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

Percentage Accurate: 100.0% → 100.0%

Time: 7.9s

Alternatives: 7

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 100.0%

   \[\frac{x - y}{x + y} \]
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. Final simplification 100.0%

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

Alternative 2: 74.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+18}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+15} \lor \neg \left(y \leq 8.5 \cdot 10^{+55}\right) \land y \leq 2.2 \cdot 10^{+89}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.6e+18)
   -1.0
   (if (or (<= y 1.16e+15) (and (not (<= y 8.5e+55)) (<= y 2.2e+89)))
     (- 1.0 (/ y x))
     -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.6e+18) {
		tmp = -1.0;
	} else if ((y <= 1.16e+15) || (!(y <= 8.5e+55) && (y <= 2.2e+89))) {
		tmp = 1.0 - (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 (y <= (-3.6d+18)) then
        tmp = -1.0d0
    else if ((y <= 1.16d+15) .or. (.not. (y <= 8.5d+55)) .and. (y <= 2.2d+89)) then
        tmp = 1.0d0 - (y / x)
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.6e+18) {
		tmp = -1.0;
	} else if ((y <= 1.16e+15) || (!(y <= 8.5e+55) && (y <= 2.2e+89))) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.6e+18:
		tmp = -1.0
	elif (y <= 1.16e+15) or (not (y <= 8.5e+55) and (y <= 2.2e+89)):
		tmp = 1.0 - (y / x)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.6e+18)
		tmp = -1.0;
	elseif ((y <= 1.16e+15) || (!(y <= 8.5e+55) && (y <= 2.2e+89)))
		tmp = Float64(1.0 - Float64(y / x));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.6e+18)
		tmp = -1.0;
	elseif ((y <= 1.16e+15) || (~((y <= 8.5e+55)) && (y <= 2.2e+89)))
		tmp = 1.0 - (y / x);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.6e+18], -1.0, If[Or[LessEqual[y, 1.16e+15], And[N[Not[LessEqual[y, 8.5e+55]], $MachinePrecision], LessEqual[y, 2.2e+89]]], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6e18 or 1.16e15 < y < 8.50000000000000002e55 or 2.2e89 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 84.5%

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

   if -3.6e18 < y < 1.16e15 or 8.50000000000000002e55 < y < 2.2e89

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   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. Step-by-step derivation

      1. frac-sub 62.7%

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

      2. associate-/r* 63.2%

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

      3. *-commutative 63.2%

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

   6. Applied egg-rr 63.2%

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

   7. Taylor expanded in x around inf 83.2%

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

   8. Taylor expanded in x around inf 83.3%

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

      1. mul-1-neg 83.3%

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

      2. unsub-neg 83.3%

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

   10. Simplified 83.3%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+18}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.16 \cdot 10^{+15} \lor \neg \left(y \leq 8.5 \cdot 10^{+55}\right) \land y \leq 2.2 \cdot 10^{+89}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y} + -1\\ t_1 := 1 - \frac{y}{x}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+18}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+58}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+89}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ x y) -1.0)) (t_1 (- 1.0 (/ y x))))
   (if (<= y -2.9e+18)
     t_0
     (if (<= y 7.5e+16)
       t_1
       (if (<= y 8.8e+58) -1.0 (if (<= y 3.4e+89) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = (x / y) + -1.0;
	double t_1 = 1.0 - (y / x);
	double tmp;
	if (y <= -2.9e+18) {
		tmp = t_0;
	} else if (y <= 7.5e+16) {
		tmp = t_1;
	} else if (y <= 8.8e+58) {
		tmp = -1.0;
	} else if (y <= 3.4e+89) {
		tmp = t_1;
	} 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 = (x / y) + (-1.0d0)
    t_1 = 1.0d0 - (y / x)
    if (y <= (-2.9d+18)) then
        tmp = t_0
    else if (y <= 7.5d+16) then
        tmp = t_1
    else if (y <= 8.8d+58) then
        tmp = -1.0d0
    else if (y <= 3.4d+89) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x / y) + -1.0;
	double t_1 = 1.0 - (y / x);
	double tmp;
	if (y <= -2.9e+18) {
		tmp = t_0;
	} else if (y <= 7.5e+16) {
		tmp = t_1;
	} else if (y <= 8.8e+58) {
		tmp = -1.0;
	} else if (y <= 3.4e+89) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x / y) + -1.0
	t_1 = 1.0 - (y / x)
	tmp = 0
	if y <= -2.9e+18:
		tmp = t_0
	elif y <= 7.5e+16:
		tmp = t_1
	elif y <= 8.8e+58:
		tmp = -1.0
	elif y <= 3.4e+89:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x / y) + -1.0)
	t_1 = Float64(1.0 - Float64(y / x))
	tmp = 0.0
	if (y <= -2.9e+18)
		tmp = t_0;
	elseif (y <= 7.5e+16)
		tmp = t_1;
	elseif (y <= 8.8e+58)
		tmp = -1.0;
	elseif (y <= 3.4e+89)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x / y) + -1.0;
	t_1 = 1.0 - (y / x);
	tmp = 0.0;
	if (y <= -2.9e+18)
		tmp = t_0;
	elseif (y <= 7.5e+16)
		tmp = t_1;
	elseif (y <= 8.8e+58)
		tmp = -1.0;
	elseif (y <= 3.4e+89)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.9e+18], t$95$0, If[LessEqual[y, 7.5e+16], t$95$1, If[LessEqual[y, 8.8e+58], -1.0, If[LessEqual[y, 3.4e+89], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9e18 or 3.4000000000000002e89 < y

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   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. Step-by-step derivation

      1. frac-sub 23.5%

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

      2. associate-/r* 25.5%

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

      3. *-commutative 25.5%

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

   6. Applied egg-rr 25.5%

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

   7. Taylor expanded in x around 0 84.8%

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

      1. neg-mul-1 84.8%

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

   9. Simplified 84.8%

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

   10. Taylor expanded in y around inf 84.9%

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

   if -2.9e18 < y < 7.5e16 or 8.8000000000000003e58 < y < 3.4000000000000002e89

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   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. Step-by-step derivation

      1. frac-sub 62.7%

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

      2. associate-/r* 63.2%

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

      3. *-commutative 63.2%

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

   6. Applied egg-rr 63.2%

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

   7. Taylor expanded in x around inf 83.2%

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

   8. Taylor expanded in x around inf 83.3%

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

      1. mul-1-neg 83.3%

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

      2. unsub-neg 83.3%

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

   10. Simplified 83.3%

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

   if 7.5e16 < y < 8.8000000000000003e58

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.9%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+18}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+16}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+58}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+89}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y} + -1\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{+17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+55}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+89}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ x y) -1.0)))
   (if (<= y -1.1e+17)
     t_0
     (if (<= y 1.9e+32)
       (/ x (+ x y))
       (if (<= y 4.6e+55) -1.0 (if (<= y 2.1e+89) (- 1.0 (/ y x)) t_0))))))

C

double code(double x, double y) {
	double t_0 = (x / y) + -1.0;
	double tmp;
	if (y <= -1.1e+17) {
		tmp = t_0;
	} else if (y <= 1.9e+32) {
		tmp = x / (x + y);
	} else if (y <= 4.6e+55) {
		tmp = -1.0;
	} else if (y <= 2.1e+89) {
		tmp = 1.0 - (y / x);
	} 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 = (x / y) + (-1.0d0)
    if (y <= (-1.1d+17)) then
        tmp = t_0
    else if (y <= 1.9d+32) then
        tmp = x / (x + y)
    else if (y <= 4.6d+55) then
        tmp = -1.0d0
    else if (y <= 2.1d+89) then
        tmp = 1.0d0 - (y / x)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x / y) + -1.0;
	double tmp;
	if (y <= -1.1e+17) {
		tmp = t_0;
	} else if (y <= 1.9e+32) {
		tmp = x / (x + y);
	} else if (y <= 4.6e+55) {
		tmp = -1.0;
	} else if (y <= 2.1e+89) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x / y) + -1.0
	tmp = 0
	if y <= -1.1e+17:
		tmp = t_0
	elif y <= 1.9e+32:
		tmp = x / (x + y)
	elif y <= 4.6e+55:
		tmp = -1.0
	elif y <= 2.1e+89:
		tmp = 1.0 - (y / x)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x / y) + -1.0)
	tmp = 0.0
	if (y <= -1.1e+17)
		tmp = t_0;
	elseif (y <= 1.9e+32)
		tmp = Float64(x / Float64(x + y));
	elseif (y <= 4.6e+55)
		tmp = -1.0;
	elseif (y <= 2.1e+89)
		tmp = Float64(1.0 - Float64(y / x));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x / y) + -1.0;
	tmp = 0.0;
	if (y <= -1.1e+17)
		tmp = t_0;
	elseif (y <= 1.9e+32)
		tmp = x / (x + y);
	elseif (y <= 4.6e+55)
		tmp = -1.0;
	elseif (y <= 2.1e+89)
		tmp = 1.0 - (y / x);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]}, If[LessEqual[y, -1.1e+17], t$95$0, If[LessEqual[y, 1.9e+32], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e+55], -1.0, If[LessEqual[y, 2.1e+89], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.1e17 or 2.09999999999999986e89 < y

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   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. Step-by-step derivation

      1. frac-sub 23.5%

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

      2. associate-/r* 25.5%

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

      3. *-commutative 25.5%

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

   6. Applied egg-rr 25.5%

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

   7. Taylor expanded in x around 0 84.8%

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

      1. neg-mul-1 84.8%

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

   9. Simplified 84.8%

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

   10. Taylor expanded in y around inf 84.9%

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

   if -1.1e17 < y < 1.9000000000000002e32

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]
   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. Step-by-step derivation

      1. frac-sub 65.1%

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

      2. associate-/r* 65.6%

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

      3. *-commutative 65.6%

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

   6. Applied egg-rr 65.6%

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

   7. Taylor expanded in x around inf 82.6%

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

   if 1.9000000000000002e32 < y < 4.59999999999999975e55

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

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

   if 4.59999999999999975e55 < y < 2.09999999999999986e89

   1. Initial program 99.8%

      \[\frac{x - y}{x + y} \]
   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. Step-by-step derivation

      1. frac-sub 14.3%

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

      2. associate-/r* 17.0%

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

      3. *-commutative 17.0%

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

   6. Applied egg-rr 17.0%

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

   7. Taylor expanded in x around inf 85.9%

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

   8. Taylor expanded in x around inf 88.0%

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

      1. mul-1-neg 88.0%

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

      2. unsub-neg 88.0%

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

   10. Simplified 88.0%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{x + y}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+55}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+89}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+19}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{+55}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+89}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.8e+19)
   -1.0
   (if (<= y 5.8e+14)
     1.0
     (if (<= y 1e+55) -1.0 (if (<= y 2.5e+89) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.8e+19) {
		tmp = -1.0;
	} else if (y <= 5.8e+14) {
		tmp = 1.0;
	} else if (y <= 1e+55) {
		tmp = -1.0;
	} else if (y <= 2.5e+89) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-6.8d+19)) then
        tmp = -1.0d0
    else if (y <= 5.8d+14) then
        tmp = 1.0d0
    else if (y <= 1d+55) then
        tmp = -1.0d0
    else if (y <= 2.5d+89) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6.8e+19) {
		tmp = -1.0;
	} else if (y <= 5.8e+14) {
		tmp = 1.0;
	} else if (y <= 1e+55) {
		tmp = -1.0;
	} else if (y <= 2.5e+89) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6.8e+19:
		tmp = -1.0
	elif y <= 5.8e+14:
		tmp = 1.0
	elif y <= 1e+55:
		tmp = -1.0
	elif y <= 2.5e+89:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6.8e+19)
		tmp = -1.0;
	elseif (y <= 5.8e+14)
		tmp = 1.0;
	elseif (y <= 1e+55)
		tmp = -1.0;
	elseif (y <= 2.5e+89)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6.8e+19)
		tmp = -1.0;
	elseif (y <= 5.8e+14)
		tmp = 1.0;
	elseif (y <= 1e+55)
		tmp = -1.0;
	elseif (y <= 2.5e+89)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6.8e+19], -1.0, If[LessEqual[y, 5.8e+14], 1.0, If[LessEqual[y, 1e+55], -1.0, If[LessEqual[y, 2.5e+89], 1.0, -1.0]]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.8e19 or 5.8e14 < y < 1.00000000000000001e55 or 2.49999999999999992e89 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 84.5%

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

   if -6.8e19 < y < 5.8e14 or 1.00000000000000001e55 < y < 2.49999999999999992e89

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.8%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+19}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+14}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 10^{+55}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+89}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 100.0%

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

3. Final simplification 100.0%

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

Alternative 7: 49.5% 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 100.0%

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

3. Taylor expanded in x around 0 49.2%

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

4. Final simplification 49.2%

   \[\leadsto -1 \]
5. 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 2024044 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

  :herbie-target
  (- (/ x (+ x y)) (/ y (+ x y)))

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