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

Percentage Accurate: 100.0% → 100.0%

Time: 4.6s

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, 0.6× 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. Step-by-step derivation

   1. div-sub 100.0%

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

3. Applied egg-rr 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 72.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-63} \lor \neg \left(y \leq 1.6 \cdot 10^{-160}\right) \land \left(y \leq 2.05 \cdot 10^{-87} \lor \neg \left(y \leq 6.5 \cdot 10^{+78}\right)\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.2e-63)
         (and (not (<= y 1.6e-160)) (or (<= y 2.05e-87) (not (<= y 6.5e+78)))))
   (+ (* 2.0 (/ x y)) -1.0)
   (+ 1.0 (* -2.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.2e-63) || (!(y <= 1.6e-160) && ((y <= 2.05e-87) || !(y <= 6.5e+78)))) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else {
		tmp = 1.0 + (-2.0 * (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 ((y <= (-2.2d-63)) .or. (.not. (y <= 1.6d-160)) .and. (y <= 2.05d-87) .or. (.not. (y <= 6.5d+78))) then
        tmp = (2.0d0 * (x / y)) + (-1.0d0)
    else
        tmp = 1.0d0 + ((-2.0d0) * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.2e-63) || (!(y <= 1.6e-160) && ((y <= 2.05e-87) || !(y <= 6.5e+78)))) {
		tmp = (2.0 * (x / y)) + -1.0;
	} else {
		tmp = 1.0 + (-2.0 * (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.2e-63) or (not (y <= 1.6e-160) and ((y <= 2.05e-87) or not (y <= 6.5e+78))):
		tmp = (2.0 * (x / y)) + -1.0
	else:
		tmp = 1.0 + (-2.0 * (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.2e-63) || (!(y <= 1.6e-160) && ((y <= 2.05e-87) || !(y <= 6.5e+78))))
		tmp = Float64(Float64(2.0 * Float64(x / y)) + -1.0);
	else
		tmp = Float64(1.0 + Float64(-2.0 * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.2e-63) || (~((y <= 1.6e-160)) && ((y <= 2.05e-87) || ~((y <= 6.5e+78)))))
		tmp = (2.0 * (x / y)) + -1.0;
	else
		tmp = 1.0 + (-2.0 * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.2e-63], And[N[Not[LessEqual[y, 1.6e-160]], $MachinePrecision], Or[LessEqual[y, 2.05e-87], N[Not[LessEqual[y, 6.5e+78]], $MachinePrecision]]]], N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e-63 or 1.60000000000000004e-160 < y < 2.05000000000000016e-87 or 6.50000000000000036e78 < y

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around 0 80.1%

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

   if -2.2e-63 < y < 1.60000000000000004e-160 or 2.05000000000000016e-87 < y < 6.50000000000000036e78

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in y around 0 79.8%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-63} \lor \neg \left(y \leq 1.6 \cdot 10^{-160}\right) \land \left(y \leq 2.05 \cdot 10^{-87} \lor \neg \left(y \leq 6.5 \cdot 10^{+78}\right)\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \]

Alternative 3: 71.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-63}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-160} \lor \neg \left(y \leq 7.6 \cdot 10^{-88}\right) \land y \leq 5.8 \cdot 10^{+78}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.7e-63)
   -1.0
   (if (or (<= y 1.6e-160) (and (not (<= y 7.6e-88)) (<= y 5.8e+78)))
     (+ 1.0 (* -2.0 (/ y x)))
     -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.7e-63) {
		tmp = -1.0;
	} else if ((y <= 1.6e-160) || (!(y <= 7.6e-88) && (y <= 5.8e+78))) {
		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 (y <= (-3.7d-63)) then
        tmp = -1.0d0
    else if ((y <= 1.6d-160) .or. (.not. (y <= 7.6d-88)) .and. (y <= 5.8d+78)) 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 (y <= -3.7e-63) {
		tmp = -1.0;
	} else if ((y <= 1.6e-160) || (!(y <= 7.6e-88) && (y <= 5.8e+78))) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.7e-63:
		tmp = -1.0
	elif (y <= 1.6e-160) or (not (y <= 7.6e-88) and (y <= 5.8e+78)):
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.7e-63)
		tmp = -1.0;
	elseif ((y <= 1.6e-160) || (!(y <= 7.6e-88) && (y <= 5.8e+78)))
		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 (y <= -3.7e-63)
		tmp = -1.0;
	elseif ((y <= 1.6e-160) || (~((y <= 7.6e-88)) && (y <= 5.8e+78)))
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.7e-63], -1.0, If[Or[LessEqual[y, 1.6e-160], And[N[Not[LessEqual[y, 7.6e-88]], $MachinePrecision], LessEqual[y, 5.8e+78]]], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.70000000000000012e-63 or 1.60000000000000004e-160 < y < 7.60000000000000022e-88 or 5.80000000000000034e78 < y

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around 0 79.0%

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

   if -3.70000000000000012e-63 < y < 1.60000000000000004e-160 or 7.60000000000000022e-88 < y < 5.80000000000000034e78

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in y around 0 79.8%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-63}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-160} \lor \neg \left(y \leq 7.6 \cdot 10^{-88}\right) \land y \leq 5.8 \cdot 10^{+78}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4: 72.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-56}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-161}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-88}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.15e-56)
   -1.0
   (if (<= y 4.5e-161)
     1.0
     (if (<= y 8e-88) -1.0 (if (<= y 1.26e+44) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.15e-56) {
		tmp = -1.0;
	} else if (y <= 4.5e-161) {
		tmp = 1.0;
	} else if (y <= 8e-88) {
		tmp = -1.0;
	} else if (y <= 1.26e+44) {
		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 <= (-1.15d-56)) then
        tmp = -1.0d0
    else if (y <= 4.5d-161) then
        tmp = 1.0d0
    else if (y <= 8d-88) then
        tmp = -1.0d0
    else if (y <= 1.26d+44) 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 <= -1.15e-56) {
		tmp = -1.0;
	} else if (y <= 4.5e-161) {
		tmp = 1.0;
	} else if (y <= 8e-88) {
		tmp = -1.0;
	} else if (y <= 1.26e+44) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.15e-56:
		tmp = -1.0
	elif y <= 4.5e-161:
		tmp = 1.0
	elif y <= 8e-88:
		tmp = -1.0
	elif y <= 1.26e+44:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.15e-56)
		tmp = -1.0;
	elseif (y <= 4.5e-161)
		tmp = 1.0;
	elseif (y <= 8e-88)
		tmp = -1.0;
	elseif (y <= 1.26e+44)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.15e-56)
		tmp = -1.0;
	elseif (y <= 4.5e-161)
		tmp = 1.0;
	elseif (y <= 8e-88)
		tmp = -1.0;
	elseif (y <= 1.26e+44)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.15e-56], -1.0, If[LessEqual[y, 4.5e-161], 1.0, If[LessEqual[y, 8e-88], -1.0, If[LessEqual[y, 1.26e+44], 1.0, -1.0]]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15000000000000001e-56 or 4.4999999999999996e-161 < y < 7.99999999999999947e-88 or 1.25999999999999996e44 < y

   1. Initial program 100.0%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around 0 78.6%

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

   if -1.15000000000000001e-56 < y < 4.4999999999999996e-161 or 7.99999999999999947e-88 < y < 1.25999999999999996e44

   1. Initial program 99.9%

      \[\frac{x - y}{x + y} \]

   2. Taylor expanded in x around inf 78.3%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-56}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-161}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-88}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

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 99.9%

   \[\frac{x - y}{x + y} \]

2. Final simplification 99.9%

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

Alternative 6: 49.8% 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. Taylor expanded in x around 0 50.7%

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

3. Final simplification 50.7%

   \[\leadsto -1 \]

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 2023268 
(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)))