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

Percentage Accurate: 100.0% → 100.0%

Time: 8.1s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 61.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-101}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-189}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-246}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-37}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-14}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 45000000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.5e+19)
   -1.0
   (if (<= x -7.8e-7)
     1.0
     (if (<= x -1.55e-101)
       (* x 0.5)
       (if (<= x -9.6e-189)
         1.0
         (if (<= x -9.2e-246)
           (* y -0.5)
           (if (<= x 3e-37)
             1.0
             (if (<= x 9.5e-14)
               (* x 0.5)
               (if (<= x 45000000000000.0) 1.0 -1.0)))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.5e+19) {
		tmp = -1.0;
	} else if (x <= -7.8e-7) {
		tmp = 1.0;
	} else if (x <= -1.55e-101) {
		tmp = x * 0.5;
	} else if (x <= -9.6e-189) {
		tmp = 1.0;
	} else if (x <= -9.2e-246) {
		tmp = y * -0.5;
	} else if (x <= 3e-37) {
		tmp = 1.0;
	} else if (x <= 9.5e-14) {
		tmp = x * 0.5;
	} else if (x <= 45000000000000.0) {
		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 <= (-1.5d+19)) then
        tmp = -1.0d0
    else if (x <= (-7.8d-7)) then
        tmp = 1.0d0
    else if (x <= (-1.55d-101)) then
        tmp = x * 0.5d0
    else if (x <= (-9.6d-189)) then
        tmp = 1.0d0
    else if (x <= (-9.2d-246)) then
        tmp = y * (-0.5d0)
    else if (x <= 3d-37) then
        tmp = 1.0d0
    else if (x <= 9.5d-14) then
        tmp = x * 0.5d0
    else if (x <= 45000000000000.0d0) 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 <= -1.5e+19) {
		tmp = -1.0;
	} else if (x <= -7.8e-7) {
		tmp = 1.0;
	} else if (x <= -1.55e-101) {
		tmp = x * 0.5;
	} else if (x <= -9.6e-189) {
		tmp = 1.0;
	} else if (x <= -9.2e-246) {
		tmp = y * -0.5;
	} else if (x <= 3e-37) {
		tmp = 1.0;
	} else if (x <= 9.5e-14) {
		tmp = x * 0.5;
	} else if (x <= 45000000000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.5e+19:
		tmp = -1.0
	elif x <= -7.8e-7:
		tmp = 1.0
	elif x <= -1.55e-101:
		tmp = x * 0.5
	elif x <= -9.6e-189:
		tmp = 1.0
	elif x <= -9.2e-246:
		tmp = y * -0.5
	elif x <= 3e-37:
		tmp = 1.0
	elif x <= 9.5e-14:
		tmp = x * 0.5
	elif x <= 45000000000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.5e+19)
		tmp = -1.0;
	elseif (x <= -7.8e-7)
		tmp = 1.0;
	elseif (x <= -1.55e-101)
		tmp = Float64(x * 0.5);
	elseif (x <= -9.6e-189)
		tmp = 1.0;
	elseif (x <= -9.2e-246)
		tmp = Float64(y * -0.5);
	elseif (x <= 3e-37)
		tmp = 1.0;
	elseif (x <= 9.5e-14)
		tmp = Float64(x * 0.5);
	elseif (x <= 45000000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.5e+19)
		tmp = -1.0;
	elseif (x <= -7.8e-7)
		tmp = 1.0;
	elseif (x <= -1.55e-101)
		tmp = x * 0.5;
	elseif (x <= -9.6e-189)
		tmp = 1.0;
	elseif (x <= -9.2e-246)
		tmp = y * -0.5;
	elseif (x <= 3e-37)
		tmp = 1.0;
	elseif (x <= 9.5e-14)
		tmp = x * 0.5;
	elseif (x <= 45000000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.5e+19], -1.0, If[LessEqual[x, -7.8e-7], 1.0, If[LessEqual[x, -1.55e-101], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, -9.6e-189], 1.0, If[LessEqual[x, -9.2e-246], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 3e-37], 1.0, If[LessEqual[x, 9.5e-14], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 45000000000000.0], 1.0, -1.0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.5e19 or 4.5e13 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 82.7%

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

   if -1.5e19 < x < -7.80000000000000049e-7 or -1.54999999999999987e-101 < x < -9.5999999999999994e-189 or -9.199999999999999e-246 < x < 3e-37 or 9.4999999999999999e-14 < x < 4.5e13

   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 64.5%

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

   if -7.80000000000000049e-7 < x < -1.54999999999999987e-101 or 3e-37 < x < 9.4999999999999999e-14

   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 74.6%

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

   5. Taylor expanded in x around 0 71.7%

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

      1. *-commutative 71.7%

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

   7. Simplified 71.7%

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

   if -9.5999999999999994e-189 < x < -9.199999999999999e-246

   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 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-neg-frac 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 79.3%

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

      1. *-commutative 79.3%

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

   9. Simplified 79.3%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+19}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-101}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-189}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-246}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-37}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-14}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 45000000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3: 61.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+19}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-8}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-102}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-189}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.46 \cdot 10^{-245}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-36}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-14}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 42000000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.02e+19)
   -1.0
   (if (<= x -9e-8)
     (+ 1.0 (/ 2.0 y))
     (if (<= x -6.2e-102)
       (* x 0.5)
       (if (<= x -1.25e-189)
         1.0
         (if (<= x -1.46e-245)
           (* y -0.5)
           (if (<= x 1.12e-36)
             1.0
             (if (<= x 6.5e-14)
               (* x 0.5)
               (if (<= x 42000000000000.0) 1.0 -1.0)))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.02e+19) {
		tmp = -1.0;
	} else if (x <= -9e-8) {
		tmp = 1.0 + (2.0 / y);
	} else if (x <= -6.2e-102) {
		tmp = x * 0.5;
	} else if (x <= -1.25e-189) {
		tmp = 1.0;
	} else if (x <= -1.46e-245) {
		tmp = y * -0.5;
	} else if (x <= 1.12e-36) {
		tmp = 1.0;
	} else if (x <= 6.5e-14) {
		tmp = x * 0.5;
	} else if (x <= 42000000000000.0) {
		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 <= (-1.02d+19)) then
        tmp = -1.0d0
    else if (x <= (-9d-8)) then
        tmp = 1.0d0 + (2.0d0 / y)
    else if (x <= (-6.2d-102)) then
        tmp = x * 0.5d0
    else if (x <= (-1.25d-189)) then
        tmp = 1.0d0
    else if (x <= (-1.46d-245)) then
        tmp = y * (-0.5d0)
    else if (x <= 1.12d-36) then
        tmp = 1.0d0
    else if (x <= 6.5d-14) then
        tmp = x * 0.5d0
    else if (x <= 42000000000000.0d0) 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 <= -1.02e+19) {
		tmp = -1.0;
	} else if (x <= -9e-8) {
		tmp = 1.0 + (2.0 / y);
	} else if (x <= -6.2e-102) {
		tmp = x * 0.5;
	} else if (x <= -1.25e-189) {
		tmp = 1.0;
	} else if (x <= -1.46e-245) {
		tmp = y * -0.5;
	} else if (x <= 1.12e-36) {
		tmp = 1.0;
	} else if (x <= 6.5e-14) {
		tmp = x * 0.5;
	} else if (x <= 42000000000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.02e+19:
		tmp = -1.0
	elif x <= -9e-8:
		tmp = 1.0 + (2.0 / y)
	elif x <= -6.2e-102:
		tmp = x * 0.5
	elif x <= -1.25e-189:
		tmp = 1.0
	elif x <= -1.46e-245:
		tmp = y * -0.5
	elif x <= 1.12e-36:
		tmp = 1.0
	elif x <= 6.5e-14:
		tmp = x * 0.5
	elif x <= 42000000000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.02e+19)
		tmp = -1.0;
	elseif (x <= -9e-8)
		tmp = Float64(1.0 + Float64(2.0 / y));
	elseif (x <= -6.2e-102)
		tmp = Float64(x * 0.5);
	elseif (x <= -1.25e-189)
		tmp = 1.0;
	elseif (x <= -1.46e-245)
		tmp = Float64(y * -0.5);
	elseif (x <= 1.12e-36)
		tmp = 1.0;
	elseif (x <= 6.5e-14)
		tmp = Float64(x * 0.5);
	elseif (x <= 42000000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.02e+19)
		tmp = -1.0;
	elseif (x <= -9e-8)
		tmp = 1.0 + (2.0 / y);
	elseif (x <= -6.2e-102)
		tmp = x * 0.5;
	elseif (x <= -1.25e-189)
		tmp = 1.0;
	elseif (x <= -1.46e-245)
		tmp = y * -0.5;
	elseif (x <= 1.12e-36)
		tmp = 1.0;
	elseif (x <= 6.5e-14)
		tmp = x * 0.5;
	elseif (x <= 42000000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.02e+19], -1.0, If[LessEqual[x, -9e-8], N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.2e-102], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, -1.25e-189], 1.0, If[LessEqual[x, -1.46e-245], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 1.12e-36], 1.0, If[LessEqual[x, 6.5e-14], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 42000000000000.0], 1.0, -1.0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.02e19 or 4.2e13 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 82.7%

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

   if -1.02e19 < x < -8.99999999999999986e-8

   1. Initial program 99.8%

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

      1. associate--r+ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 88.9%

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

      1. associate--l+ 88.9%

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

      2. associate-*r/ 88.9%

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

      3. associate-*r/ 88.9%

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

      4. div-sub 88.9%

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

      5. cancel-sign-sub-inv 88.9%

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

      6. metadata-eval 88.9%

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

      7. *-lft-identity 88.9%

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

      8. +-commutative 88.9%

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

      9. mul-1-neg 88.9%

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

      10. unsub-neg 88.9%

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

   6. Simplified 88.9%

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

   7. Taylor expanded in x around 0 87.7%

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

   if -8.99999999999999986e-8 < x < -6.20000000000000026e-102 or 1.12e-36 < x < 6.5000000000000001e-14

   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 74.6%

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

   5. Taylor expanded in x around 0 71.7%

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

      1. *-commutative 71.7%

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

   7. Simplified 71.7%

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

   if -6.20000000000000026e-102 < x < -1.2499999999999999e-189 or -1.46000000000000009e-245 < x < 1.12e-36 or 6.5000000000000001e-14 < x < 4.2e13

   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 62.7%

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

   if -1.2499999999999999e-189 < x < -1.46000000000000009e-245

   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 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-neg-frac 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 79.3%

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

      1. *-commutative 79.3%

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

   9. Simplified 79.3%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+19}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-8}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-102}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-189}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.46 \cdot 10^{-245}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-36}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-14}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 42000000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4: 62.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+19}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-102}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-36}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-13}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1e+19)
   -1.0
   (if (<= x -1.3e-7)
     1.0
     (if (<= x -3.5e-102)
       (* x 0.5)
       (if (<= x 1.1e-36)
         1.0
         (if (<= x 1.45e-13) (* x 0.5) (if (<= x 2.7e+14) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1e+19) {
		tmp = -1.0;
	} else if (x <= -1.3e-7) {
		tmp = 1.0;
	} else if (x <= -3.5e-102) {
		tmp = x * 0.5;
	} else if (x <= 1.1e-36) {
		tmp = 1.0;
	} else if (x <= 1.45e-13) {
		tmp = x * 0.5;
	} else if (x <= 2.7e+14) {
		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 <= (-1d+19)) then
        tmp = -1.0d0
    else if (x <= (-1.3d-7)) then
        tmp = 1.0d0
    else if (x <= (-3.5d-102)) then
        tmp = x * 0.5d0
    else if (x <= 1.1d-36) then
        tmp = 1.0d0
    else if (x <= 1.45d-13) then
        tmp = x * 0.5d0
    else if (x <= 2.7d+14) 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 <= -1e+19) {
		tmp = -1.0;
	} else if (x <= -1.3e-7) {
		tmp = 1.0;
	} else if (x <= -3.5e-102) {
		tmp = x * 0.5;
	} else if (x <= 1.1e-36) {
		tmp = 1.0;
	} else if (x <= 1.45e-13) {
		tmp = x * 0.5;
	} else if (x <= 2.7e+14) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1e+19:
		tmp = -1.0
	elif x <= -1.3e-7:
		tmp = 1.0
	elif x <= -3.5e-102:
		tmp = x * 0.5
	elif x <= 1.1e-36:
		tmp = 1.0
	elif x <= 1.45e-13:
		tmp = x * 0.5
	elif x <= 2.7e+14:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1e+19)
		tmp = -1.0;
	elseif (x <= -1.3e-7)
		tmp = 1.0;
	elseif (x <= -3.5e-102)
		tmp = Float64(x * 0.5);
	elseif (x <= 1.1e-36)
		tmp = 1.0;
	elseif (x <= 1.45e-13)
		tmp = Float64(x * 0.5);
	elseif (x <= 2.7e+14)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1e+19)
		tmp = -1.0;
	elseif (x <= -1.3e-7)
		tmp = 1.0;
	elseif (x <= -3.5e-102)
		tmp = x * 0.5;
	elseif (x <= 1.1e-36)
		tmp = 1.0;
	elseif (x <= 1.45e-13)
		tmp = x * 0.5;
	elseif (x <= 2.7e+14)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1e+19], -1.0, If[LessEqual[x, -1.3e-7], 1.0, If[LessEqual[x, -3.5e-102], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 1.1e-36], 1.0, If[LessEqual[x, 1.45e-13], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 2.7e+14], 1.0, -1.0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1e19 or 2.7e14 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 82.7%

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

   if -1e19 < x < -1.29999999999999999e-7 or -3.49999999999999986e-102 < x < 1.1e-36 or 1.4499999999999999e-13 < x < 2.7e14

   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 60.1%

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

   if -1.29999999999999999e-7 < x < -3.49999999999999986e-102 or 1.1e-36 < x < 1.4499999999999999e-13

   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 74.6%

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

   5. Taylor expanded in x around 0 71.7%

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

      1. *-commutative 71.7%

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

   7. Simplified 71.7%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+19}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-102}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-36}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-13}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -2 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-100}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+29}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= y -2e+37)
     1.0
     (if (<= y -3.1e-15)
       t_0
       (if (<= y -1.9e-100) (* y -0.5) (if (<= y 6.1e+29) t_0 1.0))))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -2e+37) {
		tmp = 1.0;
	} else if (y <= -3.1e-15) {
		tmp = t_0;
	} else if (y <= -1.9e-100) {
		tmp = y * -0.5;
	} else if (y <= 6.1e+29) {
		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 = x / (2.0d0 - x)
    if (y <= (-2d+37)) then
        tmp = 1.0d0
    else if (y <= (-3.1d-15)) then
        tmp = t_0
    else if (y <= (-1.9d-100)) then
        tmp = y * (-0.5d0)
    else if (y <= 6.1d+29) 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 = x / (2.0 - x);
	double tmp;
	if (y <= -2e+37) {
		tmp = 1.0;
	} else if (y <= -3.1e-15) {
		tmp = t_0;
	} else if (y <= -1.9e-100) {
		tmp = y * -0.5;
	} else if (y <= 6.1e+29) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if y <= -2e+37:
		tmp = 1.0
	elif y <= -3.1e-15:
		tmp = t_0
	elif y <= -1.9e-100:
		tmp = y * -0.5
	elif y <= 6.1e+29:
		tmp = t_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 <= -2e+37)
		tmp = 1.0;
	elseif (y <= -3.1e-15)
		tmp = t_0;
	elseif (y <= -1.9e-100)
		tmp = Float64(y * -0.5);
	elseif (y <= 6.1e+29)
		tmp = t_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 <= -2e+37)
		tmp = 1.0;
	elseif (y <= -3.1e-15)
		tmp = t_0;
	elseif (y <= -1.9e-100)
		tmp = y * -0.5;
	elseif (y <= 6.1e+29)
		tmp = t_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, -2e+37], 1.0, If[LessEqual[y, -3.1e-15], t$95$0, If[LessEqual[y, -1.9e-100], N[(y * -0.5), $MachinePrecision], If[LessEqual[y, 6.1e+29], t$95$0, 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.99999999999999991e37 or 6.0999999999999998e29 < 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 79.0%

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

   if -1.99999999999999991e37 < y < -3.0999999999999999e-15 or -1.89999999999999999e-100 < y < 6.0999999999999998e29

   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 80.7%

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

   if -3.0999999999999999e-15 < y < -1.89999999999999999e-100

   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 66.3%

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

      1. mul-1-neg 66.3%

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

      2. distribute-neg-frac 66.3%

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

   6. Simplified 66.3%

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

   7. Taylor expanded in y around 0 66.2%

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

      1. *-commutative 66.2%

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

   9. Simplified 66.2%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+37}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-15}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-100}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 73.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y + -2}\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+20}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-33}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-100}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-36}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ y -2.0))))
   (if (<= x -1.9e+20)
     -1.0
     (if (<= x -6.5e-33)
       t_0
       (if (<= x -4.4e-100)
         (* x 0.5)
         (if (<= x 1.15e-36) t_0 (/ x (- 2.0 x))))))))

C

double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double tmp;
	if (x <= -1.9e+20) {
		tmp = -1.0;
	} else if (x <= -6.5e-33) {
		tmp = t_0;
	} else if (x <= -4.4e-100) {
		tmp = x * 0.5;
	} else if (x <= 1.15e-36) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = y / (y + (-2.0d0))
    if (x <= (-1.9d+20)) then
        tmp = -1.0d0
    else if (x <= (-6.5d-33)) then
        tmp = t_0
    else if (x <= (-4.4d-100)) then
        tmp = x * 0.5d0
    else if (x <= 1.15d-36) then
        tmp = t_0
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double tmp;
	if (x <= -1.9e+20) {
		tmp = -1.0;
	} else if (x <= -6.5e-33) {
		tmp = t_0;
	} else if (x <= -4.4e-100) {
		tmp = x * 0.5;
	} else if (x <= 1.15e-36) {
		tmp = t_0;
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (y + -2.0)
	tmp = 0
	if x <= -1.9e+20:
		tmp = -1.0
	elif x <= -6.5e-33:
		tmp = t_0
	elif x <= -4.4e-100:
		tmp = x * 0.5
	elif x <= 1.15e-36:
		tmp = t_0
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y + -2.0))
	tmp = 0.0
	if (x <= -1.9e+20)
		tmp = -1.0;
	elseif (x <= -6.5e-33)
		tmp = t_0;
	elseif (x <= -4.4e-100)
		tmp = Float64(x * 0.5);
	elseif (x <= 1.15e-36)
		tmp = t_0;
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (y + -2.0);
	tmp = 0.0;
	if (x <= -1.9e+20)
		tmp = -1.0;
	elseif (x <= -6.5e-33)
		tmp = t_0;
	elseif (x <= -4.4e-100)
		tmp = x * 0.5;
	elseif (x <= 1.15e-36)
		tmp = t_0;
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.9e+20], -1.0, If[LessEqual[x, -6.5e-33], t$95$0, If[LessEqual[x, -4.4e-100], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 1.15e-36], t$95$0, N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.9e20

   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 84.1%

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

   if -1.9e20 < x < -6.4999999999999993e-33 or -4.39999999999999978e-100 < x < 1.14999999999999998e-36

   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 85.1%

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

      1. mul-1-neg 85.1%

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

      2. distribute-neg-frac 85.1%

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

   6. Simplified 85.1%

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

      1. frac-2neg 85.1%

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

      2. div-inv 85.0%

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

      3. remove-double-neg 85.0%

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

      4. sub-neg 85.0%

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

      5. distribute-neg-in 85.0%

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

      6. metadata-eval 85.0%

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

      7. remove-double-neg 85.0%

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

   8. Applied egg-rr 85.0%

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

      1. associate-*r/ 85.1%

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

      2. *-rgt-identity 85.1%

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

      3. +-commutative 85.1%

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

   10. Simplified 85.1%

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

   if -6.4999999999999993e-33 < x < -4.39999999999999978e-100

   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 75.4%

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

   5. Taylor expanded in x around 0 75.4%

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

      1. *-commutative 75.4%

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

   7. Simplified 75.4%

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

   if 1.14999999999999998e-36 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 76.9%

      \[\leadsto \color{blue}{\frac{x}{2 - x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+20}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-33}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-100}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 7: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y + -2}\\ \mathbf{if}\;x \leq -2.35 \cdot 10^{+21}:\\ \;\;\;\;\frac{y + \left(y + -2\right)}{x} + -1\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-33}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-100}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-36}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ y -2.0))))
   (if (<= x -2.35e+21)
     (+ (/ (+ y (+ y -2.0)) x) -1.0)
     (if (<= x -7e-33)
       t_0
       (if (<= x -4.4e-100)
         (* x 0.5)
         (if (<= x 1.3e-36) t_0 (/ x (- 2.0 x))))))))

C

double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double tmp;
	if (x <= -2.35e+21) {
		tmp = ((y + (y + -2.0)) / x) + -1.0;
	} else if (x <= -7e-33) {
		tmp = t_0;
	} else if (x <= -4.4e-100) {
		tmp = x * 0.5;
	} else if (x <= 1.3e-36) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = y / (y + (-2.0d0))
    if (x <= (-2.35d+21)) then
        tmp = ((y + (y + (-2.0d0))) / x) + (-1.0d0)
    else if (x <= (-7d-33)) then
        tmp = t_0
    else if (x <= (-4.4d-100)) then
        tmp = x * 0.5d0
    else if (x <= 1.3d-36) then
        tmp = t_0
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (y + -2.0);
	double tmp;
	if (x <= -2.35e+21) {
		tmp = ((y + (y + -2.0)) / x) + -1.0;
	} else if (x <= -7e-33) {
		tmp = t_0;
	} else if (x <= -4.4e-100) {
		tmp = x * 0.5;
	} else if (x <= 1.3e-36) {
		tmp = t_0;
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (y + -2.0)
	tmp = 0
	if x <= -2.35e+21:
		tmp = ((y + (y + -2.0)) / x) + -1.0
	elif x <= -7e-33:
		tmp = t_0
	elif x <= -4.4e-100:
		tmp = x * 0.5
	elif x <= 1.3e-36:
		tmp = t_0
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y + -2.0))
	tmp = 0.0
	if (x <= -2.35e+21)
		tmp = Float64(Float64(Float64(y + Float64(y + -2.0)) / x) + -1.0);
	elseif (x <= -7e-33)
		tmp = t_0;
	elseif (x <= -4.4e-100)
		tmp = Float64(x * 0.5);
	elseif (x <= 1.3e-36)
		tmp = t_0;
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (y + -2.0);
	tmp = 0.0;
	if (x <= -2.35e+21)
		tmp = ((y + (y + -2.0)) / x) + -1.0;
	elseif (x <= -7e-33)
		tmp = t_0;
	elseif (x <= -4.4e-100)
		tmp = x * 0.5;
	elseif (x <= 1.3e-36)
		tmp = t_0;
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.35e+21], N[(N[(N[(y + N[(y + -2.0), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[x, -7e-33], t$95$0, If[LessEqual[x, -4.4e-100], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 1.3e-36], t$95$0, N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.35e21

   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 100.0%

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

      2. inv-pow 100.0%

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

      3. associate--l- 100.0%

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

   5. Applied egg-rr 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l- 100.0%

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

      3. div-sub 100.0%

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in x around -inf 85.1%

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

      1. sub-neg 85.1%

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

   10. Simplified 85.1%

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

   if -2.35e21 < x < -6.9999999999999997e-33 or -4.39999999999999978e-100 < x < 1.3e-36

   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 85.1%

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

      1. mul-1-neg 85.1%

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

      2. distribute-neg-frac 85.1%

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

   6. Simplified 85.1%

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

      1. frac-2neg 85.1%

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

      2. div-inv 85.0%

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

      3. remove-double-neg 85.0%

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

      4. sub-neg 85.0%

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

      5. distribute-neg-in 85.0%

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

      6. metadata-eval 85.0%

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

      7. remove-double-neg 85.0%

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

   8. Applied egg-rr 85.0%

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

      1. associate-*r/ 85.1%

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

      2. *-rgt-identity 85.1%

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

      3. +-commutative 85.1%

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

   10. Simplified 85.1%

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

   if -6.9999999999999997e-33 < x < -4.39999999999999978e-100

   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 75.4%

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

   5. Taylor expanded in x around 0 75.4%

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

      1. *-commutative 75.4%

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

   7. Simplified 75.4%

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

   if 1.3e-36 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 76.9%

      \[\leadsto \color{blue}{\frac{x}{2 - x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+21}:\\ \;\;\;\;\frac{y + \left(y + -2\right)}{x} + -1\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-33}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-100}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-36}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]

Alternative 8: 62.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+21}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 75000000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.02e+21) -1.0 (if (<= x 75000000000000.0) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.02e+21) {
		tmp = -1.0;
	} else if (x <= 75000000000000.0) {
		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 <= (-1.02d+21)) then
        tmp = -1.0d0
    else if (x <= 75000000000000.0d0) 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 <= -1.02e+21) {
		tmp = -1.0;
	} else if (x <= 75000000000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.02e+21:
		tmp = -1.0
	elif x <= 75000000000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.02e+21)
		tmp = -1.0;
	elseif (x <= 75000000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.02e+21)
		tmp = -1.0;
	elseif (x <= 75000000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.02e+21], -1.0, If[LessEqual[x, 75000000000000.0], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.02e21 or 7.5e13 < x

   1. Initial program 99.9%

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

      1. associate--r+ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 82.7%

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

   if -1.02e21 < x < 7.5e13

   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 54.0%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+21}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 75000000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 9: 37.7% 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 38.0%

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

5. Final simplification 38.0%

   \[\leadsto -1 \]

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 2023230 
(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))))