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

Percentage Accurate: 100.0% → 100.0%

Time: 6.1s

Alternatives: 9

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{x + y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{x + y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + y} - \frac{y}{x + y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. div-sub 100.0%

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

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{x}{x + y} - \frac{y}{x + y}} \]
5. Add Preprocessing

Alternative 2: 74.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{-10}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-51}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+26}:\\ \;\;\;\;\frac{x - y}{x}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+42}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* -2.0 (/ y x)))))
   (if (<= x -6.8e-10)
     t_0
     (if (<= x 1.9e-51)
       (+ (* 2.0 (/ x y)) -1.0)
       (if (<= x 1.9e+26) (/ (- x y) x) (if (<= x 6.8e+42) -1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (-2.0 * (y / x));
	double tmp;
	if (x <= -6.8e-10) {
		tmp = t_0;
	} else if (x <= 1.9e-51) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else if (x <= 1.9e+26) {
		tmp = (x - y) / x;
	} else if (x <= 6.8e+42) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + ((-2.0d0) * (y / x))
    if (x <= (-6.8d-10)) then
        tmp = t_0
    else if (x <= 1.9d-51) then
        tmp = (2.0d0 * (x / y)) + (-1.0d0)
    else if (x <= 1.9d+26) then
        tmp = (x - y) / x
    else if (x <= 6.8d+42) 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 = 1.0 + (-2.0 * (y / x));
	double tmp;
	if (x <= -6.8e-10) {
		tmp = t_0;
	} else if (x <= 1.9e-51) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else if (x <= 1.9e+26) {
		tmp = (x - y) / x;
	} else if (x <= 6.8e+42) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (-2.0 * (y / x))
	tmp = 0
	if x <= -6.8e-10:
		tmp = t_0
	elif x <= 1.9e-51:
		tmp = (2.0 * (x / y)) + -1.0
	elif x <= 1.9e+26:
		tmp = (x - y) / x
	elif x <= 6.8e+42:
		tmp = -1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(-2.0 * Float64(y / x)))
	tmp = 0.0
	if (x <= -6.8e-10)
		tmp = t_0;
	elseif (x <= 1.9e-51)
		tmp = Float64(Float64(2.0 * Float64(x / y)) + -1.0);
	elseif (x <= 1.9e+26)
		tmp = Float64(Float64(x - y) / x);
	elseif (x <= 6.8e+42)
		tmp = -1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (-2.0 * (y / x));
	tmp = 0.0;
	if (x <= -6.8e-10)
		tmp = t_0;
	elseif (x <= 1.9e-51)
		tmp = (2.0 * (x / y)) + -1.0;
	elseif (x <= 1.9e+26)
		tmp = (x - y) / x;
	elseif (x <= 6.8e+42)
		tmp = -1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.8e-10], t$95$0, If[LessEqual[x, 1.9e-51], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], If[LessEqual[x, 1.9e+26], N[(N[(x - y), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 6.8e+42], -1.0, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.8000000000000003e-10 or 6.7999999999999995e42 < x

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 79.8%

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

   if -6.8000000000000003e-10 < x < 1.90000000000000001e-51

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 78.2%

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

   if 1.90000000000000001e-51 < x < 1.9000000000000001e26

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.3%

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

   if 1.9000000000000001e26 < x < 6.7999999999999995e42

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 100.0%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-10}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-51}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+26}:\\ \;\;\;\;\frac{x - y}{x}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+42}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + -2 \cdot \frac{y}{x}\\ \mathbf{if}\;x \leq -50000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-62}:\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+26}:\\ \;\;\;\;\frac{x - y}{x}\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+42}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (* -2.0 (/ y x)))))
   (if (<= x -50000000000.0)
     t_0
     (if (<= x 1.35e-62)
       (/ (- y) (+ x y))
       (if (<= x 2e+26) (/ (- x y) x) (if (<= x 6.8e+42) -1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (-2.0 * (y / x));
	double tmp;
	if (x <= -50000000000.0) {
		tmp = t_0;
	} else if (x <= 1.35e-62) {
		tmp = -y / (x + y);
	} else if (x <= 2e+26) {
		tmp = (x - y) / x;
	} else if (x <= 6.8e+42) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + ((-2.0d0) * (y / x))
    if (x <= (-50000000000.0d0)) then
        tmp = t_0
    else if (x <= 1.35d-62) then
        tmp = -y / (x + y)
    else if (x <= 2d+26) then
        tmp = (x - y) / x
    else if (x <= 6.8d+42) 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 = 1.0 + (-2.0 * (y / x));
	double tmp;
	if (x <= -50000000000.0) {
		tmp = t_0;
	} else if (x <= 1.35e-62) {
		tmp = -y / (x + y);
	} else if (x <= 2e+26) {
		tmp = (x - y) / x;
	} else if (x <= 6.8e+42) {
		tmp = -1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (-2.0 * (y / x))
	tmp = 0
	if x <= -50000000000.0:
		tmp = t_0
	elif x <= 1.35e-62:
		tmp = -y / (x + y)
	elif x <= 2e+26:
		tmp = (x - y) / x
	elif x <= 6.8e+42:
		tmp = -1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(-2.0 * Float64(y / x)))
	tmp = 0.0
	if (x <= -50000000000.0)
		tmp = t_0;
	elseif (x <= 1.35e-62)
		tmp = Float64(Float64(-y) / Float64(x + y));
	elseif (x <= 2e+26)
		tmp = Float64(Float64(x - y) / x);
	elseif (x <= 6.8e+42)
		tmp = -1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (-2.0 * (y / x));
	tmp = 0.0;
	if (x <= -50000000000.0)
		tmp = t_0;
	elseif (x <= 1.35e-62)
		tmp = -y / (x + y);
	elseif (x <= 2e+26)
		tmp = (x - y) / x;
	elseif (x <= 6.8e+42)
		tmp = -1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -50000000000.0], t$95$0, If[LessEqual[x, 1.35e-62], N[((-y) / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e+26], N[(N[(x - y), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 6.8e+42], -1.0, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5e10 or 6.7999999999999995e42 < x

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 81.9%

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

   if -5e10 < x < 1.3500000000000001e-62

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.3%

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

      1. neg-mul-1 76.3%

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

   5. Simplified 76.3%

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

   if 1.3500000000000001e-62 < x < 2.0000000000000001e26

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 66.4%

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

   if 2.0000000000000001e26 < x < 6.7999999999999995e42

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 100.0%

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

Alternative 4: 73.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{x}\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-62}:\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+26} \lor \neg \left(x \leq 7.6 \cdot 10^{+42}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) x)))
   (if (<= x -1.5e+14)
     t_0
     (if (<= x 1.7e-62)
       (/ (- y) (+ x y))
       (if (or (<= x 1.85e+26) (not (<= x 7.6e+42))) t_0 -1.0)))))

C

double code(double x, double y) {
	double t_0 = (x - y) / x;
	double tmp;
	if (x <= -1.5e+14) {
		tmp = t_0;
	} else if (x <= 1.7e-62) {
		tmp = -y / (x + y);
	} else if ((x <= 1.85e+26) || !(x <= 7.6e+42)) {
		tmp = t_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 = (x - y) / x
    if (x <= (-1.5d+14)) then
        tmp = t_0
    else if (x <= 1.7d-62) then
        tmp = -y / (x + y)
    else if ((x <= 1.85d+26) .or. (.not. (x <= 7.6d+42))) then
        tmp = t_0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x - y) / x;
	double tmp;
	if (x <= -1.5e+14) {
		tmp = t_0;
	} else if (x <= 1.7e-62) {
		tmp = -y / (x + y);
	} else if ((x <= 1.85e+26) || !(x <= 7.6e+42)) {
		tmp = t_0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) / x
	tmp = 0
	if x <= -1.5e+14:
		tmp = t_0
	elif x <= 1.7e-62:
		tmp = -y / (x + y)
	elif (x <= 1.85e+26) or not (x <= 7.6e+42):
		tmp = t_0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / x)
	tmp = 0.0
	if (x <= -1.5e+14)
		tmp = t_0;
	elseif (x <= 1.7e-62)
		tmp = Float64(Float64(-y) / Float64(x + y));
	elseif ((x <= 1.85e+26) || !(x <= 7.6e+42))
		tmp = t_0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) / x;
	tmp = 0.0;
	if (x <= -1.5e+14)
		tmp = t_0;
	elseif (x <= 1.7e-62)
		tmp = -y / (x + y);
	elseif ((x <= 1.85e+26) || ~((x <= 7.6e+42)))
		tmp = t_0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / x), $MachinePrecision]}, If[LessEqual[x, -1.5e+14], t$95$0, If[LessEqual[x, 1.7e-62], N[((-y) / N[(x + y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.85e+26], N[Not[LessEqual[x, 7.6e+42]], $MachinePrecision]], t$95$0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5e14 or 1.69999999999999994e-62 < x < 1.84999999999999994e26 or 7.5999999999999997e42 < x

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 79.5%

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

   if -1.5e14 < x < 1.69999999999999994e-62

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.3%

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

      1. neg-mul-1 76.3%

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

   5. Simplified 76.3%

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

   if 1.84999999999999994e26 < x < 7.5999999999999997e42

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 100.0%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{x - y}{x}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-62}:\\ \;\;\;\;\frac{-y}{x + y}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+26} \lor \neg \left(x \leq 7.6 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{x - y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{x}\\ \mathbf{if}\;x \leq -5.3 \cdot 10^{-11}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-51}:\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+26} \lor \neg \left(x \leq 6.8 \cdot 10^{+42}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) x)))
   (if (<= x -5.3e-11)
     t_0
     (if (<= x 2.8e-51)
       (/ (- x y) y)
       (if (or (<= x 1.45e+26) (not (<= x 6.8e+42))) t_0 -1.0)))))

C

double code(double x, double y) {
	double t_0 = (x - y) / x;
	double tmp;
	if (x <= -5.3e-11) {
		tmp = t_0;
	} else if (x <= 2.8e-51) {
		tmp = (x - y) / y;
	} else if ((x <= 1.45e+26) || !(x <= 6.8e+42)) {
		tmp = t_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 = (x - y) / x
    if (x <= (-5.3d-11)) then
        tmp = t_0
    else if (x <= 2.8d-51) then
        tmp = (x - y) / y
    else if ((x <= 1.45d+26) .or. (.not. (x <= 6.8d+42))) then
        tmp = t_0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x - y) / x;
	double tmp;
	if (x <= -5.3e-11) {
		tmp = t_0;
	} else if (x <= 2.8e-51) {
		tmp = (x - y) / y;
	} else if ((x <= 1.45e+26) || !(x <= 6.8e+42)) {
		tmp = t_0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) / x
	tmp = 0
	if x <= -5.3e-11:
		tmp = t_0
	elif x <= 2.8e-51:
		tmp = (x - y) / y
	elif (x <= 1.45e+26) or not (x <= 6.8e+42):
		tmp = t_0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / x)
	tmp = 0.0
	if (x <= -5.3e-11)
		tmp = t_0;
	elseif (x <= 2.8e-51)
		tmp = Float64(Float64(x - y) / y);
	elseif ((x <= 1.45e+26) || !(x <= 6.8e+42))
		tmp = t_0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) / x;
	tmp = 0.0;
	if (x <= -5.3e-11)
		tmp = t_0;
	elseif (x <= 2.8e-51)
		tmp = (x - y) / y;
	elseif ((x <= 1.45e+26) || ~((x <= 6.8e+42)))
		tmp = t_0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / x), $MachinePrecision]}, If[LessEqual[x, -5.3e-11], t$95$0, If[LessEqual[x, 2.8e-51], N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision], If[Or[LessEqual[x, 1.45e+26], N[Not[LessEqual[x, 6.8e+42]], $MachinePrecision]], t$95$0, -1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.2999999999999998e-11 or 2.8e-51 < x < 1.45e26 or 6.7999999999999995e42 < x

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 78.2%

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

   if -5.2999999999999998e-11 < x < 2.8e-51

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 77.4%

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

   if 1.45e26 < x < 6.7999999999999995e42

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 100.0%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{-11}:\\ \;\;\;\;\frac{x - y}{x}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-51}:\\ \;\;\;\;\frac{x - y}{y}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+26} \lor \neg \left(x \leq 6.8 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{x - y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{-11} \lor \neg \left(x \leq 1.8 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x - y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -9.8e-11) (not (<= x 1.8e-62))) (/ (- x y) x) -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -9.8e-11) || !(x <= 1.8e-62)) {
		tmp = (x - y) / x;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-9.8d-11)) .or. (.not. (x <= 1.8d-62))) then
        tmp = (x - y) / x
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -9.8e-11) || !(x <= 1.8e-62)) {
		tmp = (x - y) / x;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -9.8e-11) or not (x <= 1.8e-62):
		tmp = (x - y) / x
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -9.8e-11) || !(x <= 1.8e-62))
		tmp = Float64(Float64(x - y) / x);
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -9.8e-11) || ~((x <= 1.8e-62)))
		tmp = (x - y) / x;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -9.8e-11], N[Not[LessEqual[x, 1.8e-62]], $MachinePrecision]], N[(N[(x - y), $MachinePrecision] / x), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if x < -9.7999999999999998e-11 or 1.8e-62 < x

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.1%

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

   if -9.7999999999999998e-11 < x < 1.8e-62

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 77.2%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.8 \cdot 10^{-11} \lor \neg \left(x \leq 1.8 \cdot 10^{-62}\right):\\ \;\;\;\;\frac{x - y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -28000000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-55}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -28000000000000.0) 1.0 (if (<= x 8e-55) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -28000000000000.0) {
		tmp = 1.0;
	} else if (x <= 8e-55) {
		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 <= (-28000000000000.0d0)) then
        tmp = 1.0d0
    else if (x <= 8d-55) 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 <= -28000000000000.0) {
		tmp = 1.0;
	} else if (x <= 8e-55) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -28000000000000.0:
		tmp = 1.0
	elif x <= 8e-55:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -28000000000000.0)
		tmp = 1.0;
	elseif (x <= 8e-55)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -28000000000000.0)
		tmp = 1.0;
	elseif (x <= 8e-55)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -28000000000000.0], 1.0, If[LessEqual[x, 8e-55], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8e13 or 7.99999999999999996e-55 < x

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.3%

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

   if -2.8e13 < x < 7.99999999999999996e-55

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 75.1%

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

Alternative 8: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{x + y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[\frac{x - y}{x + y} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 9: 50.6% accurate, 7.0× 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 99.9%

   \[\frac{x - y}{x + y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 49.3%

   \[\leadsto \color{blue}{-1} \]
4. Add Preprocessing

Developer target: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \frac{x}{x + y} - \frac{y}{x + y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024111 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

  :alt
  (- (/ x (+ x y)) (/ y (+ x y)))

  (/ (- x y) (+ x y)))