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

Percentage Accurate: 100.0% → 100.0%

Time: 7.6s

Alternatives: 6

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, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{x + y}{x - y}} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ 1.0 (/ (+ x y) (- x y))))

C

double code(double x, double y) {
	return 1.0 / ((x + y) / (x - y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 / ((x + y) / (x - y))
end function

Java

public static double code(double x, double y) {
	return 1.0 / ((x + y) / (x - y));
}

Python

def code(x, y):
	return 1.0 / ((x + y) / (x - y))

Julia

function code(x, y)
	return Float64(1.0 / Float64(Float64(x + y) / Float64(x - y)))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 / ((x + y) / (x - y));
end

Wolfram

code[x_, y_] := N[(1.0 / N[(N[(x + y), $MachinePrecision] / 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. add-cbrt-cube 99.9%

      \[\leadsto \color{blue}{\sqrt[3]{\left(\frac{x - y}{x + y} \cdot \frac{x - y}{x + y}\right) \cdot \frac{x - y}{x + y}}} \]

   2. pow3 99.9%

      \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{x - y}{x + y}\right)}^{3}}} \]

4. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\sqrt[3]{{\left(\frac{x - y}{x + y}\right)}^{3}}} \]
5. Step-by-step derivation

   1. rem-cbrt-cube 100.0%

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

   2. clear-num 100.0%

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

6. Applied egg-rr 100.0%

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

7. Final simplification 100.0%

   \[\leadsto \frac{1}{\frac{x + y}{x - y}} \]
8. Add Preprocessing

Alternative 2: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+83} \lor \neg \left(x \leq -85\right) \land \left(x \leq -6.4 \cdot 10^{-43} \lor \neg \left(x \leq 6.8 \cdot 10^{+82}\right)\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5e+83)
         (and (not (<= x -85.0)) (or (<= x -6.4e-43) (not (<= x 6.8e+82)))))
   (+ 1.0 (* -2.0 (/ y x)))
   -1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5e+83) || (!(x <= -85.0) && ((x <= -6.4e-43) || !(x <= 6.8e+82)))) {
		tmp = 1.0 + (-2.0 * (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 <= (-5d+83)) .or. (.not. (x <= (-85.0d0))) .and. (x <= (-6.4d-43)) .or. (.not. (x <= 6.8d+82))) then
        tmp = 1.0d0 + ((-2.0d0) * (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 <= -5e+83) || (!(x <= -85.0) && ((x <= -6.4e-43) || !(x <= 6.8e+82)))) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5e+83) or (not (x <= -85.0) and ((x <= -6.4e-43) or not (x <= 6.8e+82))):
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5e+83) || (!(x <= -85.0) && ((x <= -6.4e-43) || !(x <= 6.8e+82))))
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -5e+83) || (~((x <= -85.0)) && ((x <= -6.4e-43) || ~((x <= 6.8e+82)))))
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5e+83], And[N[Not[LessEqual[x, -85.0]], $MachinePrecision], Or[LessEqual[x, -6.4e-43], N[Not[LessEqual[x, 6.8e+82]], $MachinePrecision]]]], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]

Derivation

1. Split input into 2 regimes

2. if x < -5.00000000000000029e83 or -85 < x < -6.3999999999999997e-43 or 6.79999999999999989e82 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 83.2%

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

   if -5.00000000000000029e83 < x < -85 or -6.3999999999999997e-43 < x < 6.79999999999999989e82

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.8%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+83} \lor \neg \left(x \leq -85\right) \land \left(x \leq -6.4 \cdot 10^{-43} \lor \neg \left(x \leq 6.8 \cdot 10^{+82}\right)\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+83} \lor \neg \left(x \leq -175\right) \land \left(x \leq -5.5 \cdot 10^{-43} \lor \neg \left(x \leq 1.15 \cdot 10^{+83}\right)\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5e+83)
         (and (not (<= x -175.0)) (or (<= x -5.5e-43) (not (<= x 1.15e+83)))))
   (+ 1.0 (* -2.0 (/ y x)))
   (+ (* 2.0 (/ x y)) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5e+83) || (!(x <= -175.0) && ((x <= -5.5e-43) || !(x <= 1.15e+83)))) {
		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 <= (-5d+83)) .or. (.not. (x <= (-175.0d0))) .and. (x <= (-5.5d-43)) .or. (.not. (x <= 1.15d+83))) 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 <= -5e+83) || (!(x <= -175.0) && ((x <= -5.5e-43) || !(x <= 1.15e+83)))) {
		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 <= -5e+83) or (not (x <= -175.0) and ((x <= -5.5e-43) or not (x <= 1.15e+83))):
		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 <= -5e+83) || (!(x <= -175.0) && ((x <= -5.5e-43) || !(x <= 1.15e+83))))
		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 <= -5e+83) || (~((x <= -175.0)) && ((x <= -5.5e-43) || ~((x <= 1.15e+83)))))
		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, -5e+83], And[N[Not[LessEqual[x, -175.0]], $MachinePrecision], Or[LessEqual[x, -5.5e-43], N[Not[LessEqual[x, 1.15e+83]], $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 < -5.00000000000000029e83 or -175 < x < -5.50000000000000013e-43 or 1.14999999999999997e83 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 83.2%

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

   if -5.00000000000000029e83 < x < -175 or -5.50000000000000013e-43 < x < 1.14999999999999997e83

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 78.3%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+83} \lor \neg \left(x \leq -175\right) \land \left(x \leq -5.5 \cdot 10^{-43} \lor \neg \left(x \leq 1.15 \cdot 10^{+83}\right)\right):\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+83}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -94:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-42}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+83}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5e+83)
   1.0
   (if (<= x -94.0) -1.0 (if (<= x -1e-42) 1.0 (if (<= x 1.7e+83) -1.0 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5e+83) {
		tmp = 1.0;
	} else if (x <= -94.0) {
		tmp = -1.0;
	} else if (x <= -1e-42) {
		tmp = 1.0;
	} else if (x <= 1.7e+83) {
		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 <= (-5d+83)) then
        tmp = 1.0d0
    else if (x <= (-94.0d0)) then
        tmp = -1.0d0
    else if (x <= (-1d-42)) then
        tmp = 1.0d0
    else if (x <= 1.7d+83) 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 <= -5e+83) {
		tmp = 1.0;
	} else if (x <= -94.0) {
		tmp = -1.0;
	} else if (x <= -1e-42) {
		tmp = 1.0;
	} else if (x <= 1.7e+83) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5e+83:
		tmp = 1.0
	elif x <= -94.0:
		tmp = -1.0
	elif x <= -1e-42:
		tmp = 1.0
	elif x <= 1.7e+83:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5e+83)
		tmp = 1.0;
	elseif (x <= -94.0)
		tmp = -1.0;
	elseif (x <= -1e-42)
		tmp = 1.0;
	elseif (x <= 1.7e+83)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5e+83)
		tmp = 1.0;
	elseif (x <= -94.0)
		tmp = -1.0;
	elseif (x <= -1e-42)
		tmp = 1.0;
	elseif (x <= 1.7e+83)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5e+83], 1.0, If[LessEqual[x, -94.0], -1.0, If[LessEqual[x, -1e-42], 1.0, If[LessEqual[x, 1.7e+83], -1.0, 1.0]]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.00000000000000029e83 or -94 < x < -1.00000000000000004e-42 or 1.6999999999999999e83 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.1%

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

   if -5.00000000000000029e83 < x < -94 or -1.00000000000000004e-42 < x < 1.6999999999999999e83

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.8%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{+83}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -94:\\ \;\;\;\;-1\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-42}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+83}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 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 6: 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 53.6%

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

4. Final simplification 53.6%

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