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

Percentage Accurate: 100.0% → 100.0%

Time: 5.5s

Alternatives: 8

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: 60.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} + -1\\ \mathbf{if}\;y \leq -1.52 \cdot 10^{+60}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-281}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-238}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-156}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-147}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-124}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+66}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ y x) -1.0)))
   (if (<= y -1.52e+60)
     1.0
     (if (<= y -1.3e-281)
       t_0
       (if (<= y 1.12e-238)
         (* x 0.5)
         (if (<= y 4.2e-156)
           -1.0
           (if (<= y 2.4e-147)
             (* x 0.5)
             (if (<= y 8.6e-124)
               (* y -0.5)
               (if (<= y 1.35e+66) t_0 1.0)))))))))

C

double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double tmp;
	if (y <= -1.52e+60) {
		tmp = 1.0;
	} else if (y <= -1.3e-281) {
		tmp = t_0;
	} else if (y <= 1.12e-238) {
		tmp = x * 0.5;
	} else if (y <= 4.2e-156) {
		tmp = -1.0;
	} else if (y <= 2.4e-147) {
		tmp = x * 0.5;
	} else if (y <= 8.6e-124) {
		tmp = y * -0.5;
	} else if (y <= 1.35e+66) {
		tmp = t_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 = (y / x) + (-1.0d0)
    if (y <= (-1.52d+60)) then
        tmp = 1.0d0
    else if (y <= (-1.3d-281)) then
        tmp = t_0
    else if (y <= 1.12d-238) then
        tmp = x * 0.5d0
    else if (y <= 4.2d-156) then
        tmp = -1.0d0
    else if (y <= 2.4d-147) then
        tmp = x * 0.5d0
    else if (y <= 8.6d-124) then
        tmp = y * (-0.5d0)
    else if (y <= 1.35d+66) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double tmp;
	if (y <= -1.52e+60) {
		tmp = 1.0;
	} else if (y <= -1.3e-281) {
		tmp = t_0;
	} else if (y <= 1.12e-238) {
		tmp = x * 0.5;
	} else if (y <= 4.2e-156) {
		tmp = -1.0;
	} else if (y <= 2.4e-147) {
		tmp = x * 0.5;
	} else if (y <= 8.6e-124) {
		tmp = y * -0.5;
	} else if (y <= 1.35e+66) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / x) + -1.0
	tmp = 0
	if y <= -1.52e+60:
		tmp = 1.0
	elif y <= -1.3e-281:
		tmp = t_0
	elif y <= 1.12e-238:
		tmp = x * 0.5
	elif y <= 4.2e-156:
		tmp = -1.0
	elif y <= 2.4e-147:
		tmp = x * 0.5
	elif y <= 8.6e-124:
		tmp = y * -0.5
	elif y <= 1.35e+66:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y / x) + -1.0)
	tmp = 0.0
	if (y <= -1.52e+60)
		tmp = 1.0;
	elseif (y <= -1.3e-281)
		tmp = t_0;
	elseif (y <= 1.12e-238)
		tmp = Float64(x * 0.5);
	elseif (y <= 4.2e-156)
		tmp = -1.0;
	elseif (y <= 2.4e-147)
		tmp = Float64(x * 0.5);
	elseif (y <= 8.6e-124)
		tmp = Float64(y * -0.5);
	elseif (y <= 1.35e+66)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y / x) + -1.0;
	tmp = 0.0;
	if (y <= -1.52e+60)
		tmp = 1.0;
	elseif (y <= -1.3e-281)
		tmp = t_0;
	elseif (y <= 1.12e-238)
		tmp = x * 0.5;
	elseif (y <= 4.2e-156)
		tmp = -1.0;
	elseif (y <= 2.4e-147)
		tmp = x * 0.5;
	elseif (y <= 8.6e-124)
		tmp = y * -0.5;
	elseif (y <= 1.35e+66)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision]}, If[LessEqual[y, -1.52e+60], 1.0, If[LessEqual[y, -1.3e-281], t$95$0, If[LessEqual[y, 1.12e-238], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 4.2e-156], -1.0, If[LessEqual[y, 2.4e-147], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 8.6e-124], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 1.35e+66], t$95$0, 1.0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.52e60 or 1.35e66 < y

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 87.4%

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

   if -1.52e60 < y < -1.30000000000000002e-281 or 8.6e-124 < y < 1.35e66

   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. clear-num 99.9%

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

      2. associate-/r/ 99.8%

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

      3. associate--l- 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 60.2%

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

   7. Taylor expanded in x around 0 60.3%

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

   if -1.30000000000000002e-281 < y < 1.12000000000000005e-238 or 4.20000000000000025e-156 < y < 2.39999999999999998e-147

   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 0 91.6%

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

   5. Taylor expanded in x around 0 69.1%

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

      1. *-commutative 69.1%

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

   7. Simplified 69.1%

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

   if 1.12000000000000005e-238 < y < 4.20000000000000025e-156

   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 61.7%

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

   if 2.39999999999999998e-147 < y < 8.6e-124

   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 59.9%

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

      1. mul-1-neg 59.9%

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

      2. distribute-neg-frac 59.9%

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

   6. Simplified 59.9%

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

   7. Taylor expanded in y around 0 59.9%

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

      1. *-commutative 59.9%

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

   9. Simplified 59.9%

      \[\leadsto \color{blue}{y \cdot -0.5} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.52 \cdot 10^{+60}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-281}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-238}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-156}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-147}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-124}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 60.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+60}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-282}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-242}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-155}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-147}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-125}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+65}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.4e+60)
   1.0
   (if (<= y -4.8e-282)
     -1.0
     (if (<= y 2.9e-242)
       (* x 0.5)
       (if (<= y 1.3e-155)
         -1.0
         (if (<= y 2.4e-147)
           (* x 0.5)
           (if (<= y 7.5e-125) (* y -0.5) (if (<= y 2.2e+65) -1.0 1.0))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.4e+60) {
		tmp = 1.0;
	} else if (y <= -4.8e-282) {
		tmp = -1.0;
	} else if (y <= 2.9e-242) {
		tmp = x * 0.5;
	} else if (y <= 1.3e-155) {
		tmp = -1.0;
	} else if (y <= 2.4e-147) {
		tmp = x * 0.5;
	} else if (y <= 7.5e-125) {
		tmp = y * -0.5;
	} else if (y <= 2.2e+65) {
		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 <= (-1.4d+60)) then
        tmp = 1.0d0
    else if (y <= (-4.8d-282)) then
        tmp = -1.0d0
    else if (y <= 2.9d-242) then
        tmp = x * 0.5d0
    else if (y <= 1.3d-155) then
        tmp = -1.0d0
    else if (y <= 2.4d-147) then
        tmp = x * 0.5d0
    else if (y <= 7.5d-125) then
        tmp = y * (-0.5d0)
    else if (y <= 2.2d+65) 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 <= -1.4e+60) {
		tmp = 1.0;
	} else if (y <= -4.8e-282) {
		tmp = -1.0;
	} else if (y <= 2.9e-242) {
		tmp = x * 0.5;
	} else if (y <= 1.3e-155) {
		tmp = -1.0;
	} else if (y <= 2.4e-147) {
		tmp = x * 0.5;
	} else if (y <= 7.5e-125) {
		tmp = y * -0.5;
	} else if (y <= 2.2e+65) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.4e+60:
		tmp = 1.0
	elif y <= -4.8e-282:
		tmp = -1.0
	elif y <= 2.9e-242:
		tmp = x * 0.5
	elif y <= 1.3e-155:
		tmp = -1.0
	elif y <= 2.4e-147:
		tmp = x * 0.5
	elif y <= 7.5e-125:
		tmp = y * -0.5
	elif y <= 2.2e+65:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.4e+60)
		tmp = 1.0;
	elseif (y <= -4.8e-282)
		tmp = -1.0;
	elseif (y <= 2.9e-242)
		tmp = Float64(x * 0.5);
	elseif (y <= 1.3e-155)
		tmp = -1.0;
	elseif (y <= 2.4e-147)
		tmp = Float64(x * 0.5);
	elseif (y <= 7.5e-125)
		tmp = Float64(y * -0.5);
	elseif (y <= 2.2e+65)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.4e+60)
		tmp = 1.0;
	elseif (y <= -4.8e-282)
		tmp = -1.0;
	elseif (y <= 2.9e-242)
		tmp = x * 0.5;
	elseif (y <= 1.3e-155)
		tmp = -1.0;
	elseif (y <= 2.4e-147)
		tmp = x * 0.5;
	elseif (y <= 7.5e-125)
		tmp = y * -0.5;
	elseif (y <= 2.2e+65)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.4e+60], 1.0, If[LessEqual[y, -4.8e-282], -1.0, If[LessEqual[y, 2.9e-242], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 1.3e-155], -1.0, If[LessEqual[y, 2.4e-147], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 7.5e-125], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 2.2e+65], -1.0, 1.0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.4e60 or 2.1999999999999998e65 < y

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 87.4%

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

   if -1.4e60 < y < -4.79999999999999994e-282 or 2.9000000000000001e-242 < y < 1.30000000000000004e-155 or 7.5e-125 < y < 2.1999999999999998e65

   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 60.3%

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

   if -4.79999999999999994e-282 < y < 2.9000000000000001e-242 or 1.30000000000000004e-155 < y < 2.39999999999999998e-147

   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 0 91.6%

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

   5. Taylor expanded in x around 0 69.1%

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

      1. *-commutative 69.1%

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

   7. Simplified 69.1%

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

   if 2.39999999999999998e-147 < y < 7.5e-125

   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 59.9%

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

      1. mul-1-neg 59.9%

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

      2. distribute-neg-frac 59.9%

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

   6. Simplified 59.9%

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

   7. Taylor expanded in y around 0 59.9%

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

      1. *-commutative 59.9%

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

   9. Simplified 59.9%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+60}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-282}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-242}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-155}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-147}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-125}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+65}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 74.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+60} \lor \neg \left(y \leq 2.2 \cdot 10^{+65}\right):\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.1e+60) (not (<= y 2.2e+65)))
   (+ 1.0 (/ (* x -2.0) y))
   (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.1e+60) || !(y <= 2.2e+65)) {
		tmp = 1.0 + ((x * -2.0) / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2.1d+60)) .or. (.not. (y <= 2.2d+65))) then
        tmp = 1.0d0 + ((x * (-2.0d0)) / y)
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.1e+60) || !(y <= 2.2e+65)) {
		tmp = 1.0 + ((x * -2.0) / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.1e+60) or not (y <= 2.2e+65):
		tmp = 1.0 + ((x * -2.0) / y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.1e+60) || !(y <= 2.2e+65))
		tmp = Float64(1.0 + Float64(Float64(x * -2.0) / y));
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.1e+60) || ~((y <= 2.2e+65)))
		tmp = 1.0 + ((x * -2.0) / y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.1e+60], N[Not[LessEqual[y, 2.2e+65]], $MachinePrecision]], N[(1.0 + N[(N[(x * -2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1000000000000001e60 or 2.1999999999999998e65 < y

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 88.2%

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

      1. associate--l+ 88.2%

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

      2. associate-*r/ 88.2%

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

      3. associate-*r/ 88.2%

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

      4. div-sub 88.2%

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

      5. cancel-sign-sub-inv 88.2%

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

      6. metadata-eval 88.2%

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

      7. *-lft-identity 88.2%

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

      8. +-commutative 88.2%

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

      9. mul-1-neg 88.2%

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

      10. unsub-neg 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in x around inf 88.2%

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

      1. associate-*r/ 88.2%

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

      2. *-commutative 88.2%

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

   9. Simplified 88.2%

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

   if -2.1000000000000001e60 < y < 2.1999999999999998e65

   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 77.1%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+60} \lor \neg \left(y \leq 2.2 \cdot 10^{+65}\right):\\ \;\;\;\;1 + \frac{x \cdot -2}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 5: 60.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+60}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-282}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-236}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+66}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3e+60)
   1.0
   (if (<= y -3.2e-282)
     -1.0
     (if (<= y 8.2e-236) (* x 0.5) (if (<= y 4e+66) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3e+60) {
		tmp = 1.0;
	} else if (y <= -3.2e-282) {
		tmp = -1.0;
	} else if (y <= 8.2e-236) {
		tmp = x * 0.5;
	} else if (y <= 4e+66) {
		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 <= (-3d+60)) then
        tmp = 1.0d0
    else if (y <= (-3.2d-282)) then
        tmp = -1.0d0
    else if (y <= 8.2d-236) then
        tmp = x * 0.5d0
    else if (y <= 4d+66) 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 <= -3e+60) {
		tmp = 1.0;
	} else if (y <= -3.2e-282) {
		tmp = -1.0;
	} else if (y <= 8.2e-236) {
		tmp = x * 0.5;
	} else if (y <= 4e+66) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3e+60:
		tmp = 1.0
	elif y <= -3.2e-282:
		tmp = -1.0
	elif y <= 8.2e-236:
		tmp = x * 0.5
	elif y <= 4e+66:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3e+60)
		tmp = 1.0;
	elseif (y <= -3.2e-282)
		tmp = -1.0;
	elseif (y <= 8.2e-236)
		tmp = Float64(x * 0.5);
	elseif (y <= 4e+66)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3e+60)
		tmp = 1.0;
	elseif (y <= -3.2e-282)
		tmp = -1.0;
	elseif (y <= 8.2e-236)
		tmp = x * 0.5;
	elseif (y <= 4e+66)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3e+60], 1.0, If[LessEqual[y, -3.2e-282], -1.0, If[LessEqual[y, 8.2e-236], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 4e+66], -1.0, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9999999999999998e60 or 3.99999999999999978e66 < y

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 87.4%

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

   if -2.9999999999999998e60 < y < -3.19999999999999983e-282 or 8.2000000000000006e-236 < y < 3.99999999999999978e66

   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 57.8%

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

   if -3.19999999999999983e-282 < y < 8.2000000000000006e-236

   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 0 94.8%

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

   5. Taylor expanded in x around 0 67.3%

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

      1. *-commutative 67.3%

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

   7. Simplified 67.3%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+60}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-282}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-236}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+66}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.35e+61) 1.0 (if (<= y 6.2e+66) (/ x (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.35e+61) {
		tmp = 1.0;
	} else if (y <= 6.2e+66) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.35d+61)) then
        tmp = 1.0d0
    else if (y <= 6.2d+66) then
        tmp = x / (2.0d0 - x)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.35e+61) {
		tmp = 1.0;
	} else if (y <= 6.2e+66) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.35e+61:
		tmp = 1.0
	elif y <= 6.2e+66:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.35e+61)
		tmp = 1.0;
	elseif (y <= 6.2e+66)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.35e+61)
		tmp = 1.0;
	elseif (y <= 6.2e+66)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.35e+61], 1.0, If[LessEqual[y, 6.2e+66], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3500000000000001e61 or 6.20000000000000037e66 < y

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 87.4%

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

   if -1.3500000000000001e61 < y < 6.20000000000000037e66

   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 77.1%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+66}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 61.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+60}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+65}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.5e+60) 1.0 (if (<= y 4e+65) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.5e+60) {
		tmp = 1.0;
	} else if (y <= 4e+65) {
		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 <= (-6.5d+60)) then
        tmp = 1.0d0
    else if (y <= 4d+65) 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 <= -6.5e+60) {
		tmp = 1.0;
	} else if (y <= 4e+65) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6.5e+60:
		tmp = 1.0
	elif y <= 4e+65:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6.5e+60)
		tmp = 1.0;
	elseif (y <= 4e+65)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6.5e+60)
		tmp = 1.0;
	elseif (y <= 4e+65)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6.5e+60], 1.0, If[LessEqual[y, 4e+65], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -6.49999999999999931e60 or 4e65 < y

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 87.4%

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

   if -6.49999999999999931e60 < y < 4e65

   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 54.7%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+60}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+65}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 38.0% 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 37.9%

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

5. Final simplification 37.9%

   \[\leadsto -1 \]

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 2023224 
(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))))