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

Percentage Accurate: 100.0% → 100.0%

Time: 8.6s

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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 2: 60.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+28}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-222}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-182}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-154}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-7}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 530000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.15e+28)
   -1.0
   (if (<= x 7.2e-222)
     1.0
     (if (<= x 1.7e-182)
       (* y -0.5)
       (if (<= x 4.8e-154)
         1.0
         (if (<= x 1.1e-7) (* x 0.5) (if (<= x 530000000000.0) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.15e+28) {
		tmp = -1.0;
	} else if (x <= 7.2e-222) {
		tmp = 1.0;
	} else if (x <= 1.7e-182) {
		tmp = y * -0.5;
	} else if (x <= 4.8e-154) {
		tmp = 1.0;
	} else if (x <= 1.1e-7) {
		tmp = x * 0.5;
	} else if (x <= 530000000000.0) {
		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 <= (-1.15d+28)) then
        tmp = -1.0d0
    else if (x <= 7.2d-222) then
        tmp = 1.0d0
    else if (x <= 1.7d-182) then
        tmp = y * (-0.5d0)
    else if (x <= 4.8d-154) then
        tmp = 1.0d0
    else if (x <= 1.1d-7) then
        tmp = x * 0.5d0
    else if (x <= 530000000000.0d0) 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 <= -1.15e+28) {
		tmp = -1.0;
	} else if (x <= 7.2e-222) {
		tmp = 1.0;
	} else if (x <= 1.7e-182) {
		tmp = y * -0.5;
	} else if (x <= 4.8e-154) {
		tmp = 1.0;
	} else if (x <= 1.1e-7) {
		tmp = x * 0.5;
	} else if (x <= 530000000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.15e+28:
		tmp = -1.0
	elif x <= 7.2e-222:
		tmp = 1.0
	elif x <= 1.7e-182:
		tmp = y * -0.5
	elif x <= 4.8e-154:
		tmp = 1.0
	elif x <= 1.1e-7:
		tmp = x * 0.5
	elif x <= 530000000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.15e+28)
		tmp = -1.0;
	elseif (x <= 7.2e-222)
		tmp = 1.0;
	elseif (x <= 1.7e-182)
		tmp = Float64(y * -0.5);
	elseif (x <= 4.8e-154)
		tmp = 1.0;
	elseif (x <= 1.1e-7)
		tmp = Float64(x * 0.5);
	elseif (x <= 530000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.15e+28)
		tmp = -1.0;
	elseif (x <= 7.2e-222)
		tmp = 1.0;
	elseif (x <= 1.7e-182)
		tmp = y * -0.5;
	elseif (x <= 4.8e-154)
		tmp = 1.0;
	elseif (x <= 1.1e-7)
		tmp = x * 0.5;
	elseif (x <= 530000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.15e+28], -1.0, If[LessEqual[x, 7.2e-222], 1.0, If[LessEqual[x, 1.7e-182], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 4.8e-154], 1.0, If[LessEqual[x, 1.1e-7], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 530000000000.0], 1.0, -1.0]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.14999999999999992e28 or 5.3e11 < x

   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. Add Preprocessing

   5. Taylor expanded in x around inf 83.6%

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

   if -1.14999999999999992e28 < x < 7.19999999999999948e-222 or 1.69999999999999995e-182 < x < 4.79999999999999974e-154 or 1.1000000000000001e-7 < x < 5.3e11

   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. Add Preprocessing

   5. Taylor expanded in y around inf 59.7%

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

   if 7.19999999999999948e-222 < x < 1.69999999999999995e-182

   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. Add Preprocessing

   5. Taylor expanded in x around 0 77.0%

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

      1. associate-*r/ 77.0%

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

      2. neg-mul-1 77.0%

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

   7. Simplified 77.0%

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

   8. Taylor expanded in y around 0 77.0%

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

      1. *-commutative 77.0%

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

   10. Simplified 77.0%

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

   if 4.79999999999999974e-154 < x < 1.1000000000000001e-7

   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. Add Preprocessing

   5. Taylor expanded in y around 0 48.6%

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

   6. Taylor expanded in x around 0 47.2%

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

      1. *-commutative 47.2%

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

   8. Simplified 47.2%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+28}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-222}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-182}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-154}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-7}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 530000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+27}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-153}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-7}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 820000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.7e+27)
   -1.0
   (if (<= x 3.4e-153)
     1.0
     (if (<= x 1.1e-7) (* x 0.5) (if (<= x 820000000000.0) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.7e+27) {
		tmp = -1.0;
	} else if (x <= 3.4e-153) {
		tmp = 1.0;
	} else if (x <= 1.1e-7) {
		tmp = x * 0.5;
	} else if (x <= 820000000000.0) {
		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 <= (-3.7d+27)) then
        tmp = -1.0d0
    else if (x <= 3.4d-153) then
        tmp = 1.0d0
    else if (x <= 1.1d-7) then
        tmp = x * 0.5d0
    else if (x <= 820000000000.0d0) 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 <= -3.7e+27) {
		tmp = -1.0;
	} else if (x <= 3.4e-153) {
		tmp = 1.0;
	} else if (x <= 1.1e-7) {
		tmp = x * 0.5;
	} else if (x <= 820000000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.7e+27:
		tmp = -1.0
	elif x <= 3.4e-153:
		tmp = 1.0
	elif x <= 1.1e-7:
		tmp = x * 0.5
	elif x <= 820000000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.7e+27)
		tmp = -1.0;
	elseif (x <= 3.4e-153)
		tmp = 1.0;
	elseif (x <= 1.1e-7)
		tmp = Float64(x * 0.5);
	elseif (x <= 820000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.7e+27)
		tmp = -1.0;
	elseif (x <= 3.4e-153)
		tmp = 1.0;
	elseif (x <= 1.1e-7)
		tmp = x * 0.5;
	elseif (x <= 820000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.7e+27], -1.0, If[LessEqual[x, 3.4e-153], 1.0, If[LessEqual[x, 1.1e-7], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 820000000000.0], 1.0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.70000000000000002e27 or 8.2e11 < x

   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. Add Preprocessing

   5. Taylor expanded in x around inf 83.6%

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

   if -3.70000000000000002e27 < x < 3.3999999999999998e-153 or 1.1000000000000001e-7 < x < 8.2e11

   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. Add Preprocessing

   5. Taylor expanded in y around inf 56.6%

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

   if 3.3999999999999998e-153 < x < 1.1000000000000001e-7

   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. Add Preprocessing

   5. Taylor expanded in y around 0 48.6%

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

   6. Taylor expanded in x around 0 47.2%

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

      1. *-commutative 47.2%

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

   8. Simplified 47.2%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+27}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-153}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-7}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 820000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-17} \lor \neg \left(x \leq 6.5 \cdot 10^{-98}\right):\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.7e-17) (not (<= x 6.5e-98)))
   (/ x (- 2.0 x))
   (/ y (+ y -2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.7e-17) || !(x <= 6.5e-98)) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-3.7d-17)) .or. (.not. (x <= 6.5d-98))) then
        tmp = x / (2.0d0 - x)
    else
        tmp = y / (y + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -3.7e-17) || !(x <= 6.5e-98)) {
		tmp = x / (2.0 - x);
	} else {
		tmp = y / (y + -2.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.7e-17) or not (x <= 6.5e-98):
		tmp = x / (2.0 - x)
	else:
		tmp = y / (y + -2.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.7e-17) || !(x <= 6.5e-98))
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = Float64(y / Float64(y + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -3.7e-17) || ~((x <= 6.5e-98)))
		tmp = x / (2.0 - x);
	else
		tmp = y / (y + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.7e-17], N[Not[LessEqual[x, 6.5e-98]], $MachinePrecision]], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6999999999999997e-17 or 6.50000000000000017e-98 < 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. Add Preprocessing

   5. Taylor expanded in y around 0 77.8%

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

   if -3.6999999999999997e-17 < x < 6.50000000000000017e-98

   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. Add Preprocessing

   5. Taylor expanded in x around 0 83.3%

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

      1. associate-*r/ 83.3%

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

      2. neg-mul-1 83.3%

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

   7. Simplified 83.3%

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

      1. frac-2neg 83.3%

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

      2. div-inv 83.2%

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

      3. remove-double-neg 83.2%

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

      4. sub-neg 83.2%

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

      5. distribute-neg-in 83.2%

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

      6. metadata-eval 83.2%

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

      7. remove-double-neg 83.2%

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

   9. Applied egg-rr 83.2%

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

       1. associate-*r/ 83.3%

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

       2. *-rgt-identity 83.3%

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

       3. +-commutative 83.3%

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

   11. Simplified 83.3%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-17} \lor \neg \left(x \leq 6.5 \cdot 10^{-98}\right):\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + -2}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+90}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 29000000:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.8e+90) 1.0 (if (<= y 29000000.0) (/ x (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.8e+90) {
		tmp = 1.0;
	} else if (y <= 29000000.0) {
		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 <= (-6.8d+90)) then
        tmp = 1.0d0
    else if (y <= 29000000.0d0) 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 <= -6.8e+90) {
		tmp = 1.0;
	} else if (y <= 29000000.0) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6.8e+90:
		tmp = 1.0
	elif y <= 29000000.0:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6.8e+90)
		tmp = 1.0;
	elseif (y <= 29000000.0)
		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 <= -6.8e+90)
		tmp = 1.0;
	elseif (y <= 29000000.0)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6.8e+90], 1.0, If[LessEqual[y, 29000000.0], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -6.80000000000000036e90 or 2.9e7 < y

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 78.5%

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

   if -6.80000000000000036e90 < y < 2.9e7

   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. Add Preprocessing

   5. Taylor expanded in y around 0 73.6%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+90}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 29000000:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-18}:\\ \;\;\;\;\frac{1}{\frac{2}{x} + -1}\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-97}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5.7e-18)
   (/ 1.0 (+ (/ 2.0 x) -1.0))
   (if (<= x 1.02e-97) (/ y (+ y -2.0)) (/ x (- 2.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.7e-18) {
		tmp = 1.0 / ((2.0 / x) + -1.0);
	} else if (x <= 1.02e-97) {
		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 <= (-5.7d-18)) then
        tmp = 1.0d0 / ((2.0d0 / x) + (-1.0d0))
    else if (x <= 1.02d-97) 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 <= -5.7e-18) {
		tmp = 1.0 / ((2.0 / x) + -1.0);
	} else if (x <= 1.02e-97) {
		tmp = y / (y + -2.0);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.7e-18:
		tmp = 1.0 / ((2.0 / x) + -1.0)
	elif x <= 1.02e-97:
		tmp = y / (y + -2.0)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.7e-18)
		tmp = Float64(1.0 / Float64(Float64(2.0 / x) + -1.0));
	elseif (x <= 1.02e-97)
		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 <= -5.7e-18)
		tmp = 1.0 / ((2.0 / x) + -1.0);
	elseif (x <= 1.02e-97)
		tmp = y / (y + -2.0);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.7e-18], N[(1.0 / N[(N[(2.0 / x), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.02e-97], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.69999999999999971e-18

   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. Add Preprocessing

   5. Taylor expanded in y around 0 83.6%

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

      1. clear-num 83.6%

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

      2. inv-pow 83.6%

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

   7. Applied egg-rr 83.6%

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

      1. unpow-1 83.6%

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

      2. div-sub 83.7%

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

      3. sub-neg 83.7%

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

      4. *-inverses 83.7%

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

      5. metadata-eval 83.7%

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

   9. Simplified 83.7%

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

   if -5.69999999999999971e-18 < x < 1.02000000000000004e-97

   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. Add Preprocessing

   5. Taylor expanded in x around 0 83.3%

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

      1. associate-*r/ 83.3%

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

      2. neg-mul-1 83.3%

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

   7. Simplified 83.3%

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

      1. frac-2neg 83.3%

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

      2. div-inv 83.2%

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

      3. remove-double-neg 83.2%

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

      4. sub-neg 83.2%

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

      5. distribute-neg-in 83.2%

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

      6. metadata-eval 83.2%

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

      7. remove-double-neg 83.2%

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

   9. Applied egg-rr 83.2%

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

       1. associate-*r/ 83.3%

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

       2. *-rgt-identity 83.3%

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

       3. +-commutative 83.3%

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

   11. Simplified 83.3%

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

   if 1.02000000000000004e-97 < x

   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. Add Preprocessing

   5. Taylor expanded in y around 0 73.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-18}:\\ \;\;\;\;\frac{1}{\frac{2}{x} + -1}\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-97}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+27}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 112000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.6e+27) -1.0 (if (<= x 112000000000.0) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.6e+27) {
		tmp = -1.0;
	} else if (x <= 112000000000.0) {
		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 <= (-9.6d+27)) then
        tmp = -1.0d0
    else if (x <= 112000000000.0d0) 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 <= -9.6e+27) {
		tmp = -1.0;
	} else if (x <= 112000000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.6e+27:
		tmp = -1.0
	elif x <= 112000000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.6e+27)
		tmp = -1.0;
	elseif (x <= 112000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9.6e+27)
		tmp = -1.0;
	elseif (x <= 112000000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.6e+27], -1.0, If[LessEqual[x, 112000000000.0], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -9.59999999999999991e27 or 1.12e11 < x

   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. Add Preprocessing

   5. Taylor expanded in x around inf 83.6%

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

   if -9.59999999999999991e27 < x < 1.12e11

   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. Add Preprocessing

   5. Taylor expanded in y around inf 51.3%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.6 \cdot 10^{+27}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 112000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.3% 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. Add Preprocessing

5. Taylor expanded in x around inf 41.1%

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

6. Final simplification 41.1%

   \[\leadsto -1 \]
7. Add Preprocessing

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 2024034 
(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))))