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

Percentage Accurate: 100.0% → 100.0%

Time: 4.0s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00325:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+57}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.00325)
   (/ x (- 2.0 x))
   (if (<= x 1.05e+57) (/ (- x y) (- 2.0 y)) (+ (/ y x) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.00325) {
		tmp = x / (2.0 - x);
	} else if (x <= 1.05e+57) {
		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 <= (-0.00325d0)) then
        tmp = x / (2.0d0 - x)
    else if (x <= 1.05d+57) 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 <= -0.00325) {
		tmp = x / (2.0 - x);
	} else if (x <= 1.05e+57) {
		tmp = (x - y) / (2.0 - y);
	} else {
		tmp = (y / x) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.00325:
		tmp = x / (2.0 - x)
	elif x <= 1.05e+57:
		tmp = (x - y) / (2.0 - y)
	else:
		tmp = (y / x) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.00325)
		tmp = Float64(x / Float64(2.0 - x));
	elseif (x <= 1.05e+57)
		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 <= -0.00325)
		tmp = x / (2.0 - x);
	elseif (x <= 1.05e+57)
		tmp = (x - y) / (2.0 - y);
	else
		tmp = (y / x) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.00325], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e+57], 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 < -0.00324999999999999985

   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 74.8%

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

   if -0.00324999999999999985 < x < 1.04999999999999995e57

   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 94.2%

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

   if 1.04999999999999995e57 < 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 81.4%

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

      1. neg-mul-1 81.4%

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

   6. Simplified 81.4%

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

   7. Taylor expanded in x around 0 81.4%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.00325:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+57}:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]

Alternative 3: 60.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+59}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-249}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-219}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+59}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.3e+59)
   1.0
   (if (<= y 1.55e-249)
     -1.0
     (if (<= y 5.2e-219) (* x 0.5) (if (<= y 1.45e+59) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.3e+59) {
		tmp = 1.0;
	} else if (y <= 1.55e-249) {
		tmp = -1.0;
	} else if (y <= 5.2e-219) {
		tmp = x * 0.5;
	} else if (y <= 1.45e+59) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-3.3d+59)) then
        tmp = 1.0d0
    else if (y <= 1.55d-249) then
        tmp = -1.0d0
    else if (y <= 5.2d-219) then
        tmp = x * 0.5d0
    else if (y <= 1.45d+59) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.3e+59) {
		tmp = 1.0;
	} else if (y <= 1.55e-249) {
		tmp = -1.0;
	} else if (y <= 5.2e-219) {
		tmp = x * 0.5;
	} else if (y <= 1.45e+59) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.3e+59:
		tmp = 1.0
	elif y <= 1.55e-249:
		tmp = -1.0
	elif y <= 5.2e-219:
		tmp = x * 0.5
	elif y <= 1.45e+59:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.3e+59)
		tmp = 1.0;
	elseif (y <= 1.55e-249)
		tmp = -1.0;
	elseif (y <= 5.2e-219)
		tmp = Float64(x * 0.5);
	elseif (y <= 1.45e+59)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.3e+59)
		tmp = 1.0;
	elseif (y <= 1.55e-249)
		tmp = -1.0;
	elseif (y <= 5.2e-219)
		tmp = x * 0.5;
	elseif (y <= 1.45e+59)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.3e+59], 1.0, If[LessEqual[y, 1.55e-249], -1.0, If[LessEqual[y, 5.2e-219], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 1.45e+59], -1.0, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2999999999999999e59 or 1.44999999999999995e59 < 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 87.3%

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

   if -3.2999999999999999e59 < y < 1.54999999999999993e-249 or 5.20000000000000004e-219 < y < 1.44999999999999995e59

   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 55.5%

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

   if 1.54999999999999993e-249 < y < 5.20000000000000004e-219

   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 0 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+59}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-249}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-219}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{+59}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+59}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-250}:\\ \;\;\;\;-1 + \frac{-2}{x}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-219}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+56}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.5e+59)
   1.0
   (if (<= y 4.1e-250)
     (+ -1.0 (/ -2.0 x))
     (if (<= y 5.4e-219) (* x 0.5) (if (<= y 7.5e+56) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.5e+59) {
		tmp = 1.0;
	} else if (y <= 4.1e-250) {
		tmp = -1.0 + (-2.0 / x);
	} else if (y <= 5.4e-219) {
		tmp = x * 0.5;
	} else if (y <= 7.5e+56) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-5.5d+59)) then
        tmp = 1.0d0
    else if (y <= 4.1d-250) then
        tmp = (-1.0d0) + ((-2.0d0) / x)
    else if (y <= 5.4d-219) then
        tmp = x * 0.5d0
    else if (y <= 7.5d+56) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5.5e+59) {
		tmp = 1.0;
	} else if (y <= 4.1e-250) {
		tmp = -1.0 + (-2.0 / x);
	} else if (y <= 5.4e-219) {
		tmp = x * 0.5;
	} else if (y <= 7.5e+56) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.5e+59:
		tmp = 1.0
	elif y <= 4.1e-250:
		tmp = -1.0 + (-2.0 / x)
	elif y <= 5.4e-219:
		tmp = x * 0.5
	elif y <= 7.5e+56:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.5e+59)
		tmp = 1.0;
	elseif (y <= 4.1e-250)
		tmp = Float64(-1.0 + Float64(-2.0 / x));
	elseif (y <= 5.4e-219)
		tmp = Float64(x * 0.5);
	elseif (y <= 7.5e+56)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.5e+59)
		tmp = 1.0;
	elseif (y <= 4.1e-250)
		tmp = -1.0 + (-2.0 / x);
	elseif (y <= 5.4e-219)
		tmp = x * 0.5;
	elseif (y <= 7.5e+56)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.5e+59], 1.0, If[LessEqual[y, 4.1e-250], N[(-1.0 + N[(-2.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e-219], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 7.5e+56], -1.0, 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.4999999999999999e59 or 7.4999999999999999e56 < 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 87.3%

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

   if -5.4999999999999999e59 < y < 4.10000000000000016e-250

   1. Initial program 100.0%

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

      1. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 77.7%

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

   5. Taylor expanded in x around inf 58.9%

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

      1. distribute-neg-in 58.9%

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

      2. metadata-eval 58.9%

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

      3. associate-*r/ 58.9%

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

      4. metadata-eval 58.9%

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

      5. distribute-neg-frac 58.9%

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

      6. metadata-eval 58.9%

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

   7. Simplified 58.9%

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

   if 4.10000000000000016e-250 < y < 5.3999999999999999e-219

   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 0 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if 5.3999999999999999e-219 < y < 7.4999999999999999e56

   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 51.4%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+59}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-250}:\\ \;\;\;\;-1 + \frac{-2}{x}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-219}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+56}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 60.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+59}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-249}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-219}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{+58}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.6e+59)
   1.0
   (if (<= y 1.85e-249)
     (+ (/ y x) -1.0)
     (if (<= y 5.4e-219) (* x 0.5) (if (<= y 1.04e+58) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.6e+59) {
		tmp = 1.0;
	} else if (y <= 1.85e-249) {
		tmp = (y / x) + -1.0;
	} else if (y <= 5.4e-219) {
		tmp = x * 0.5;
	} else if (y <= 1.04e+58) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-4.6d+59)) then
        tmp = 1.0d0
    else if (y <= 1.85d-249) then
        tmp = (y / x) + (-1.0d0)
    else if (y <= 5.4d-219) then
        tmp = x * 0.5d0
    else if (y <= 1.04d+58) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.6e+59) {
		tmp = 1.0;
	} else if (y <= 1.85e-249) {
		tmp = (y / x) + -1.0;
	} else if (y <= 5.4e-219) {
		tmp = x * 0.5;
	} else if (y <= 1.04e+58) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.6e+59:
		tmp = 1.0
	elif y <= 1.85e-249:
		tmp = (y / x) + -1.0
	elif y <= 5.4e-219:
		tmp = x * 0.5
	elif y <= 1.04e+58:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.6e+59)
		tmp = 1.0;
	elseif (y <= 1.85e-249)
		tmp = Float64(Float64(y / x) + -1.0);
	elseif (y <= 5.4e-219)
		tmp = Float64(x * 0.5);
	elseif (y <= 1.04e+58)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.6e+59)
		tmp = 1.0;
	elseif (y <= 1.85e-249)
		tmp = (y / x) + -1.0;
	elseif (y <= 5.4e-219)
		tmp = x * 0.5;
	elseif (y <= 1.04e+58)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.6e+59], 1.0, If[LessEqual[y, 1.85e-249], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[y, 5.4e-219], N[(x * 0.5), $MachinePrecision], If[LessEqual[y, 1.04e+58], -1.0, 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.60000000000000016e59 or 1.04e58 < 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 87.3%

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

   if -4.60000000000000016e59 < y < 1.84999999999999988e-249

   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 59.1%

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

      1. neg-mul-1 59.1%

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

   6. Simplified 59.1%

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

   7. Taylor expanded in x around 0 59.1%

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

   if 1.84999999999999988e-249 < y < 5.3999999999999999e-219

   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 0 100.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if 5.3999999999999999e-219 < y < 1.04e58

   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 51.4%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{+59}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-249}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-219}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{+58}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+60}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+78}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.42e+60) 1.0 (if (<= y 8.2e+78) (/ x (- 2.0 x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.42e+60) {
		tmp = 1.0;
	} else if (y <= 8.2e+78) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.42d+60)) then
        tmp = 1.0d0
    else if (y <= 8.2d+78) then
        tmp = x / (2.0d0 - x)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.42e+60) {
		tmp = 1.0;
	} else if (y <= 8.2e+78) {
		tmp = x / (2.0 - x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.42e+60:
		tmp = 1.0
	elif y <= 8.2e+78:
		tmp = x / (2.0 - x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.42e+60)
		tmp = 1.0;
	elseif (y <= 8.2e+78)
		tmp = Float64(x / Float64(2.0 - x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.42e+60)
		tmp = 1.0;
	elseif (y <= 8.2e+78)
		tmp = x / (2.0 - x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.42e+60], 1.0, If[LessEqual[y, 8.2e+78], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.42000000000000001e60 or 8.1999999999999994e78 < 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 88.1%

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

   if -1.42000000000000001e60 < y < 8.1999999999999994e78

   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 72.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{+60}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{+78}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 60.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+59}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+68}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.9e+59) 1.0 (if (<= y 1.25e+68) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.9e+59) {
		tmp = 1.0;
	} else if (y <= 1.25e+68) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-3.9d+59)) then
        tmp = 1.0d0
    else if (y <= 1.25d+68) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.9e+59) {
		tmp = 1.0;
	} else if (y <= 1.25e+68) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.9e+59:
		tmp = 1.0
	elif y <= 1.25e+68:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.9e+59)
		tmp = 1.0;
	elseif (y <= 1.25e+68)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.9e+59)
		tmp = 1.0;
	elseif (y <= 1.25e+68)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.9e+59], 1.0, If[LessEqual[y, 1.25e+68], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.90000000000000021e59 or 1.2500000000000001e68 < 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 87.3%

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

   if -3.90000000000000021e59 < y < 1.2500000000000001e68

   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 53.5%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+59}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+68}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 38.7% 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 2023178 
(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))))