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

Percentage Accurate: 100.0% → 100.0%

Time: 7.0s

Alternatives: 10

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: 59.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} + -1\\ \mathbf{if}\;x \leq -0.84:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-68}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-243}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-192}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ y x) -1.0)))
   (if (<= x -0.84)
     t_0
     (if (<= x -2e-68)
       (* x 0.5)
       (if (<= x 4.5e-243)
         1.0
         (if (<= x 2.6e-192) (* y -0.5) (if (<= x 4.8e+70) 1.0 t_0)))))))

C

double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double tmp;
	if (x <= -0.84) {
		tmp = t_0;
	} else if (x <= -2e-68) {
		tmp = x * 0.5;
	} else if (x <= 4.5e-243) {
		tmp = 1.0;
	} else if (x <= 2.6e-192) {
		tmp = y * -0.5;
	} else if (x <= 4.8e+70) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y / x) + (-1.0d0)
    if (x <= (-0.84d0)) then
        tmp = t_0
    else if (x <= (-2d-68)) then
        tmp = x * 0.5d0
    else if (x <= 4.5d-243) then
        tmp = 1.0d0
    else if (x <= 2.6d-192) then
        tmp = y * (-0.5d0)
    else if (x <= 4.8d+70) then
        tmp = 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double tmp;
	if (x <= -0.84) {
		tmp = t_0;
	} else if (x <= -2e-68) {
		tmp = x * 0.5;
	} else if (x <= 4.5e-243) {
		tmp = 1.0;
	} else if (x <= 2.6e-192) {
		tmp = y * -0.5;
	} else if (x <= 4.8e+70) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / x) + -1.0
	tmp = 0
	if x <= -0.84:
		tmp = t_0
	elif x <= -2e-68:
		tmp = x * 0.5
	elif x <= 4.5e-243:
		tmp = 1.0
	elif x <= 2.6e-192:
		tmp = y * -0.5
	elif x <= 4.8e+70:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y / x) + -1.0)
	tmp = 0.0
	if (x <= -0.84)
		tmp = t_0;
	elseif (x <= -2e-68)
		tmp = Float64(x * 0.5);
	elseif (x <= 4.5e-243)
		tmp = 1.0;
	elseif (x <= 2.6e-192)
		tmp = Float64(y * -0.5);
	elseif (x <= 4.8e+70)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y / x) + -1.0;
	tmp = 0.0;
	if (x <= -0.84)
		tmp = t_0;
	elseif (x <= -2e-68)
		tmp = x * 0.5;
	elseif (x <= 4.5e-243)
		tmp = 1.0;
	elseif (x <= 2.6e-192)
		tmp = y * -0.5;
	elseif (x <= 4.8e+70)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision]}, If[LessEqual[x, -0.84], t$95$0, If[LessEqual[x, -2e-68], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 4.5e-243], 1.0, If[LessEqual[x, 2.6e-192], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 4.8e+70], 1.0, t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -0.839999999999999969 or 4.79999999999999974e70 < 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. Taylor expanded in x around inf 82.8%

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

      1. neg-mul-1 82.8%

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

   6. Simplified 82.8%

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

   7. Taylor expanded in x around 0 82.8%

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

   if -0.839999999999999969 < x < -2.00000000000000013e-68

   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 70.1%

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

   5. Taylor expanded in x around 0 66.2%

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

      1. *-commutative 66.2%

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

   7. Simplified 66.2%

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

   if -2.00000000000000013e-68 < x < 4.50000000000000017e-243 or 2.6000000000000002e-192 < x < 4.79999999999999974e70

   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 60.5%

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

   if 4.50000000000000017e-243 < x < 2.6000000000000002e-192

   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 71.1%

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

      1. associate-*r/ 71.1%

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

      2. neg-mul-1 71.1%

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

   6. Simplified 71.1%

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

   7. Taylor expanded in y around 0 57.3%

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

      1. *-commutative 57.3%

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

   9. Simplified 57.3%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.84:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-68}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-243}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-192}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]

Alternative 3: 98.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \lor \neg \left(x \leq 4.2 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x - y}{\left(-x\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.0) (not (<= x 4.2e-6)))
   (/ (- x y) (- (- x) y))
   (/ (- x y) (- 2.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.0) || !(x <= 4.2e-6)) {
		tmp = (x - y) / (-x - y);
	} else {
		tmp = (x - y) / (2.0 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-2.0d0)) .or. (.not. (x <= 4.2d-6))) then
        tmp = (x - y) / (-x - y)
    else
        tmp = (x - y) / (2.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.0) || !(x <= 4.2e-6)) {
		tmp = (x - y) / (-x - y);
	} else {
		tmp = (x - y) / (2.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.0) or not (x <= 4.2e-6):
		tmp = (x - y) / (-x - y)
	else:
		tmp = (x - y) / (2.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.0) || !(x <= 4.2e-6))
		tmp = Float64(Float64(x - y) / Float64(Float64(-x) - y));
	else
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.0) || ~((x <= 4.2e-6)))
		tmp = (x - y) / (-x - y);
	else
		tmp = (x - y) / (2.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.0], N[Not[LessEqual[x, 4.2e-6]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] / N[((-x) - y), $MachinePrecision]), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2 or 4.1999999999999996e-6 < 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. Step-by-step derivation

      1. flip-- 52.3%

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

      2. div-inv 52.2%

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

      3. fma-neg 52.2%

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

      4. metadata-eval 52.2%

         \[\leadsto \frac{x - y}{\mathsf{fma}\left(\color{blue}{4} - x \cdot x, \frac{1}{2 + x}, -y\right)} \]

      5. +-commutative 52.2%

         \[\leadsto \frac{x - y}{\mathsf{fma}\left(4 - x \cdot x, \frac{1}{\color{blue}{x + 2}}, -y\right)} \]

   5. Applied egg-rr 52.2%

      \[\leadsto \frac{x - y}{\color{blue}{\mathsf{fma}\left(4 - x \cdot x, \frac{1}{x + 2}, -y\right)}} \]
   6. Step-by-step derivation

      1. fma-neg 52.2%

         \[\leadsto \frac{x - y}{\color{blue}{\left(4 - x \cdot x\right) \cdot \frac{1}{x + 2} - y}} \]

      2. +-commutative 52.2%

         \[\leadsto \frac{x - y}{\left(4 - x \cdot x\right) \cdot \frac{1}{\color{blue}{2 + x}} - y} \]

   7. Simplified 52.2%

      \[\leadsto \frac{x - y}{\color{blue}{\left(4 - x \cdot x\right) \cdot \frac{1}{2 + x} - y}} \]

   8. Taylor expanded in x around inf 98.8%

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

      1. neg-mul-1 98.8%

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

   10. Simplified 98.8%

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

   if -2 < x < 4.1999999999999996e-6

   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 99.1%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \lor \neg \left(x \leq 4.2 \cdot 10^{-6}\right):\\ \;\;\;\;\frac{x - y}{\left(-x\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \end{array} \]

Alternative 4: 59.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-68}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-242}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-193}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.0)
   -1.0
   (if (<= x -1.45e-68)
     (* x 0.5)
     (if (<= x 1.4e-242)
       1.0
       (if (<= x 9e-193) (* y -0.5) (if (<= x 1.25e+72) 1.0 -1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.0) {
		tmp = -1.0;
	} else if (x <= -1.45e-68) {
		tmp = x * 0.5;
	} else if (x <= 1.4e-242) {
		tmp = 1.0;
	} else if (x <= 9e-193) {
		tmp = y * -0.5;
	} else if (x <= 1.25e+72) {
		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 <= (-2.0d0)) then
        tmp = -1.0d0
    else if (x <= (-1.45d-68)) then
        tmp = x * 0.5d0
    else if (x <= 1.4d-242) then
        tmp = 1.0d0
    else if (x <= 9d-193) then
        tmp = y * (-0.5d0)
    else if (x <= 1.25d+72) 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 <= -2.0) {
		tmp = -1.0;
	} else if (x <= -1.45e-68) {
		tmp = x * 0.5;
	} else if (x <= 1.4e-242) {
		tmp = 1.0;
	} else if (x <= 9e-193) {
		tmp = y * -0.5;
	} else if (x <= 1.25e+72) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.0:
		tmp = -1.0
	elif x <= -1.45e-68:
		tmp = x * 0.5
	elif x <= 1.4e-242:
		tmp = 1.0
	elif x <= 9e-193:
		tmp = y * -0.5
	elif x <= 1.25e+72:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.0)
		tmp = -1.0;
	elseif (x <= -1.45e-68)
		tmp = Float64(x * 0.5);
	elseif (x <= 1.4e-242)
		tmp = 1.0;
	elseif (x <= 9e-193)
		tmp = Float64(y * -0.5);
	elseif (x <= 1.25e+72)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.0)
		tmp = -1.0;
	elseif (x <= -1.45e-68)
		tmp = x * 0.5;
	elseif (x <= 1.4e-242)
		tmp = 1.0;
	elseif (x <= 9e-193)
		tmp = y * -0.5;
	elseif (x <= 1.25e+72)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.0], -1.0, If[LessEqual[x, -1.45e-68], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 1.4e-242], 1.0, If[LessEqual[x, 9e-193], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 1.25e+72], 1.0, -1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2 or 1.24999999999999998e72 < 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. Taylor expanded in x around inf 82.4%

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

   if -2 < x < -1.45e-68

   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 70.1%

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

   5. Taylor expanded in x around 0 66.2%

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

      1. *-commutative 66.2%

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

   7. Simplified 66.2%

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

   if -1.45e-68 < x < 1.39999999999999992e-242 or 8.9999999999999997e-193 < x < 1.24999999999999998e72

   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 60.5%

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

   if 1.39999999999999992e-242 < x < 8.9999999999999997e-193

   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 71.1%

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

      1. associate-*r/ 71.1%

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

      2. neg-mul-1 71.1%

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

   6. Simplified 71.1%

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

   7. Taylor expanded in y around 0 57.3%

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

      1. *-commutative 57.3%

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

   9. Simplified 57.3%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-68}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-242}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-193}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+72}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 5: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+72}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.5e-5)
   (/ x (- 2.0 x))
   (if (<= x 6e+72) (/ (- x y) (- 2.0 y)) (+ (/ y x) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.5e-5) {
		tmp = x / (2.0 - x);
	} else if (x <= 6e+72) {
		tmp = (x - y) / (2.0 - y);
	} else {
		tmp = (y / x) + -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 <= (-3.5d-5)) then
        tmp = x / (2.0d0 - x)
    else if (x <= 6d+72) then
        tmp = (x - y) / (2.0d0 - y)
    else
        tmp = (y / x) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.5e-5) {
		tmp = x / (2.0 - x);
	} else if (x <= 6e+72) {
		tmp = (x - y) / (2.0 - y);
	} else {
		tmp = (y / x) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.5e-5:
		tmp = x / (2.0 - x)
	elif x <= 6e+72:
		tmp = (x - y) / (2.0 - y)
	else:
		tmp = (y / x) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.5e-5)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (x <= 6e+72)
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	else
		tmp = Float64(Float64(y / x) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.5e-5)
		tmp = x / (2.0 - x);
	elseif (x <= 6e+72)
		tmp = (x - y) / (2.0 - y);
	else
		tmp = (y / x) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.5e-5], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e+72], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.4999999999999997e-5

   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 79.9%

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

   if -3.4999999999999997e-5 < x < 6.00000000000000006e72

   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 97.1%

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

   if 6.00000000000000006e72 < 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. Taylor expanded in x around inf 88.0%

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

      1. neg-mul-1 88.0%

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

   6. Simplified 88.0%

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

   7. Taylor expanded in x around 0 88.0%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-5}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+72}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]

Alternative 6: 74.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.0) 1.0 (if (<= y 8.5e+32) (/ x (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.0) {
		tmp = 1.0;
	} else if (y <= 8.5e+32) {
		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 <= (-2.0d0)) then
        tmp = 1.0d0
    else if (y <= 8.5d+32) 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 <= -2.0) {
		tmp = 1.0;
	} else if (y <= 8.5e+32) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.0:
		tmp = 1.0
	elif y <= 8.5e+32:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.0)
		tmp = 1.0;
	elseif (y <= 8.5e+32)
		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 <= -2.0)
		tmp = 1.0;
	elseif (y <= 8.5e+32)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.0], 1.0, If[LessEqual[y, 8.5e+32], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2 or 8.4999999999999998e32 < y

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 72.2%

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

   if -2 < y < 8.4999999999999998e32

   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 76.9%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.2e-68)
   (/ x (- 2.0 x))
   (if (<= x 2.3e+71) (/ y (+ y -2.0)) (+ (/ y x) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.2e-68) {
		tmp = x / (2.0 - x);
	} else if (x <= 2.3e+71) {
		tmp = y / (y + -2.0);
	} else {
		tmp = (y / x) + -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 <= (-2.2d-68)) then
        tmp = x / (2.0d0 - x)
    else if (x <= 2.3d+71) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = (y / x) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.2e-68) {
		tmp = x / (2.0 - x);
	} else if (x <= 2.3e+71) {
		tmp = y / (y + -2.0);
	} else {
		tmp = (y / x) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.2e-68:
		tmp = x / (2.0 - x)
	elif x <= 2.3e+71:
		tmp = y / (y + -2.0)
	else:
		tmp = (y / x) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.2e-68)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (x <= 2.3e+71)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = Float64(Float64(y / x) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.2e-68)
		tmp = x / (2.0 - x);
	elseif (x <= 2.3e+71)
		tmp = y / (y + -2.0);
	else
		tmp = (y / x) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.2e-68], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e+71], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.20000000000000002e-68

   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 77.8%

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

   if -2.20000000000000002e-68 < x < 2.3000000000000002e71

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 78.9%

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

      1. associate-*r/ 78.9%

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

      2. neg-mul-1 78.9%

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

   6. Simplified 78.9%

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

      1. frac-2neg 78.9%

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

      2. div-inv 78.7%

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

      3. remove-double-neg 78.7%

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

      4. sub-neg 78.7%

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

      5. distribute-neg-in 78.7%

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

      6. metadata-eval 78.7%

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

      7. remove-double-neg 78.7%

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

   8. Applied egg-rr 78.7%

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

      1. associate-*r/ 78.9%

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

      2. *-rgt-identity 78.9%

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

      3. +-commutative 78.9%

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

   10. Simplified 78.9%

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

   if 2.3000000000000002e71 < 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. Taylor expanded in x around inf 88.0%

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

      1. neg-mul-1 88.0%

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

   6. Simplified 88.0%

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

   7. Taylor expanded in x around 0 88.0%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-68}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]

Alternative 8: 60.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-68}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.0)
   -1.0
   (if (<= x -1.75e-68) (* x 0.5) (if (<= x 4.8e+70) 1.0 -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.0) {
		tmp = -1.0;
	} else if (x <= -1.75e-68) {
		tmp = x * 0.5;
	} else if (x <= 4.8e+70) {
		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 <= (-2.0d0)) then
        tmp = -1.0d0
    else if (x <= (-1.75d-68)) then
        tmp = x * 0.5d0
    else if (x <= 4.8d+70) 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 <= -2.0) {
		tmp = -1.0;
	} else if (x <= -1.75e-68) {
		tmp = x * 0.5;
	} else if (x <= 4.8e+70) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.0:
		tmp = -1.0
	elif x <= -1.75e-68:
		tmp = x * 0.5
	elif x <= 4.8e+70:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.0)
		tmp = -1.0;
	elseif (x <= -1.75e-68)
		tmp = Float64(x * 0.5);
	elseif (x <= 4.8e+70)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.0)
		tmp = -1.0;
	elseif (x <= -1.75e-68)
		tmp = x * 0.5;
	elseif (x <= 4.8e+70)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.0], -1.0, If[LessEqual[x, -1.75e-68], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 4.8e+70], 1.0, -1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -2 or 4.79999999999999974e70 < 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. Taylor expanded in x around inf 82.4%

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

   if -2 < x < -1.75000000000000006e-68

   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 70.1%

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

   5. Taylor expanded in x around 0 66.2%

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

      1. *-commutative 66.2%

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

   7. Simplified 66.2%

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

   if -1.75000000000000006e-68 < x < 4.79999999999999974e70

   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 55.3%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-68}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 9: 59.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-37}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -8.5e-37) -1.0 (if (<= x 5e+70) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -8.5e-37) {
		tmp = -1.0;
	} else if (x <= 5e+70) {
		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 <= (-8.5d-37)) then
        tmp = -1.0d0
    else if (x <= 5d+70) 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 <= -8.5e-37) {
		tmp = -1.0;
	} else if (x <= 5e+70) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -8.5e-37:
		tmp = -1.0
	elif x <= 5e+70:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -8.5e-37)
		tmp = -1.0;
	elseif (x <= 5e+70)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -8.5e-37)
		tmp = -1.0;
	elseif (x <= 5e+70)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -8.5e-37], -1.0, If[LessEqual[x, 5e+70], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5000000000000007e-37 or 5.0000000000000002e70 < 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. Taylor expanded in x around inf 78.2%

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

   if -8.5000000000000007e-37 < x < 5.0000000000000002e70

   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 53.1%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-37}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+70}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 10: 37.9% 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 40.2%

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

5. Final simplification 40.2%

   \[\leadsto -1 \]

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 2023214 
(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))))