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

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 8

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, 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. Add Preprocessing

Alternative 2: 76.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{+30} \lor \neg \left(x \leq 4.15 \cdot 10^{-53}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -7.4e+30) (not (<= x 4.15e-53)))
   (+ 1.0 (* -2.0 (/ y x)))
   (+ (* 2.0 (/ x y)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -7.4e+30) || !(x <= 4.15e-53)) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = (2.0 * (x / y)) + -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 <= (-7.4d+30)) .or. (.not. (x <= 4.15d-53))) then
        tmp = 1.0d0 + ((-2.0d0) * (y / x))
    else
        tmp = (2.0d0 * (x / y)) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -7.4e+30) || !(x <= 4.15e-53)) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = (2.0 * (x / y)) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -7.4e+30) or not (x <= 4.15e-53):
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = (2.0 * (x / y)) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -7.4e+30) || !(x <= 4.15e-53))
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	else
		tmp = Float64(Float64(2.0 * Float64(x / y)) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -7.4e+30) || ~((x <= 4.15e-53)))
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = (2.0 * (x / y)) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -7.4e+30], N[Not[LessEqual[x, 4.15e-53]], $MachinePrecision]], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.40000000000000032e30 or 4.1499999999999998e-53 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.3%

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

   if -7.40000000000000032e30 < x < 4.1499999999999998e-53

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 76.3%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.4 \cdot 10^{+30} \lor \neg \left(x \leq 4.15 \cdot 10^{-53}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+28} \lor \neg \left(x \leq 4.8 \cdot 10^{-53}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.2e+28) (not (<= x 4.8e-53)))
   (+ 1.0 (* -2.0 (/ y x)))
   (+ (/ x y) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.2e+28) || !(x <= 4.8e-53)) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = (x / y) + -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 <= (-1.2d+28)) .or. (.not. (x <= 4.8d-53))) then
        tmp = 1.0d0 + ((-2.0d0) * (y / x))
    else
        tmp = (x / y) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.2e+28) || !(x <= 4.8e-53)) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = (x / y) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.2e+28) or not (x <= 4.8e-53):
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = (x / y) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.2e+28) || !(x <= 4.8e-53))
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	else
		tmp = Float64(Float64(x / y) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.2e+28) || ~((x <= 4.8e-53)))
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = (x / y) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.2e+28], N[Not[LessEqual[x, 4.8e-53]], $MachinePrecision]], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.19999999999999991e28 or 4.80000000000000015e-53 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.3%

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

   if -1.19999999999999991e28 < x < 4.80000000000000015e-53

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 74.7%

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

      1. neg-mul-1 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in y around inf 74.9%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.2 \cdot 10^{+28} \lor \neg \left(x \leq 4.8 \cdot 10^{-53}\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+29} \lor \neg \left(x \leq 1.95 \cdot 10^{-53}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.15e+29) (not (<= x 1.95e-53)))
   (- 1.0 (/ y x))
   (+ (/ x y) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.15e+29) || !(x <= 1.95e-53)) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = (x / y) + -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 <= (-1.15d+29)) .or. (.not. (x <= 1.95d-53))) then
        tmp = 1.0d0 - (y / x)
    else
        tmp = (x / y) + (-1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.15e+29) || !(x <= 1.95e-53)) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = (x / y) + -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.15e+29) or not (x <= 1.95e-53):
		tmp = 1.0 - (y / x)
	else:
		tmp = (x / y) + -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.15e+29) || !(x <= 1.95e-53))
		tmp = Float64(1.0 - Float64(y / x));
	else
		tmp = Float64(Float64(x / y) + -1.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.15e+29) || ~((x <= 1.95e-53)))
		tmp = 1.0 - (y / x);
	else
		tmp = (x / y) + -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.15e+29], N[Not[LessEqual[x, 1.95e-53]], $MachinePrecision]], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1500000000000001e29 or 1.9500000000000001e-53 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.8%

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

   4. Taylor expanded in x around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. mul-1-neg 76.8%

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

      3. remove-double-neg 76.8%

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

      4. distribute-neg-in 76.8%

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

      5. distribute-neg-frac 76.8%

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

      6. neg-sub0 76.8%

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

      7. sub-neg 76.8%

         \[\leadsto 0 - \frac{\color{blue}{y - x}}{x} \]

      8. div-sub 76.8%

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

      9. *-rgt-identity 76.8%

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

      10. associate-*r/ 76.6%

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

      11. rgt-mult-inverse 76.8%

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

      12. associate-+l- 76.8%

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

      13. neg-sub0 76.8%

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

      14. +-commutative 76.8%

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

      15. sub-neg 76.8%

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

   6. Simplified 76.8%

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

   if -1.1500000000000001e29 < x < 1.9500000000000001e-53

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 74.7%

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

      1. neg-mul-1 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in y around inf 74.9%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+29} \lor \neg \left(x \leq 1.95 \cdot 10^{-53}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+29} \lor \neg \left(x \leq 4.8 \cdot 10^{-53}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -9.5e+29) (not (<= x 4.8e-53))) (- 1.0 (/ y x)) -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -9.5e+29) || !(x <= 4.8e-53)) {
		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 ((x <= (-9.5d+29)) .or. (.not. (x <= 4.8d-53))) 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 ((x <= -9.5e+29) || !(x <= 4.8e-53)) {
		tmp = 1.0 - (y / x);
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -9.5e+29) or not (x <= 4.8e-53):
		tmp = 1.0 - (y / x)
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -9.5e+29) || !(x <= 4.8e-53))
		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 ((x <= -9.5e+29) || ~((x <= 4.8e-53)))
		tmp = 1.0 - (y / x);
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -9.5e+29], N[Not[LessEqual[x, 4.8e-53]], $MachinePrecision]], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if x < -9.5000000000000003e29 or 4.80000000000000015e-53 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.8%

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

   4. Taylor expanded in x around 0 76.8%

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

      1. +-commutative 76.8%

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

      2. mul-1-neg 76.8%

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

      3. remove-double-neg 76.8%

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

      4. distribute-neg-in 76.8%

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

      5. distribute-neg-frac 76.8%

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

      6. neg-sub0 76.8%

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

      7. sub-neg 76.8%

         \[\leadsto 0 - \frac{\color{blue}{y - x}}{x} \]

      8. div-sub 76.8%

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

      9. *-rgt-identity 76.8%

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

      10. associate-*r/ 76.6%

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

      11. rgt-mult-inverse 76.8%

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

      12. associate-+l- 76.8%

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

      13. neg-sub0 76.8%

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

      14. +-commutative 76.8%

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

      15. sub-neg 76.8%

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

   6. Simplified 76.8%

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

   if -9.5000000000000003e29 < x < 4.80000000000000015e-53

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 74.0%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+29} \lor \neg \left(x \leq 4.8 \cdot 10^{-53}\right):\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+31}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 4.15 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.85e+31)
   (- 1.0 (/ y x))
   (if (<= x 4.15e-53) (+ (/ x y) -1.0) (/ (- x y) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.85e+31) {
		tmp = 1.0 - (y / x);
	} else if (x <= 4.15e-53) {
		tmp = (x / y) + -1.0;
	} else {
		tmp = (x - y) / 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 <= (-1.85d+31)) then
        tmp = 1.0d0 - (y / x)
    else if (x <= 4.15d-53) then
        tmp = (x / y) + (-1.0d0)
    else
        tmp = (x - y) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.85e+31) {
		tmp = 1.0 - (y / x);
	} else if (x <= 4.15e-53) {
		tmp = (x / y) + -1.0;
	} else {
		tmp = (x - y) / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.85e+31:
		tmp = 1.0 - (y / x)
	elif x <= 4.15e-53:
		tmp = (x / y) + -1.0
	else:
		tmp = (x - y) / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.85e+31)
		tmp = Float64(1.0 - Float64(y / x));
	elseif (x <= 4.15e-53)
		tmp = Float64(Float64(x / y) + -1.0);
	else
		tmp = Float64(Float64(x - y) / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.85e+31)
		tmp = 1.0 - (y / x);
	elseif (x <= 4.15e-53)
		tmp = (x / y) + -1.0;
	else
		tmp = (x - y) / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.85e+31], N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.15e-53], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision], N[(N[(x - y), $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.8499999999999999e31

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 77.3%

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

   4. Taylor expanded in x around 0 77.3%

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

      1. +-commutative 77.3%

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

      2. mul-1-neg 77.3%

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

      3. remove-double-neg 77.3%

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

      4. distribute-neg-in 77.3%

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

      5. distribute-neg-frac 77.3%

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

      6. neg-sub0 77.3%

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

      7. sub-neg 77.3%

         \[\leadsto 0 - \frac{\color{blue}{y - x}}{x} \]

      8. div-sub 77.3%

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

      9. *-rgt-identity 77.3%

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

      10. associate-*r/ 77.1%

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

      11. rgt-mult-inverse 77.3%

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

      12. associate-+l- 77.3%

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

      13. neg-sub0 77.3%

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

      14. +-commutative 77.3%

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

      15. sub-neg 77.3%

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

   6. Simplified 77.3%

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

   if -1.8499999999999999e31 < x < 4.1499999999999998e-53

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 74.7%

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

      1. neg-mul-1 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in y around inf 74.9%

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

   if 4.1499999999999998e-53 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.2%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+31}:\\ \;\;\;\;1 - \frac{y}{x}\\ \mathbf{elif}\;x \leq 4.15 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x - y}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+27}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-53}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.4e+27) 1.0 (if (<= x 3.8e-53) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.4e+27) {
		tmp = 1.0;
	} else if (x <= 3.8e-53) {
		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 <= (-3.4d+27)) then
        tmp = 1.0d0
    else if (x <= 3.8d-53) 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 <= -3.4e+27) {
		tmp = 1.0;
	} else if (x <= 3.8e-53) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.4e+27:
		tmp = 1.0
	elif x <= 3.8e-53:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.4e+27)
		tmp = 1.0;
	elseif (x <= 3.8e-53)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.4e+27)
		tmp = 1.0;
	elseif (x <= 3.8e-53)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.4e+27], 1.0, If[LessEqual[x, 3.8e-53], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.4e27 or 3.7999999999999998e-53 < 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 -3.4e27 < x < 3.7999999999999998e-53

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 74.0%

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

Alternative 8: 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 100.0%

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

3. Taylor expanded in x around 0 47.2%

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

Developer Target 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]

Reproduce

herbie shell --seed 2024113 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ x (+ x y)) (/ y (+ x y))))

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