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

Percentage Accurate: 100.0% → 100.0%

Time: 9.6s

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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 2: 61.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} + -1\\ t_1 := 1 + \frac{2}{y}\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+64}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-119}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-258}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-265}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 140000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ y x) -1.0)) (t_1 (+ 1.0 (/ 2.0 y))))
   (if (<= x -4.8e+64)
     t_0
     (if (<= x -1.2e-43)
       t_1
       (if (<= x -2.3e-119)
         (* x 0.5)
         (if (<= x -1.95e-258)
           t_1
           (if (<= x 1.5e-265)
             (* y -0.5)
             (if (<= x 140000000.0) 1.0 t_0))))))))

C

double code(double x, double y) {
	double t_0 = (y / x) + -1.0;
	double t_1 = 1.0 + (2.0 / y);
	double tmp;
	if (x <= -4.8e+64) {
		tmp = t_0;
	} else if (x <= -1.2e-43) {
		tmp = t_1;
	} else if (x <= -2.3e-119) {
		tmp = x * 0.5;
	} else if (x <= -1.95e-258) {
		tmp = t_1;
	} else if (x <= 1.5e-265) {
		tmp = y * -0.5;
	} else if (x <= 140000000.0) {
		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) :: t_1
    real(8) :: tmp
    t_0 = (y / x) + (-1.0d0)
    t_1 = 1.0d0 + (2.0d0 / y)
    if (x <= (-4.8d+64)) then
        tmp = t_0
    else if (x <= (-1.2d-43)) then
        tmp = t_1
    else if (x <= (-2.3d-119)) then
        tmp = x * 0.5d0
    else if (x <= (-1.95d-258)) then
        tmp = t_1
    else if (x <= 1.5d-265) then
        tmp = y * (-0.5d0)
    else if (x <= 140000000.0d0) 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 t_1 = 1.0 + (2.0 / y);
	double tmp;
	if (x <= -4.8e+64) {
		tmp = t_0;
	} else if (x <= -1.2e-43) {
		tmp = t_1;
	} else if (x <= -2.3e-119) {
		tmp = x * 0.5;
	} else if (x <= -1.95e-258) {
		tmp = t_1;
	} else if (x <= 1.5e-265) {
		tmp = y * -0.5;
	} else if (x <= 140000000.0) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y / x) + -1.0
	t_1 = 1.0 + (2.0 / y)
	tmp = 0
	if x <= -4.8e+64:
		tmp = t_0
	elif x <= -1.2e-43:
		tmp = t_1
	elif x <= -2.3e-119:
		tmp = x * 0.5
	elif x <= -1.95e-258:
		tmp = t_1
	elif x <= 1.5e-265:
		tmp = y * -0.5
	elif x <= 140000000.0:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y / x) + -1.0)
	t_1 = Float64(1.0 + Float64(2.0 / y))
	tmp = 0.0
	if (x <= -4.8e+64)
		tmp = t_0;
	elseif (x <= -1.2e-43)
		tmp = t_1;
	elseif (x <= -2.3e-119)
		tmp = Float64(x * 0.5);
	elseif (x <= -1.95e-258)
		tmp = t_1;
	elseif (x <= 1.5e-265)
		tmp = Float64(y * -0.5);
	elseif (x <= 140000000.0)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y / x) + -1.0;
	t_1 = 1.0 + (2.0 / y);
	tmp = 0.0;
	if (x <= -4.8e+64)
		tmp = t_0;
	elseif (x <= -1.2e-43)
		tmp = t_1;
	elseif (x <= -2.3e-119)
		tmp = x * 0.5;
	elseif (x <= -1.95e-258)
		tmp = t_1;
	elseif (x <= 1.5e-265)
		tmp = y * -0.5;
	elseif (x <= 140000000.0)
		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]}, Block[{t$95$1 = N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.8e+64], t$95$0, If[LessEqual[x, -1.2e-43], t$95$1, If[LessEqual[x, -2.3e-119], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, -1.95e-258], t$95$1, If[LessEqual[x, 1.5e-265], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 140000000.0], 1.0, t$95$0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -4.79999999999999999e64 or 1.4e8 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.4%

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

      1. mul-1-neg 82.4%

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

   5. Simplified 82.4%

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

   6. Taylor expanded in x around 0 82.4%

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

   if -4.79999999999999999e64 < x < -1.2000000000000001e-43 or -2.29999999999999993e-119 < x < -1.95000000000000002e-258

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 50.1%

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

      1. sub-neg 50.1%

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

      2. mul-1-neg 50.1%

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

      3. unsub-neg 50.1%

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

      4. mul-1-neg 50.1%

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

      5. remove-double-neg 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in x around 0 50.2%

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

      1. associate-*r/ 50.2%

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

      2. metadata-eval 50.2%

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

   8. Simplified 50.2%

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

   if -1.2000000000000001e-43 < x < -2.29999999999999993e-119

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in y around 0 59.9%

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

      1. *-commutative 59.9%

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

   6. Simplified 59.9%

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

   if -1.95000000000000002e-258 < x < 1.4999999999999999e-265

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.3%

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

      1. associate-*r/ 81.3%

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

      2. neg-mul-1 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in y around 0 64.9%

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

      1. *-commutative 64.9%

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

   8. Simplified 64.9%

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

   if 1.4999999999999999e-265 < x < 1.4e8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 62.3%

      \[\leadsto \color{blue}{1} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-43}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-119}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-258}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-265}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 140000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+64}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.26 \cdot 10^{-36}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-122}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.82 \cdot 10^{-258}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-267}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 125000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.2e+64)
   -1.0
   (if (<= x -1.26e-36)
     1.0
     (if (<= x -4.5e-122)
       (* x 0.5)
       (if (<= x -1.82e-258)
         1.0
         (if (<= x 5.2e-267) (* y -0.5) (if (<= x 125000000.0) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.2e+64) {
		tmp = -1.0;
	} else if (x <= -1.26e-36) {
		tmp = 1.0;
	} else if (x <= -4.5e-122) {
		tmp = x * 0.5;
	} else if (x <= -1.82e-258) {
		tmp = 1.0;
	} else if (x <= 5.2e-267) {
		tmp = y * -0.5;
	} else if (x <= 125000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-9.2d+64)) then
        tmp = -1.0d0
    else if (x <= (-1.26d-36)) then
        tmp = 1.0d0
    else if (x <= (-4.5d-122)) then
        tmp = x * 0.5d0
    else if (x <= (-1.82d-258)) then
        tmp = 1.0d0
    else if (x <= 5.2d-267) then
        tmp = y * (-0.5d0)
    else if (x <= 125000000.0d0) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -9.2e+64) {
		tmp = -1.0;
	} else if (x <= -1.26e-36) {
		tmp = 1.0;
	} else if (x <= -4.5e-122) {
		tmp = x * 0.5;
	} else if (x <= -1.82e-258) {
		tmp = 1.0;
	} else if (x <= 5.2e-267) {
		tmp = y * -0.5;
	} else if (x <= 125000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.2e+64:
		tmp = -1.0
	elif x <= -1.26e-36:
		tmp = 1.0
	elif x <= -4.5e-122:
		tmp = x * 0.5
	elif x <= -1.82e-258:
		tmp = 1.0
	elif x <= 5.2e-267:
		tmp = y * -0.5
	elif x <= 125000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.2e+64)
		tmp = -1.0;
	elseif (x <= -1.26e-36)
		tmp = 1.0;
	elseif (x <= -4.5e-122)
		tmp = Float64(x * 0.5);
	elseif (x <= -1.82e-258)
		tmp = 1.0;
	elseif (x <= 5.2e-267)
		tmp = Float64(y * -0.5);
	elseif (x <= 125000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9.2e+64)
		tmp = -1.0;
	elseif (x <= -1.26e-36)
		tmp = 1.0;
	elseif (x <= -4.5e-122)
		tmp = x * 0.5;
	elseif (x <= -1.82e-258)
		tmp = 1.0;
	elseif (x <= 5.2e-267)
		tmp = y * -0.5;
	elseif (x <= 125000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.2e+64], -1.0, If[LessEqual[x, -1.26e-36], 1.0, If[LessEqual[x, -4.5e-122], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, -1.82e-258], 1.0, If[LessEqual[x, 5.2e-267], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 125000000.0], 1.0, -1.0]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -9.2e64 or 1.25e8 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.0%

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

   if -9.2e64 < x < -1.26000000000000005e-36 or -4.4999999999999998e-122 < x < -1.82000000000000003e-258 or 5.2000000000000003e-267 < x < 1.25e8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 56.2%

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

   if -1.26000000000000005e-36 < x < -4.4999999999999998e-122

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in y around 0 59.9%

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

      1. *-commutative 59.9%

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

   6. Simplified 59.9%

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

   if -1.82000000000000003e-258 < x < 5.2000000000000003e-267

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.3%

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

      1. associate-*r/ 81.3%

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

      2. neg-mul-1 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in y around 0 64.9%

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

      1. *-commutative 64.9%

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

   8. Simplified 64.9%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+64}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1.26 \cdot 10^{-36}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-122}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.82 \cdot 10^{-258}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-267}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 125000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{2}{y}\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{+65}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-43}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-119}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-257}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-268}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 140000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ 2.0 y))))
   (if (<= x -6.6e+65)
     -1.0
     (if (<= x -2.1e-43)
       t_0
       (if (<= x -2.3e-119)
         (* x 0.5)
         (if (<= x -4.5e-257)
           t_0
           (if (<= x 1.75e-268)
             (* y -0.5)
             (if (<= x 140000000.0) 1.0 -1.0))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (2.0 / y);
	double tmp;
	if (x <= -6.6e+65) {
		tmp = -1.0;
	} else if (x <= -2.1e-43) {
		tmp = t_0;
	} else if (x <= -2.3e-119) {
		tmp = x * 0.5;
	} else if (x <= -4.5e-257) {
		tmp = t_0;
	} else if (x <= 1.75e-268) {
		tmp = y * -0.5;
	} else if (x <= 140000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + (2.0d0 / y)
    if (x <= (-6.6d+65)) then
        tmp = -1.0d0
    else if (x <= (-2.1d-43)) then
        tmp = t_0
    else if (x <= (-2.3d-119)) then
        tmp = x * 0.5d0
    else if (x <= (-4.5d-257)) then
        tmp = t_0
    else if (x <= 1.75d-268) then
        tmp = y * (-0.5d0)
    else if (x <= 140000000.0d0) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (2.0 / y);
	double tmp;
	if (x <= -6.6e+65) {
		tmp = -1.0;
	} else if (x <= -2.1e-43) {
		tmp = t_0;
	} else if (x <= -2.3e-119) {
		tmp = x * 0.5;
	} else if (x <= -4.5e-257) {
		tmp = t_0;
	} else if (x <= 1.75e-268) {
		tmp = y * -0.5;
	} else if (x <= 140000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (2.0 / y)
	tmp = 0
	if x <= -6.6e+65:
		tmp = -1.0
	elif x <= -2.1e-43:
		tmp = t_0
	elif x <= -2.3e-119:
		tmp = x * 0.5
	elif x <= -4.5e-257:
		tmp = t_0
	elif x <= 1.75e-268:
		tmp = y * -0.5
	elif x <= 140000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(2.0 / y))
	tmp = 0.0
	if (x <= -6.6e+65)
		tmp = -1.0;
	elseif (x <= -2.1e-43)
		tmp = t_0;
	elseif (x <= -2.3e-119)
		tmp = Float64(x * 0.5);
	elseif (x <= -4.5e-257)
		tmp = t_0;
	elseif (x <= 1.75e-268)
		tmp = Float64(y * -0.5);
	elseif (x <= 140000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (2.0 / y);
	tmp = 0.0;
	if (x <= -6.6e+65)
		tmp = -1.0;
	elseif (x <= -2.1e-43)
		tmp = t_0;
	elseif (x <= -2.3e-119)
		tmp = x * 0.5;
	elseif (x <= -4.5e-257)
		tmp = t_0;
	elseif (x <= 1.75e-268)
		tmp = y * -0.5;
	elseif (x <= 140000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.6e+65], -1.0, If[LessEqual[x, -2.1e-43], t$95$0, If[LessEqual[x, -2.3e-119], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, -4.5e-257], t$95$0, If[LessEqual[x, 1.75e-268], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 140000000.0], 1.0, -1.0]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -6.60000000000000046e65 or 1.4e8 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.0%

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

   if -6.60000000000000046e65 < x < -2.1000000000000001e-43 or -2.29999999999999993e-119 < x < -4.5000000000000003e-257

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 50.1%

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

      1. sub-neg 50.1%

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

      2. mul-1-neg 50.1%

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

      3. unsub-neg 50.1%

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

      4. mul-1-neg 50.1%

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

      5. remove-double-neg 50.1%

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

   5. Simplified 50.1%

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

   6. Taylor expanded in x around 0 50.2%

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

      1. associate-*r/ 50.2%

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

      2. metadata-eval 50.2%

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

   8. Simplified 50.2%

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

   if -2.1000000000000001e-43 < x < -2.29999999999999993e-119

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in y around 0 59.9%

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

      1. *-commutative 59.9%

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

   6. Simplified 59.9%

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

   if -4.5000000000000003e-257 < x < 1.75000000000000003e-268

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.3%

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

      1. associate-*r/ 81.3%

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

      2. neg-mul-1 81.3%

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

   5. Simplified 81.3%

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

   6. Taylor expanded in y around 0 64.9%

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

      1. *-commutative 64.9%

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

   8. Simplified 64.9%

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

   if 1.75000000000000003e-268 < x < 1.4e8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 62.3%

      \[\leadsto \color{blue}{1} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+65}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-43}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-119}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-257}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-268}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 140000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+148}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+109}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+41}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1020:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= y -1.1e+148)
     1.0
     (if (<= y -6e+109)
       t_0
       (if (<= y -4e+41) 1.0 (if (<= y 1020.0) t_0 (+ 1.0 (/ 2.0 y))))))))

C

double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -1.1e+148) {
		tmp = 1.0;
	} else if (y <= -6e+109) {
		tmp = t_0;
	} else if (y <= -4e+41) {
		tmp = 1.0;
	} else if (y <= 1020.0) {
		tmp = t_0;
	} else {
		tmp = 1.0 + (2.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (2.0d0 - x)
    if (y <= (-1.1d+148)) then
        tmp = 1.0d0
    else if (y <= (-6d+109)) then
        tmp = t_0
    else if (y <= (-4d+41)) then
        tmp = 1.0d0
    else if (y <= 1020.0d0) then
        tmp = t_0
    else
        tmp = 1.0d0 + (2.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (2.0 - x);
	double tmp;
	if (y <= -1.1e+148) {
		tmp = 1.0;
	} else if (y <= -6e+109) {
		tmp = t_0;
	} else if (y <= -4e+41) {
		tmp = 1.0;
	} else if (y <= 1020.0) {
		tmp = t_0;
	} else {
		tmp = 1.0 + (2.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (2.0 - x)
	tmp = 0
	if y <= -1.1e+148:
		tmp = 1.0
	elif y <= -6e+109:
		tmp = t_0
	elif y <= -4e+41:
		tmp = 1.0
	elif y <= 1020.0:
		tmp = t_0
	else:
		tmp = 1.0 + (2.0 / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(2.0 - x))
	tmp = 0.0
	if (y <= -1.1e+148)
		tmp = 1.0;
	elseif (y <= -6e+109)
		tmp = t_0;
	elseif (y <= -4e+41)
		tmp = 1.0;
	elseif (y <= 1020.0)
		tmp = t_0;
	else
		tmp = Float64(1.0 + Float64(2.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (2.0 - x);
	tmp = 0.0;
	if (y <= -1.1e+148)
		tmp = 1.0;
	elseif (y <= -6e+109)
		tmp = t_0;
	elseif (y <= -4e+41)
		tmp = 1.0;
	elseif (y <= 1020.0)
		tmp = t_0;
	else
		tmp = 1.0 + (2.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.1e+148], 1.0, If[LessEqual[y, -6e+109], t$95$0, If[LessEqual[y, -4e+41], 1.0, If[LessEqual[y, 1020.0], t$95$0, N[(1.0 + N[(2.0 / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0999999999999999e148 or -6.00000000000000031e109 < y < -4.00000000000000002e41

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 83.1%

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

   if -1.0999999999999999e148 < y < -6.00000000000000031e109 or -4.00000000000000002e41 < y < 1020

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.0%

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

   if 1020 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.5%

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

      1. sub-neg 72.5%

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

      2. mul-1-neg 72.5%

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

      3. unsub-neg 72.5%

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

      4. mul-1-neg 72.5%

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

      5. remove-double-neg 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in x around 0 71.8%

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

      1. associate-*r/ 71.8%

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

      2. metadata-eval 71.8%

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

   8. Simplified 71.8%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+148}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+109}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+41}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1020:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{2}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+65}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-40}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-119}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1900000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.6e+65)
   -1.0
   (if (<= x -4.8e-40)
     1.0
     (if (<= x -6.6e-119) (* x 0.5) (if (<= x 1900000.0) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.6e+65) {
		tmp = -1.0;
	} else if (x <= -4.8e-40) {
		tmp = 1.0;
	} else if (x <= -6.6e-119) {
		tmp = x * 0.5;
	} else if (x <= 1900000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-6.6d+65)) then
        tmp = -1.0d0
    else if (x <= (-4.8d-40)) then
        tmp = 1.0d0
    else if (x <= (-6.6d-119)) then
        tmp = x * 0.5d0
    else if (x <= 1900000.0d0) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.6e+65) {
		tmp = -1.0;
	} else if (x <= -4.8e-40) {
		tmp = 1.0;
	} else if (x <= -6.6e-119) {
		tmp = x * 0.5;
	} else if (x <= 1900000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.6e+65:
		tmp = -1.0
	elif x <= -4.8e-40:
		tmp = 1.0
	elif x <= -6.6e-119:
		tmp = x * 0.5
	elif x <= 1900000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.6e+65)
		tmp = -1.0;
	elseif (x <= -4.8e-40)
		tmp = 1.0;
	elseif (x <= -6.6e-119)
		tmp = Float64(x * 0.5);
	elseif (x <= 1900000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.6e+65)
		tmp = -1.0;
	elseif (x <= -4.8e-40)
		tmp = 1.0;
	elseif (x <= -6.6e-119)
		tmp = x * 0.5;
	elseif (x <= 1900000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.6e+65], -1.0, If[LessEqual[x, -4.8e-40], 1.0, If[LessEqual[x, -6.6e-119], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 1900000.0], 1.0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.60000000000000046e65 or 1.9e6 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.0%

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

   if -6.60000000000000046e65 < x < -4.79999999999999982e-40 or -6.60000000000000017e-119 < x < 1.9e6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 51.1%

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

   if -4.79999999999999982e-40 < x < -6.60000000000000017e-119

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   4. Taylor expanded in y around 0 59.9%

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

      1. *-commutative 59.9%

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

   6. Simplified 59.9%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+65}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-40}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-119}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 1900000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+64}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 650000:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.6e+64)
   (+ (/ y x) -1.0)
   (if (<= x 650000.0) (/ (- x y) (- 2.0 y)) (/ x (- 2.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.6e+64) {
		tmp = (y / x) + -1.0;
	} else if (x <= 650000.0) {
		tmp = (x - y) / (2.0 - 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 (x <= (-6.6d+64)) then
        tmp = (y / x) + (-1.0d0)
    else if (x <= 650000.0d0) then
        tmp = (x - y) / (2.0d0 - 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 (x <= -6.6e+64) {
		tmp = (y / x) + -1.0;
	} else if (x <= 650000.0) {
		tmp = (x - y) / (2.0 - y);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.6e+64:
		tmp = (y / x) + -1.0
	elif x <= 650000.0:
		tmp = (x - y) / (2.0 - y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.6e+64)
		tmp = Float64(Float64(y / x) + -1.0);
	elseif (x <= 650000.0)
		tmp = Float64(Float64(x - y) / Float64(2.0 - y));
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.6e+64)
		tmp = (y / x) + -1.0;
	elseif (x <= 650000.0)
		tmp = (x - y) / (2.0 - y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.6e+64], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[x, 650000.0], N[(N[(x - y), $MachinePrecision] / N[(2.0 - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.59999999999999976e64

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.2%

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

      1. mul-1-neg 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in x around 0 81.2%

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

   if -6.59999999999999976e64 < x < 6.5e5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 94.5%

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

   if 6.5e5 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 84.7%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+64}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 650000:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 52000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.8e+64)
   (+ (/ y x) -1.0)
   (if (<= x 52000.0) (/ y (+ y -2.0)) (/ x (- 2.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.8e+64) {
		tmp = (y / x) + -1.0;
	} else if (x <= 52000.0) {
		tmp = y / (y + -2.0);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-4.8d+64)) then
        tmp = (y / x) + (-1.0d0)
    else if (x <= 52000.0d0) then
        tmp = y / (y + (-2.0d0))
    else
        tmp = x / (2.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.8e+64) {
		tmp = (y / x) + -1.0;
	} else if (x <= 52000.0) {
		tmp = y / (y + -2.0);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.8e+64:
		tmp = (y / x) + -1.0
	elif x <= 52000.0:
		tmp = y / (y + -2.0)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.8e+64)
		tmp = Float64(Float64(y / x) + -1.0);
	elseif (x <= 52000.0)
		tmp = Float64(y / Float64(y + -2.0));
	else
		tmp = Float64(x / Float64(2.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.8e+64)
		tmp = (y / x) + -1.0;
	elseif (x <= 52000.0)
		tmp = y / (y + -2.0);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.8e+64], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[x, 52000.0], N[(y / N[(y + -2.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(2.0 - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.79999999999999999e64

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.2%

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

      1. mul-1-neg 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in x around 0 81.2%

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

   if -4.79999999999999999e64 < x < 52000

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 72.9%

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

      1. associate-*r/ 72.9%

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

      2. neg-mul-1 72.9%

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

   5. Simplified 72.9%

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

      1. frac-2neg 72.9%

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

      2. div-inv 72.8%

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

      3. remove-double-neg 72.8%

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

      4. sub-neg 72.8%

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

      5. distribute-neg-in 72.8%

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

      6. metadata-eval 72.8%

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

      7. remove-double-neg 72.8%

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

   7. Applied egg-rr 72.8%

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

      1. associate-*r/ 72.9%

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

      2. *-rgt-identity 72.9%

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

      3. +-commutative 72.9%

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

   9. Simplified 72.9%

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

   if 52000 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 84.7%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 52000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+64}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 140000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.8e+64) -1.0 (if (<= x 140000000.0) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.8e+64) {
		tmp = -1.0;
	} else if (x <= 140000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-4.8d+64)) then
        tmp = -1.0d0
    else if (x <= 140000000.0d0) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.8e+64) {
		tmp = -1.0;
	} else if (x <= 140000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.8e+64:
		tmp = -1.0
	elif x <= 140000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.8e+64)
		tmp = -1.0;
	elseif (x <= 140000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.8e+64)
		tmp = -1.0;
	elseif (x <= 140000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.8e+64], -1.0, If[LessEqual[x, 140000000.0], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999999e64 or 1.4e8 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.0%

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

   if -4.79999999999999999e64 < x < 1.4e8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 48.6%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+64}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 140000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.6% 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 40.8%

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

4. Final simplification 40.8%

   \[\leadsto -1 \]
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 2024031 
(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))))