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

Percentage Accurate: 100.0% → 100.0%

Time: 9.7s

Alternatives: 10

Speedup: 1.0×

• could not determine a ground truth

  1. x = 1.0852339697947445e-205
  2. y = 4.558625256172917e-206

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: 61.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{x} + -1\\ t_1 := 1 + \frac{2}{y}\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+64}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-121}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-259}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-265}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 125000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ y x) -1.0)) (t_1 (+ 1.0 (/ 2.0 y))))
   (if (<= x -5.5e+64)
     t_0
     (if (<= x -2.15e-40)
       t_1
       (if (<= x -1.15e-121)
         (* x 0.5)
         (if (<= x -3.1e-259)
           t_1
           (if (<= x 1.6e-265)
             (* y -0.5)
             (if (<= x 125000000.0) 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 <= -5.5e+64) {
		tmp = t_0;
	} else if (x <= -2.15e-40) {
		tmp = t_1;
	} else if (x <= -1.15e-121) {
		tmp = x * 0.5;
	} else if (x <= -3.1e-259) {
		tmp = t_1;
	} else if (x <= 1.6e-265) {
		tmp = y * -0.5;
	} else if (x <= 125000000.0) {
		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 <= (-5.5d+64)) then
        tmp = t_0
    else if (x <= (-2.15d-40)) then
        tmp = t_1
    else if (x <= (-1.15d-121)) then
        tmp = x * 0.5d0
    else if (x <= (-3.1d-259)) then
        tmp = t_1
    else if (x <= 1.6d-265) then
        tmp = y * (-0.5d0)
    else if (x <= 125000000.0d0) 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 <= -5.5e+64) {
		tmp = t_0;
	} else if (x <= -2.15e-40) {
		tmp = t_1;
	} else if (x <= -1.15e-121) {
		tmp = x * 0.5;
	} else if (x <= -3.1e-259) {
		tmp = t_1;
	} else if (x <= 1.6e-265) {
		tmp = y * -0.5;
	} else if (x <= 125000000.0) {
		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 <= -5.5e+64:
		tmp = t_0
	elif x <= -2.15e-40:
		tmp = t_1
	elif x <= -1.15e-121:
		tmp = x * 0.5
	elif x <= -3.1e-259:
		tmp = t_1
	elif x <= 1.6e-265:
		tmp = y * -0.5
	elif x <= 125000000.0:
		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 <= -5.5e+64)
		tmp = t_0;
	elseif (x <= -2.15e-40)
		tmp = t_1;
	elseif (x <= -1.15e-121)
		tmp = Float64(x * 0.5);
	elseif (x <= -3.1e-259)
		tmp = t_1;
	elseif (x <= 1.6e-265)
		tmp = Float64(y * -0.5);
	elseif (x <= 125000000.0)
		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 <= -5.5e+64)
		tmp = t_0;
	elseif (x <= -2.15e-40)
		tmp = t_1;
	elseif (x <= -1.15e-121)
		tmp = x * 0.5;
	elseif (x <= -3.1e-259)
		tmp = t_1;
	elseif (x <= 1.6e-265)
		tmp = y * -0.5;
	elseif (x <= 125000000.0)
		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, -5.5e+64], t$95$0, If[LessEqual[x, -2.15e-40], t$95$1, If[LessEqual[x, -1.15e-121], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, -3.1e-259], t$95$1, If[LessEqual[x, 1.6e-265], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 125000000.0], 1.0, t$95$0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -5.4999999999999996e64 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 82.4%

      \[\leadsto \frac{x - y}{\color{blue}{-1 \cdot x}} \]
   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 -5.4999999999999996e64 < x < -2.1500000000000001e-40 or -1.15000000000000006e-121 < x < -3.0999999999999998e-259

   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 -2.1500000000000001e-40 < x < -1.15000000000000006e-121

   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 -3.0999999999999998e-259 < x < 1.6e-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 1.6e-265 < 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 60.6%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+64}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-40}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-121}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-259}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-265}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 125000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{x} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+66}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -7.9 \cdot 10^{-35}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-119}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-256}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-266}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 85000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2e+66)
   -1.0
   (if (<= x -7.9e-35)
     1.0
     (if (<= x -3.9e-119)
       (* x 0.5)
       (if (<= x -1.15e-256)
         1.0
         (if (<= x 3.2e-266) (* y -0.5) (if (<= x 85000000.0) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2e+66) {
		tmp = -1.0;
	} else if (x <= -7.9e-35) {
		tmp = 1.0;
	} else if (x <= -3.9e-119) {
		tmp = x * 0.5;
	} else if (x <= -1.15e-256) {
		tmp = 1.0;
	} else if (x <= 3.2e-266) {
		tmp = y * -0.5;
	} else if (x <= 85000000.0) {
		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 <= (-2d+66)) then
        tmp = -1.0d0
    else if (x <= (-7.9d-35)) then
        tmp = 1.0d0
    else if (x <= (-3.9d-119)) then
        tmp = x * 0.5d0
    else if (x <= (-1.15d-256)) then
        tmp = 1.0d0
    else if (x <= 3.2d-266) then
        tmp = y * (-0.5d0)
    else if (x <= 85000000.0d0) 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 <= -2e+66) {
		tmp = -1.0;
	} else if (x <= -7.9e-35) {
		tmp = 1.0;
	} else if (x <= -3.9e-119) {
		tmp = x * 0.5;
	} else if (x <= -1.15e-256) {
		tmp = 1.0;
	} else if (x <= 3.2e-266) {
		tmp = y * -0.5;
	} else if (x <= 85000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2e+66:
		tmp = -1.0
	elif x <= -7.9e-35:
		tmp = 1.0
	elif x <= -3.9e-119:
		tmp = x * 0.5
	elif x <= -1.15e-256:
		tmp = 1.0
	elif x <= 3.2e-266:
		tmp = y * -0.5
	elif x <= 85000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2e+66)
		tmp = -1.0;
	elseif (x <= -7.9e-35)
		tmp = 1.0;
	elseif (x <= -3.9e-119)
		tmp = Float64(x * 0.5);
	elseif (x <= -1.15e-256)
		tmp = 1.0;
	elseif (x <= 3.2e-266)
		tmp = Float64(y * -0.5);
	elseif (x <= 85000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2e+66)
		tmp = -1.0;
	elseif (x <= -7.9e-35)
		tmp = 1.0;
	elseif (x <= -3.9e-119)
		tmp = x * 0.5;
	elseif (x <= -1.15e-256)
		tmp = 1.0;
	elseif (x <= 3.2e-266)
		tmp = y * -0.5;
	elseif (x <= 85000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2e+66], -1.0, If[LessEqual[x, -7.9e-35], 1.0, If[LessEqual[x, -3.9e-119], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, -1.15e-256], 1.0, If[LessEqual[x, 3.2e-266], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 85000000.0], 1.0, -1.0]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.99999999999999989e66 or 8.5e7 < 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 -1.99999999999999989e66 < x < -7.89999999999999983e-35 or -3.8999999999999999e-119 < x < -1.15e-256 or 3.2e-266 < x < 8.5e7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 55.3%

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

   if -7.89999999999999983e-35 < x < -3.8999999999999999e-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 -1.15e-256 < x < 3.2e-266

   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 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+66}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -7.9 \cdot 10^{-35}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-119}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-256}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-266}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 85000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{2}{y}\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+65}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-39}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-119}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-259}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-267}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1700000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ 2.0 y))))
   (if (<= x -1.3e+65)
     -1.0
     (if (<= x -2.25e-39)
       t_0
       (if (<= x -6e-119)
         (* x 0.5)
         (if (<= x -9.6e-259)
           t_0
           (if (<= x 1.2e-267) (* y -0.5) (if (<= x 1700000.0) 1.0 -1.0))))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (2.0 / y);
	double tmp;
	if (x <= -1.3e+65) {
		tmp = -1.0;
	} else if (x <= -2.25e-39) {
		tmp = t_0;
	} else if (x <= -6e-119) {
		tmp = x * 0.5;
	} else if (x <= -9.6e-259) {
		tmp = t_0;
	} else if (x <= 1.2e-267) {
		tmp = y * -0.5;
	} else if (x <= 1700000.0) {
		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 <= (-1.3d+65)) then
        tmp = -1.0d0
    else if (x <= (-2.25d-39)) then
        tmp = t_0
    else if (x <= (-6d-119)) then
        tmp = x * 0.5d0
    else if (x <= (-9.6d-259)) then
        tmp = t_0
    else if (x <= 1.2d-267) then
        tmp = y * (-0.5d0)
    else if (x <= 1700000.0d0) 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 <= -1.3e+65) {
		tmp = -1.0;
	} else if (x <= -2.25e-39) {
		tmp = t_0;
	} else if (x <= -6e-119) {
		tmp = x * 0.5;
	} else if (x <= -9.6e-259) {
		tmp = t_0;
	} else if (x <= 1.2e-267) {
		tmp = y * -0.5;
	} else if (x <= 1700000.0) {
		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 <= -1.3e+65:
		tmp = -1.0
	elif x <= -2.25e-39:
		tmp = t_0
	elif x <= -6e-119:
		tmp = x * 0.5
	elif x <= -9.6e-259:
		tmp = t_0
	elif x <= 1.2e-267:
		tmp = y * -0.5
	elif x <= 1700000.0:
		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 <= -1.3e+65)
		tmp = -1.0;
	elseif (x <= -2.25e-39)
		tmp = t_0;
	elseif (x <= -6e-119)
		tmp = Float64(x * 0.5);
	elseif (x <= -9.6e-259)
		tmp = t_0;
	elseif (x <= 1.2e-267)
		tmp = Float64(y * -0.5);
	elseif (x <= 1700000.0)
		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 <= -1.3e+65)
		tmp = -1.0;
	elseif (x <= -2.25e-39)
		tmp = t_0;
	elseif (x <= -6e-119)
		tmp = x * 0.5;
	elseif (x <= -9.6e-259)
		tmp = t_0;
	elseif (x <= 1.2e-267)
		tmp = y * -0.5;
	elseif (x <= 1700000.0)
		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, -1.3e+65], -1.0, If[LessEqual[x, -2.25e-39], t$95$0, If[LessEqual[x, -6e-119], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, -9.6e-259], t$95$0, If[LessEqual[x, 1.2e-267], N[(y * -0.5), $MachinePrecision], If[LessEqual[x, 1700000.0], 1.0, -1.0]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.30000000000000001e65 or 1.7e6 < 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 -1.30000000000000001e65 < x < -2.25e-39 or -6.0000000000000004e-119 < x < -9.6000000000000002e-259

   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 -2.25e-39 < x < -6.0000000000000004e-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 -9.6000000000000002e-259 < x < 1.1999999999999999e-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%

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

   if 1.1999999999999999e-267 < x < 1.7e6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 60.6%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+65}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{-39}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-119}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq -9.6 \cdot 10^{-259}:\\ \;\;\;\;1 + \frac{2}{y}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-267}:\\ \;\;\;\;y \cdot -0.5\\ \mathbf{elif}\;x \leq 1700000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{2 - x}\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+148}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{+110}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+41}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1020:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{2}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- 2.0 x))))
   (if (<= y -1.1e+148)
     1.0
     (if (<= y -1.32e+110)
       t_0
       (if (<= y -3.2e+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 <= -1.32e+110) {
		tmp = t_0;
	} else if (y <= -3.2e+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 <= (-1.32d+110)) then
        tmp = t_0
    else if (y <= (-3.2d+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 <= -1.32e+110) {
		tmp = t_0;
	} else if (y <= -3.2e+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 <= -1.32e+110:
		tmp = t_0
	elif y <= -3.2e+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 <= -1.32e+110)
		tmp = t_0;
	elseif (y <= -3.2e+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 <= -1.32e+110)
		tmp = t_0;
	elseif (y <= -3.2e+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, -1.32e+110], t$95$0, If[LessEqual[y, -3.2e+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 -1.32e110 < y < -3.2000000000000001e41

   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 < -1.32e110 or -3.2000000000000001e41 < 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 73.2%

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

   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 72.0%

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

      1. sub-neg 72.0%

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

      2. mul-1-neg 72.0%

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

      3. unsub-neg 72.0%

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

      4. mul-1-neg 72.0%

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

      5. remove-double-neg 72.0%

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

   5. Simplified 72.0%

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

   6. Taylor expanded in x around 0 71.3%

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

      1. associate-*r/ 71.3%

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

      2. metadata-eval 71.3%

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

   8. Simplified 71.3%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+148}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{+110}:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+41}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1020:\\ \;\;\;\;\frac{x}{2 - x}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{2}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+64}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-34}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-123}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 85000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.5e+64)
   -1.0
   (if (<= x -5e-34)
     1.0
     (if (<= x -5.5e-123) (* x 0.5) (if (<= x 85000000.0) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.5e+64) {
		tmp = -1.0;
	} else if (x <= -5e-34) {
		tmp = 1.0;
	} else if (x <= -5.5e-123) {
		tmp = x * 0.5;
	} else if (x <= 85000000.0) {
		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 <= (-9.5d+64)) then
        tmp = -1.0d0
    else if (x <= (-5d-34)) then
        tmp = 1.0d0
    else if (x <= (-5.5d-123)) then
        tmp = x * 0.5d0
    else if (x <= 85000000.0d0) 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 <= -9.5e+64) {
		tmp = -1.0;
	} else if (x <= -5e-34) {
		tmp = 1.0;
	} else if (x <= -5.5e-123) {
		tmp = x * 0.5;
	} else if (x <= 85000000.0) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.5e+64:
		tmp = -1.0
	elif x <= -5e-34:
		tmp = 1.0
	elif x <= -5.5e-123:
		tmp = x * 0.5
	elif x <= 85000000.0:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.5e+64)
		tmp = -1.0;
	elseif (x <= -5e-34)
		tmp = 1.0;
	elseif (x <= -5.5e-123)
		tmp = Float64(x * 0.5);
	elseif (x <= 85000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9.5e+64)
		tmp = -1.0;
	elseif (x <= -5e-34)
		tmp = 1.0;
	elseif (x <= -5.5e-123)
		tmp = x * 0.5;
	elseif (x <= 85000000.0)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.5e+64], -1.0, If[LessEqual[x, -5e-34], 1.0, If[LessEqual[x, -5.5e-123], N[(x * 0.5), $MachinePrecision], If[LessEqual[x, 85000000.0], 1.0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.50000000000000028e64 or 8.5e7 < 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 -9.50000000000000028e64 < x < -5.0000000000000003e-34 or -5.5e-123 < x < 8.5e7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 50.3%

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

   if -5.0000000000000003e-34 < x < -5.5e-123

   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 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+64}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-34}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-123}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{elif}\;x \leq 85000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 900000:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.8e+64)
   (+ (/ y x) -1.0)
   (if (<= x 900000.0) (/ (- x y) (- 2.0 y)) (/ 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 <= 900000.0) {
		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 <= (-4.8d+64)) then
        tmp = (y / x) + (-1.0d0)
    else if (x <= 900000.0d0) 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 <= -4.8e+64) {
		tmp = (y / x) + -1.0;
	} else if (x <= 900000.0) {
		tmp = (x - y) / (2.0 - y);
	} 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 <= 900000.0:
		tmp = (x - y) / (2.0 - y)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.8e+64)
		tmp = Float64(Float64(y / x) + -1.0);
	elseif (x <= 900000.0)
		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 <= -4.8e+64)
		tmp = (y / x) + -1.0;
	elseif (x <= 900000.0)
		tmp = (x - y) / (2.0 - y);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.8e+64], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[x, 900000.0], 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 < -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 < 9e5

   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 9e5 < 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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+64}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 900000:\\ \;\;\;\;\frac{x - y}{2 - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+64}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 62000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7.2e+64)
   (+ (/ y x) -1.0)
   (if (<= x 62000.0) (/ y (+ y -2.0)) (/ x (- 2.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7.2e+64) {
		tmp = (y / x) + -1.0;
	} else if (x <= 62000.0) {
		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 <= (-7.2d+64)) then
        tmp = (y / x) + (-1.0d0)
    else if (x <= 62000.0d0) 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 <= -7.2e+64) {
		tmp = (y / x) + -1.0;
	} else if (x <= 62000.0) {
		tmp = y / (y + -2.0);
	} else {
		tmp = x / (2.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7.2e+64:
		tmp = (y / x) + -1.0
	elif x <= 62000.0:
		tmp = y / (y + -2.0)
	else:
		tmp = x / (2.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7.2e+64)
		tmp = Float64(Float64(y / x) + -1.0);
	elseif (x <= 62000.0)
		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 <= -7.2e+64)
		tmp = (y / x) + -1.0;
	elseif (x <= 62000.0)
		tmp = y / (y + -2.0);
	else
		tmp = x / (2.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7.2e+64], N[(N[(y / x), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[x, 62000.0], 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 < -7.20000000000000027e64

   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 -7.20000000000000027e64 < x < 62000

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 72.2%

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

      1. associate-*r/ 72.2%

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

      2. neg-mul-1 72.2%

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

   5. Simplified 72.2%

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

      1. frac-2neg 72.2%

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

      2. div-inv 72.1%

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

      3. remove-double-neg 72.1%

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

      4. sub-neg 72.1%

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

      5. distribute-neg-in 72.1%

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

      6. metadata-eval 72.1%

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

      7. remove-double-neg 72.1%

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

   7. Applied egg-rr 72.1%

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

      1. associate-*r/ 72.2%

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

      2. *-rgt-identity 72.2%

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

      3. +-commutative 72.2%

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

   9. Simplified 72.2%

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

   if 62000 < 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 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+64}:\\ \;\;\;\;\frac{y}{x} + -1\\ \mathbf{elif}\;x \leq 62000:\\ \;\;\;\;\frac{y}{y + -2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{2 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+64}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 130000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.8e+64) -1.0 (if (<= x 130000000.0) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.8e+64) {
		tmp = -1.0;
	} else if (x <= 130000000.0) {
		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 <= 130000000.0d0) 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 <= 130000000.0) {
		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 <= 130000000.0:
		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 <= 130000000.0)
		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 <= 130000000.0)
		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, 130000000.0], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999999e64 or 1.3e8 < 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 < 1.3e8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 47.9%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+64}:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq 130000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
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))))