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

Percentage Accurate: 100.0% → 100.0%

Time: 5.1s

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 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. Step-by-step derivation

   1. sub-div 99.9%

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

   2. clear-num 100.0%

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

5. Applied egg-rr 100.0%

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

6. Final simplification 100.0%

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

Alternative 2: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+63} \lor \neg \left(y \leq -0.0095\right) \land \left(y \leq -5.2 \cdot 10^{-84} \lor \neg \left(y \leq 1.05 \cdot 10^{+35}\right)\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5.1e+63)
         (and (not (<= y -0.0095)) (or (<= y -5.2e-84) (not (<= y 1.05e+35)))))
   (+ (* 2.0 (/ x y)) -1.0)
   (+ 1.0 (* -2.0 (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5.1e+63) || (!(y <= -0.0095) && ((y <= -5.2e-84) || !(y <= 1.05e+35)))) {
		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 <= (-5.1d+63)) .or. (.not. (y <= (-0.0095d0))) .and. (y <= (-5.2d-84)) .or. (.not. (y <= 1.05d+35))) 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 <= -5.1e+63) || (!(y <= -0.0095) && ((y <= -5.2e-84) || !(y <= 1.05e+35)))) {
		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 <= -5.1e+63) or (not (y <= -0.0095) and ((y <= -5.2e-84) or not (y <= 1.05e+35))):
		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 <= -5.1e+63) || (!(y <= -0.0095) && ((y <= -5.2e-84) || !(y <= 1.05e+35))))
		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 <= -5.1e+63) || (~((y <= -0.0095)) && ((y <= -5.2e-84) || ~((y <= 1.05e+35)))))
		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, -5.1e+63], And[N[Not[LessEqual[y, -0.0095]], $MachinePrecision], Or[LessEqual[y, -5.2e-84], N[Not[LessEqual[y, 1.05e+35]], $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 < -5.0999999999999998e63 or -0.00949999999999999976 < y < -5.2e-84 or 1.0499999999999999e35 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 88.3%

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

   if -5.0999999999999998e63 < y < -0.00949999999999999976 or -5.2e-84 < y < 1.0499999999999999e35

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 79.3%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+63} \lor \neg \left(y \leq -0.0095\right) \land \left(y \leq -5.2 \cdot 10^{-84} \lor \neg \left(y \leq 1.05 \cdot 10^{+35}\right)\right):\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \end{array} \]

Alternative 3: 72.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+63}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -0.018 \lor \neg \left(y \leq -6.2 \cdot 10^{-85}\right) \land y \leq 8.4 \cdot 10^{+33}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.1e+63)
   -1.0
   (if (or (<= y -0.018) (and (not (<= y -6.2e-85)) (<= y 8.4e+33)))
     (+ 1.0 (* -2.0 (/ y x)))
     -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.1e+63) {
		tmp = -1.0;
	} else if ((y <= -0.018) || (!(y <= -6.2e-85) && (y <= 8.4e+33))) {
		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 <= (-2.1d+63)) then
        tmp = -1.0d0
    else if ((y <= (-0.018d0)) .or. (.not. (y <= (-6.2d-85))) .and. (y <= 8.4d+33)) 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 <= -2.1e+63) {
		tmp = -1.0;
	} else if ((y <= -0.018) || (!(y <= -6.2e-85) && (y <= 8.4e+33))) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.1e+63:
		tmp = -1.0
	elif (y <= -0.018) or (not (y <= -6.2e-85) and (y <= 8.4e+33)):
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.1e+63)
		tmp = -1.0;
	elseif ((y <= -0.018) || (!(y <= -6.2e-85) && (y <= 8.4e+33)))
		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 <= -2.1e+63)
		tmp = -1.0;
	elseif ((y <= -0.018) || (~((y <= -6.2e-85)) && (y <= 8.4e+33)))
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.1e+63], -1.0, If[Or[LessEqual[y, -0.018], And[N[Not[LessEqual[y, -6.2e-85]], $MachinePrecision], LessEqual[y, 8.4e+33]]], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1000000000000002e63 or -0.0179999999999999986 < y < -6.2000000000000005e-85 or 8.4000000000000002e33 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 86.9%

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

   if -2.1000000000000002e63 < y < -0.0179999999999999986 or -6.2000000000000005e-85 < y < 8.4000000000000002e33

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 79.3%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+63}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -0.018 \lor \neg \left(y \leq -6.2 \cdot 10^{-85}\right) \land y \leq 8.4 \cdot 10^{+33}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4: 71.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+64}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -30000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-84}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 10^{+35}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7.2e+64)
   -1.0
   (if (<= y -30000000000.0)
     1.0
     (if (<= y -9e-84) -1.0 (if (<= y 1e+35) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7.2e+64) {
		tmp = -1.0;
	} else if (y <= -30000000000.0) {
		tmp = 1.0;
	} else if (y <= -9e-84) {
		tmp = -1.0;
	} else if (y <= 1e+35) {
		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 <= (-7.2d+64)) then
        tmp = -1.0d0
    else if (y <= (-30000000000.0d0)) then
        tmp = 1.0d0
    else if (y <= (-9d-84)) then
        tmp = -1.0d0
    else if (y <= 1d+35) 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 <= -7.2e+64) {
		tmp = -1.0;
	} else if (y <= -30000000000.0) {
		tmp = 1.0;
	} else if (y <= -9e-84) {
		tmp = -1.0;
	} else if (y <= 1e+35) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7.2e+64:
		tmp = -1.0
	elif y <= -30000000000.0:
		tmp = 1.0
	elif y <= -9e-84:
		tmp = -1.0
	elif y <= 1e+35:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7.2e+64)
		tmp = -1.0;
	elseif (y <= -30000000000.0)
		tmp = 1.0;
	elseif (y <= -9e-84)
		tmp = -1.0;
	elseif (y <= 1e+35)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -7.2e+64)
		tmp = -1.0;
	elseif (y <= -30000000000.0)
		tmp = 1.0;
	elseif (y <= -9e-84)
		tmp = -1.0;
	elseif (y <= 1e+35)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7.2e+64], -1.0, If[LessEqual[y, -30000000000.0], 1.0, If[LessEqual[y, -9e-84], -1.0, If[LessEqual[y, 1e+35], 1.0, -1.0]]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.20000000000000027e64 or -3e10 < y < -9.00000000000000031e-84 or 9.9999999999999997e34 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 85.8%

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

   if -7.20000000000000027e64 < y < -3e10 or -9.00000000000000031e-84 < y < 9.9999999999999997e34

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 78.9%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+64}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -30000000000:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-84}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 10^{+35}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

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: 49.5% 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 99.9%

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

2. Taylor expanded in x around 0 53.1%

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

3. Final simplification 53.1%

   \[\leadsto -1 \]

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 2023207 
(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)))