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

Percentage Accurate: 100.0% → 100.0%

Time: 6.2s

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, 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: 75.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-30} \lor \neg \left(y \leq 1.35 \cdot 10^{-40}\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.8e-30) (not (<= y 1.35e-40)))
   (+ (* 2.0 (/ x y)) -1.0)
   (/ x (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.8e-30) || !(y <= 1.35e-40)) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-4.8d-30)) .or. (.not. (y <= 1.35d-40))) then
        tmp = (2.0d0 * (x / y)) + (-1.0d0)
    else
        tmp = x / (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -4.8e-30) || !(y <= 1.35e-40)) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.8e-30) or not (y <= 1.35e-40):
		tmp = (2.0 * (x / y)) + -1.0
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.8e-30) || !(y <= 1.35e-40))
		tmp = Float64(Float64(2.0 * Float64(x / y)) + -1.0);
	else
		tmp = Float64(x / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.8e-30) || ~((y <= 1.35e-40)))
		tmp = (2.0 * (x / y)) + -1.0;
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.8e-30], N[Not[LessEqual[y, 1.35e-40]], $MachinePrecision]], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.7999999999999997e-30 or 1.35e-40 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.7%

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

   if -4.7999999999999997e-30 < y < 1.35e-40

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 77.8%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-30} \lor \neg \left(y \leq 1.35 \cdot 10^{-40}\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{-30} \lor \neg \left(y \leq 5.7 \cdot 10^{-64}\right):\\ \;\;\;\;\frac{y}{\left(-x\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -9.6e-30) (not (<= y 5.7e-64)))
   (/ y (- (- x) y))
   (/ x (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -9.6e-30) || !(y <= 5.7e-64)) {
		tmp = y / (-x - y);
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-9.6d-30)) .or. (.not. (y <= 5.7d-64))) then
        tmp = y / (-x - y)
    else
        tmp = x / (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -9.6e-30) || !(y <= 5.7e-64)) {
		tmp = y / (-x - y);
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -9.6e-30) or not (y <= 5.7e-64):
		tmp = y / (-x - y)
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -9.6e-30) || !(y <= 5.7e-64))
		tmp = Float64(y / Float64(Float64(-x) - y));
	else
		tmp = Float64(x / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -9.6e-30) || ~((y <= 5.7e-64)))
		tmp = y / (-x - y);
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -9.6e-30], N[Not[LessEqual[y, 5.7e-64]], $MachinePrecision]], N[(y / N[((-x) - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5999999999999994e-30 or 5.7000000000000003e-64 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.6%

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

      1. neg-mul-1 75.6%

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

   5. Simplified 75.6%

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

   if -9.5999999999999994e-30 < y < 5.7000000000000003e-64

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 78.8%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{-30} \lor \neg \left(y \leq 5.7 \cdot 10^{-64}\right):\\ \;\;\;\;\frac{y}{\left(-x\right) - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-30} \lor \neg \left(y \leq 1.35 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -9e-30) (not (<= y 1.35e-40))) (+ (/ x y) -1.0) (/ x (+ x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -9e-30) || !(y <= 1.35e-40)) {
		tmp = (x / y) + -1.0;
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-9d-30)) .or. (.not. (y <= 1.35d-40))) then
        tmp = (x / y) + (-1.0d0)
    else
        tmp = x / (x + y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -9e-30) || !(y <= 1.35e-40)) {
		tmp = (x / y) + -1.0;
	} else {
		tmp = x / (x + y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -9e-30) or not (y <= 1.35e-40):
		tmp = (x / y) + -1.0
	else:
		tmp = x / (x + y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -9e-30) || !(y <= 1.35e-40))
		tmp = Float64(Float64(x / y) + -1.0);
	else
		tmp = Float64(x / Float64(x + y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -9e-30) || ~((y <= 1.35e-40)))
		tmp = (x / y) + -1.0;
	else
		tmp = x / (x + y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -9e-30], N[Not[LessEqual[y, 1.35e-40]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision], N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.99999999999999935e-30 or 1.35e-40 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.2%

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

      1. neg-mul-1 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in y around inf 76.1%

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

   if -8.99999999999999935e-30 < y < 1.35e-40

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 77.8%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-30} \lor \neg \left(y \leq 1.35 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-30} \lor \neg \left(y \leq 1.25 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.7e-30) (not (<= y 1.25e-40))) (+ (/ x y) -1.0) 1.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.7e-30) || !(y <= 1.25e-40)) {
		tmp = (x / y) + -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 <= (-3.7d-30)) .or. (.not. (y <= 1.25d-40))) then
        tmp = (x / y) + (-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 <= -3.7e-30) || !(y <= 1.25e-40)) {
		tmp = (x / y) + -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3.7e-30) or not (y <= 1.25e-40):
		tmp = (x / y) + -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3.7e-30) || !(y <= 1.25e-40))
		tmp = Float64(Float64(x / y) + -1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3.7e-30) || ~((y <= 1.25e-40)))
		tmp = (x / y) + -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3.7e-30], N[Not[LessEqual[y, 1.25e-40]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if y < -3.7000000000000003e-30 or 1.24999999999999991e-40 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.2%

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

      1. neg-mul-1 76.2%

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

   5. Simplified 76.2%

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

   6. Taylor expanded in y around inf 76.1%

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

   if -3.7000000000000003e-30 < y < 1.24999999999999991e-40

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 77.2%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-30} \lor \neg \left(y \leq 1.25 \cdot 10^{-40}\right):\\ \;\;\;\;\frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0001:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-61}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -0.0001) -1.0 (if (<= y 1.5e-61) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.0001) {
		tmp = -1.0;
	} else if (y <= 1.5e-61) {
		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 <= (-0.0001d0)) then
        tmp = -1.0d0
    else if (y <= 1.5d-61) 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 <= -0.0001) {
		tmp = -1.0;
	} else if (y <= 1.5e-61) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.0001:
		tmp = -1.0
	elif y <= 1.5e-61:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.0001)
		tmp = -1.0;
	elseif (y <= 1.5e-61)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.0001)
		tmp = -1.0;
	elseif (y <= 1.5e-61)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.0001], -1.0, If[LessEqual[y, 1.5e-61], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.00000000000000005e-4 or 1.50000000000000006e-61 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.6%

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

   if -1.00000000000000005e-4 < y < 1.50000000000000006e-61

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 77.2%

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

Alternative 7: 48.7% 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 52.4%

   \[\leadsto \color{blue}{-1} \]
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 2024170 
(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)))