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

Percentage Accurate: 100.0% → 100.0%

Time: 10.7s

Alternatives: 11

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: 62.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} + -1\\ \mathbf{if}\;x \leq -1 \cdot 10^{+14}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-54}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -5.7 \cdot 10^{-92}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+54}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ y x) -1.0)))
   (if (<= x -1e+14)
     t_0
     (if (<= x -4e-54)
       (- 1.0 (/ x y))
       (if (<= x -5.7e-92) (* x 0.5) (if (<= x 1.7e+54) 1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double tmp;
	if (x <= -1e+14) {
		tmp = t_0;
	} else if (x <= -4e-54) {
		tmp = 1.0 - (x / y);
	} else if (x <= -5.7e-92) {
		tmp = x * 0.5;
	} else if (x <= 1.7e+54) {
		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 <= (-1d+14)) then
        tmp = t_0
    else if (x <= (-4d-54)) then
        tmp = 1.0d0 - (x / y)
    else if (x <= (-5.7d-92)) then
        tmp = x * 0.5d0
    else if (x <= 1.7d+54) 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 <= -1e+14) {
		tmp = t_0;
	} else if (x <= -4e-54) {
		tmp = 1.0 - (x / y);
	} else if (x <= -5.7e-92) {
		tmp = x * 0.5;
	} else if (x <= 1.7e+54) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / x) + -1.0
	tmp = 0
	if x <= -1e+14:
		tmp = t_0
	elif x <= -4e-54:
		tmp = 1.0 - (x / y)
	elif x <= -5.7e-92:
		tmp = x * 0.5
	elif x <= 1.7e+54:
		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 <= -1e+14)
		tmp = t_0;
	elseif (x <= -4e-54)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (x <= -5.7e-92)
		tmp = Float64(x * 0.5);
	elseif (x <= 1.7e+54)
		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 <= -1e+14)
		tmp = t_0;
	elseif (x <= -4e-54)
		tmp = 1.0 - (x / y);
	elseif (x <= -5.7e-92)
		tmp = x * 0.5;
	elseif (x <= 1.7e+54)
		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, -1e+14], t$95$0, If[LessEqual[x, -4e-54], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.7e-92], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 1.7e+54], 1.0, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1e14 or 1.7e54 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 78.9%

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

      1. mul-1-neg 78.9%

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

   5. Simplified 78.9%

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

   6. Taylor expanded in x around 0 78.9%

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

   if -1e14 < x < -4.0000000000000001e-54

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 61.9%

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

      1. neg-mul-1 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in x around 0 61.9%

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

      1. mul-1-neg 61.9%

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

      2. unsub-neg 61.9%

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

   8. Simplified 61.9%

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

   if -4.0000000000000001e-54 < x < -5.70000000000000009e-92

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 61.4%

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

   4. Taylor expanded in x around 0 61.4%

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

      1. *-commutative 61.4%

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

   6. Simplified 61.4%

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

   if -5.70000000000000009e-92 < x < 1.7e54

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 62.0%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+14}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-54}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -5.7 \cdot 10^{-92}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+54}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -75000000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-54}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-92}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -75000000000000.0)
   -1.0
   (if (<= x -3.8e-54)
     1.0
     (if (<= x -2.5e-92) (* x 0.5) (if (<= x 2.7e+44) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -75000000000000.0) {
		tmp = -1.0;
	} else if (x <= -3.8e-54) {
		tmp = 1.0;
	} else if (x <= -2.5e-92) {
		tmp = x * 0.5;
	} else if (x <= 2.7e+44) {
		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 <= (-75000000000000.0d0)) then
        tmp = -1.0d0
    else if (x <= (-3.8d-54)) then
        tmp = 1.0d0
    else if (x <= (-2.5d-92)) then
        tmp = x * 0.5d0
    else if (x <= 2.7d+44) 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 <= -75000000000000.0) {
		tmp = -1.0;
	} else if (x <= -3.8e-54) {
		tmp = 1.0;
	} else if (x <= -2.5e-92) {
		tmp = x * 0.5;
	} else if (x <= 2.7e+44) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -75000000000000.0:
		tmp = -1.0
	elif x <= -3.8e-54:
		tmp = 1.0
	elif x <= -2.5e-92:
		tmp = x * 0.5
	elif x <= 2.7e+44:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -75000000000000.0)
		tmp = -1.0;
	elseif (x <= -3.8e-54)
		tmp = 1.0;
	elseif (x <= -2.5e-92)
		tmp = Float64(x * 0.5);
	elseif (x <= 2.7e+44)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -75000000000000.0)
		tmp = -1.0;
	elseif (x <= -3.8e-54)
		tmp = 1.0;
	elseif (x <= -2.5e-92)
		tmp = x * 0.5;
	elseif (x <= 2.7e+44)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -75000000000000.0], -1.0, If[LessEqual[x, -3.8e-54], 1.0, If[LessEqual[x, -2.5e-92], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 2.7e+44], 1.0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.5e13 or 2.7e44 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 78.3%

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

   if -7.5e13 < x < -3.8000000000000002e-54 or -2.50000000000000006e-92 < x < 2.7e44

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 62.0%

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

   if -3.8000000000000002e-54 < x < -2.50000000000000006e-92

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 61.4%

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

   4. Taylor expanded in x around 0 61.4%

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

      1. *-commutative 61.4%

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

   6. Simplified 61.4%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -75000000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-54}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-92}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -17200000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-53}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-92}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+45}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -17200000000000.0)
   -1.0
   (if (<= x -1.7e-53)
     (+ 1.0 (/ 2.0 y))
     (if (<= x -5.6e-92) (* x 0.5) (if (<= x 6e+45) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -17200000000000.0) {
		tmp = -1.0;
	} else if (x <= -1.7e-53) {
		tmp = 1.0 + (2.0 / y);
	} else if (x <= -5.6e-92) {
		tmp = x * 0.5;
	} else if (x <= 6e+45) {
		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 <= (-17200000000000.0d0)) then
        tmp = -1.0d0
    else if (x <= (-1.7d-53)) then
        tmp = 1.0d0 + (2.0d0 / y)
    else if (x <= (-5.6d-92)) then
        tmp = x * 0.5d0
    else if (x <= 6d+45) 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 <= -17200000000000.0) {
		tmp = -1.0;
	} else if (x <= -1.7e-53) {
		tmp = 1.0 + (2.0 / y);
	} else if (x <= -5.6e-92) {
		tmp = x * 0.5;
	} else if (x <= 6e+45) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -17200000000000.0:
		tmp = -1.0
	elif x <= -1.7e-53:
		tmp = 1.0 + (2.0 / y)
	elif x <= -5.6e-92:
		tmp = x * 0.5
	elif x <= 6e+45:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -17200000000000.0)
		tmp = -1.0;
	elseif (x <= -1.7e-53)
		tmp = Float64(1.0 + Float64(2.0 / y));
	elseif (x <= -5.6e-92)
		tmp = Float64(x * 0.5);
	elseif (x <= 6e+45)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -17200000000000.0)
		tmp = -1.0;
	elseif (x <= -1.7e-53)
		tmp = 1.0 + (2.0 / y);
	elseif (x <= -5.6e-92)
		tmp = x * 0.5;
	elseif (x <= 6e+45)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -17200000000000.0], -1.0, If[LessEqual[x, -1.7e-53], N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.6e-92], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 6e+45], 1.0, -1.0]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.72e13 or 6.00000000000000021e45 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 78.3%

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

   if -1.72e13 < x < -1.7e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in y around -inf 61.8%

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

   4. Taylor expanded in x around 0 61.8%

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

      1. associate-*r/ 61.8%

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

      2. metadata-eval 61.8%

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

   6. Simplified 61.8%

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

   if -1.7e-53 < x < -5.6e-92

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 61.4%

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

   4. Taylor expanded in x around 0 61.4%

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

      1. *-commutative 61.4%

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

   6. Simplified 61.4%

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

   if -5.6e-92 < x < 6.00000000000000021e45

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 62.0%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -17200000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-53}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-92}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+45}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -32000000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-53}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-92}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+40}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -32000000000000.0)
   -1.0
   (if (<= x -6.2e-53)
     (- 1.0 (/ x y))
     (if (<= x -3e-92) (* x 0.5) (if (<= x 2e+40) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -32000000000000.0) {
		tmp = -1.0;
	} else if (x <= -6.2e-53) {
		tmp = 1.0 - (x / y);
	} else if (x <= -3e-92) {
		tmp = x * 0.5;
	} else if (x <= 2e+40) {
		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 <= (-32000000000000.0d0)) then
        tmp = -1.0d0
    else if (x <= (-6.2d-53)) then
        tmp = 1.0d0 - (x / y)
    else if (x <= (-3d-92)) then
        tmp = x * 0.5d0
    else if (x <= 2d+40) 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 <= -32000000000000.0) {
		tmp = -1.0;
	} else if (x <= -6.2e-53) {
		tmp = 1.0 - (x / y);
	} else if (x <= -3e-92) {
		tmp = x * 0.5;
	} else if (x <= 2e+40) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -32000000000000.0:
		tmp = -1.0
	elif x <= -6.2e-53:
		tmp = 1.0 - (x / y)
	elif x <= -3e-92:
		tmp = x * 0.5
	elif x <= 2e+40:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -32000000000000.0)
		tmp = -1.0;
	elseif (x <= -6.2e-53)
		tmp = Float64(1.0 - Float64(x / y));
	elseif (x <= -3e-92)
		tmp = Float64(x * 0.5);
	elseif (x <= 2e+40)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -32000000000000.0)
		tmp = -1.0;
	elseif (x <= -6.2e-53)
		tmp = 1.0 - (x / y);
	elseif (x <= -3e-92)
		tmp = x * 0.5;
	elseif (x <= 2e+40)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -32000000000000.0], -1.0, If[LessEqual[x, -6.2e-53], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3e-92], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 2e+40], 1.0, -1.0]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.2e13 or 2.00000000000000006e40 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 78.3%

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

   if -3.2e13 < x < -6.20000000000000031e-53

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 61.9%

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

      1. neg-mul-1 61.9%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in x around 0 61.9%

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

      1. mul-1-neg 61.9%

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

      2. unsub-neg 61.9%

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

   8. Simplified 61.9%

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

   if -6.20000000000000031e-53 < x < -3.00000000000000013e-92

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 61.4%

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

   4. Taylor expanded in x around 0 61.4%

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

      1. *-commutative 61.4%

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

   6. Simplified 61.4%

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

   if -3.00000000000000013e-92 < x < 2.00000000000000006e40

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 62.0%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -32000000000000:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-53}:\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-92}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+40}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-10}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+16}:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{2 + x \cdot -2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.7e-10)
   (/ y (+ y -2.0))
   (if (<= y 5.1e+16) (/ (- x y) (- 2.0 x)) (+ 1.0 (/ (+ 2.0 (* x -2.0)) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.7e-10) {
		tmp = y / (y + -2.0);
	} else if (y <= 5.1e+16) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = 1.0 + ((2.0 + (x * -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 (y <= (-1.7d-10)) then
        tmp = y / (y + (-2.0d0))
    else if (y <= 5.1d+16) then
        tmp = (x - y) / (2.0d0 - x)
    else
        tmp = 1.0d0 + ((2.0d0 + (x * (-2.0d0))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.7e-10) {
		tmp = y / (y + -2.0);
	} else if (y <= 5.1e+16) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = 1.0 + ((2.0 + (x * -2.0)) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.7e-10:
		tmp = y / (y + -2.0)
	elif y <= 5.1e+16:
		tmp = (x - y) / (2.0 - x)
	else:
		tmp = 1.0 + ((2.0 + (x * -2.0)) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.7e-10)
		tmp = Float64(y / Float64(y + -2.0));
	elseif (y <= 5.1e+16)
		tmp = Float64(Float64(x - y) / Float64(2.0 - x));
	else
		tmp = Float64(1.0 + Float64(Float64(2.0 + Float64(x * -2.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.7e-10)
		tmp = y / (y + -2.0);
	elseif (y <= 5.1e+16)
		tmp = (x - y) / (2.0 - x);
	else
		tmp = 1.0 + ((2.0 + (x * -2.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.7e-10], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.1e+16], N[(N[(x - y), $MachinePrecision] / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(2.0 + N[(x * -2.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.70000000000000007e-10

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.1%

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

      1. associate-*r/ 80.1%

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

      2. neg-mul-1 80.1%

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

   5. Simplified 80.1%

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

      1. frac-2neg 80.1%

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

      2. div-inv 79.8%

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

      3. remove-double-neg 79.8%

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

      4. sub-neg 79.8%

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

      5. distribute-neg-in 79.8%

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

      6. metadata-eval 79.8%

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

      7. remove-double-neg 79.8%

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

   7. Applied egg-rr 79.8%

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

      1. associate-*r/ 80.1%

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

      2. *-rgt-identity 80.1%

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

      3. +-commutative 80.1%

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

   9. Simplified 80.1%

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

   if -1.70000000000000007e-10 < y < 5.1e16

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.5%

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

   if 5.1e16 < y

   1. Initial program 100.0%

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

      1. flip-- 39.7%

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

      2. associate-/r/ 39.7%

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

      3. metadata-eval 39.7%

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

      4. pow2 39.7%

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

   4. Applied egg-rr 39.7%

      \[\leadsto \color{blue}{\frac{x - y}{4 - {\left(x + y\right)}^{2}} \cdot \left(2 + \left(x + y\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 39.7%

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

      2. associate-*r/ 37.8%

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

      3. associate-+r+ 37.8%

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

      4. +-commutative 37.8%

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

      5. +-commutative 37.8%

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

   6. Simplified 37.8%

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

   7. Taylor expanded in y around -inf 69.3%

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

      1. associate-*r/ 69.3%

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

      2. cancel-sign-sub-inv 69.3%

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

      3. metadata-eval 69.3%

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

      4. distribute-lft-in 69.3%

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

      5. distribute-rgt1-in 69.3%

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

      6. metadata-eval 69.3%

         \[\leadsto 1 + \frac{-1 \cdot \left(-1 \cdot \left(2 + \color{blue}{0} \cdot x\right)\right) + -1 \cdot \left(2 \cdot x\right)}{y} \]

      7. mul0-lft 69.3%

         \[\leadsto 1 + \frac{-1 \cdot \left(-1 \cdot \left(2 + \color{blue}{0}\right)\right) + -1 \cdot \left(2 \cdot x\right)}{y} \]

      8. metadata-eval 69.3%

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

      9. metadata-eval 69.3%

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

      10. metadata-eval 69.3%

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

      11. neg-mul-1 69.3%

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

      12. distribute-lft-neg-in 69.3%

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

      13. metadata-eval 69.3%

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

      14. *-commutative 69.3%

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

   9. Simplified 69.3%

      \[\leadsto \color{blue}{1 + \frac{2 + x \cdot -2}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-10}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+16}:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{2 + x \cdot -2}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-10}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+17}:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.7e-10)
   (/ y (+ y -2.0))
   (if (<= y 2.4e+17) (/ (- x y) (- 2.0 x)) (- 1.0 (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.7e-10) {
		tmp = y / (y + -2.0);
	} else if (y <= 2.4e+17) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.7d-10)) then
        tmp = y / (y + (-2.0d0))
    else if (y <= 2.4d+17) then
        tmp = (x - y) / (2.0d0 - x)
    else
        tmp = 1.0d0 - (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.7e-10) {
		tmp = y / (y + -2.0);
	} else if (y <= 2.4e+17) {
		tmp = (x - y) / (2.0 - x);
	} else {
		tmp = 1.0 - (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.7e-10:
		tmp = y / (y + -2.0)
	elif y <= 2.4e+17:
		tmp = (x - y) / (2.0 - x)
	else:
		tmp = 1.0 - (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.7e-10)
		tmp = Float64(y / Float64(y + -2.0));
	elseif (y <= 2.4e+17)
		tmp = Float64(Float64(x - y) / Float64(2.0 - x));
	else
		tmp = Float64(1.0 - Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.7e-10)
		tmp = y / (y + -2.0);
	elseif (y <= 2.4e+17)
		tmp = (x - y) / (2.0 - x);
	else
		tmp = 1.0 - (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.7e-10], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+17], N[(N[(x - y), $MachinePrecision] / N[(2.0 - x), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.70000000000000007e-10

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.1%

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

      1. associate-*r/ 80.1%

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

      2. neg-mul-1 80.1%

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

   5. Simplified 80.1%

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

      1. frac-2neg 80.1%

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

      2. div-inv 79.8%

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

      3. remove-double-neg 79.8%

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

      4. sub-neg 79.8%

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

      5. distribute-neg-in 79.8%

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

      6. metadata-eval 79.8%

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

      7. remove-double-neg 79.8%

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

   7. Applied egg-rr 79.8%

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

      1. associate-*r/ 80.1%

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

      2. *-rgt-identity 80.1%

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

      3. +-commutative 80.1%

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

   9. Simplified 80.1%

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

   if -1.70000000000000007e-10 < y < 2.4e17

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.5%

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

   if 2.4e17 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 68.4%

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

      1. neg-mul-1 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in x around 0 68.4%

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

      1. mul-1-neg 68.4%

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

      2. unsub-neg 68.4%

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

   8. Simplified 68.4%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-10}:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+17}:\\ \;\;\;\;\frac{x - y}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+69} \lor \neg \left(y \leq 3.5 \cdot 10^{+14}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.5e+69) (not (<= y 3.5e+14)))
   (- 1.0 (/ x y))
   (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.5e+69) || !(y <= 3.5e+14)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.5d+69)) .or. (.not. (y <= 3.5d+14))) then
        tmp = 1.0d0 - (x / y)
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.5e+69) || !(y <= 3.5e+14)) {
		tmp = 1.0 - (x / y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.5e+69) or not (y <= 3.5e+14):
		tmp = 1.0 - (x / y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.5e+69) || !(y <= 3.5e+14))
		tmp = Float64(1.0 - Float64(x / y));
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.5e+69) || ~((y <= 3.5e+14)))
		tmp = 1.0 - (x / y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.5e+69], N[Not[LessEqual[y, 3.5e+14]], $MachinePrecision]], N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.49999999999999992e69 or 3.5e14 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 75.6%

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

      1. neg-mul-1 75.6%

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

   5. Simplified 75.6%

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

   6. Taylor expanded in x around 0 75.6%

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

      1. mul-1-neg 75.6%

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

      2. unsub-neg 75.6%

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

   8. Simplified 75.6%

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

   if -1.49999999999999992e69 < y < 3.5e14

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.7%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+69} \lor \neg \left(y \leq 3.5 \cdot 10^{+14}\right):\\ \;\;\;\;1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-12} \lor \neg \left(y \leq 8 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -6e-12) (not (<= y 8e-19))) (/ y (+ y -2.0)) (/ x (- 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -6e-12) || !(y <= 8e-19)) {
		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 ((y <= (-6d-12)) .or. (.not. (y <= 8d-19))) 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 ((y <= -6e-12) || !(y <= 8e-19)) {
		tmp = y / (y + -2.0);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -6e-12) or not (y <= 8e-19):
		tmp = y / (y + -2.0)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -6e-12) || !(y <= 8e-19))
		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 ((y <= -6e-12) || ~((y <= 8e-19)))
		tmp = y / (y + -2.0);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -6e-12], N[Not[LessEqual[y, 8e-19]], $MachinePrecision]], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.0000000000000003e-12 or 7.9999999999999998e-19 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 73.1%

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

      1. associate-*r/ 73.1%

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

      2. neg-mul-1 73.1%

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

   5. Simplified 73.1%

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

      1. frac-2neg 73.1%

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

      2. div-inv 72.9%

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

      3. remove-double-neg 72.9%

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

      4. sub-neg 72.9%

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

      5. distribute-neg-in 72.9%

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

      6. metadata-eval 72.9%

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

      7. remove-double-neg 72.9%

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

   7. Applied egg-rr 72.9%

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

      1. associate-*r/ 73.1%

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

      2. *-rgt-identity 73.1%

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

      3. +-commutative 73.1%

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

   9. Simplified 73.1%

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

   if -6.0000000000000003e-12 < y < 7.9999999999999998e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 81.6%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-12} \lor \neg \left(y \leq 8 \cdot 10^{-19}\right):\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 62.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+14}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+40}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.35e+14) -1.0 (if (<= x 7e+40) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.35e+14) {
		tmp = -1.0;
	} else if (x <= 7e+40) {
		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 <= (-2.35d+14)) then
        tmp = -1.0d0
    else if (x <= 7d+40) 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 <= -2.35e+14) {
		tmp = -1.0;
	} else if (x <= 7e+40) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.35e+14:
		tmp = -1.0
	elif x <= 7e+40:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.35e+14)
		tmp = -1.0;
	elseif (x <= 7e+40)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.35e+14)
		tmp = -1.0;
	elseif (x <= 7e+40)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.35e+14], -1.0, If[LessEqual[x, 7e+40], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.35e14 or 6.9999999999999998e40 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 78.3%

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

   if -2.35e14 < x < 6.9999999999999998e40

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 58.7%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{+14}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{+40}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 38.2% 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. Add Preprocessing

3. Taylor expanded in x around inf 37.4%

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

4. Final simplification 37.4%

   \[\leadsto -1 \]
5. 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 2024024 
(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))))