 9: 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 10: 62.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+49}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 600000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.12e+49) -1.0 (if (<= x 600000.0) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.12e+49) {
		tmp = -1.0;
	} else if (x <= 600000.0) {
		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 <= (-1.12d+49)) then
        tmp = -1.0d0
    else if (x <= 600000.0d0) 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 <= -1.12e+49) {
		tmp = -1.0;
	} else if (x <= 600000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.12e+49:
		tmp = -1.0
	elif x <= 600000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.12e+49)
		tmp = -1.0;
	elseif (x <= 600000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.12e+49)
		tmp = -1.0;
	elseif (x <= 600000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.12e+49], -1.0, If[LessEqual[x, 600000.0], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.12000000000000005e49 or 6e5 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 75.2%

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

   if -1.12000000000000005e49 < x < 6e5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 52.8%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{+49}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 600000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 11: 38.8% 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 34.9%

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

3. Final simplification 34.9%

   \[\leadsto -1 \]

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 2023322 
(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))))