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

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

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 100.0%

   \[\frac{x - y}{x + y} \]
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: 71.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-120}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+45} \lor \neg \left(y \leq 3.2 \cdot 10^{+101}\right) \land y \leq 2.6 \cdot 10^{+142}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.7e-120)
   -1.0
   (if (or (<= y 2.4e+45) (and (not (<= y 3.2e+101)) (<= y 2.6e+142)))
     (+ 1.0 (* -2.0 (/ y x)))
     -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.7e-120) {
		tmp = -1.0;
	} else if ((y <= 2.4e+45) || (!(y <= 3.2e+101) && (y <= 2.6e+142))) {
		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 <= (-2.7d-120)) then
        tmp = -1.0d0
    else if ((y <= 2.4d+45) .or. (.not. (y <= 3.2d+101)) .and. (y <= 2.6d+142)) 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 <= -2.7e-120) {
		tmp = -1.0;
	} else if ((y <= 2.4e+45) || (!(y <= 3.2e+101) && (y <= 2.6e+142))) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.7e-120:
		tmp = -1.0
	elif (y <= 2.4e+45) or (not (y <= 3.2e+101) and (y <= 2.6e+142)):
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.7e-120)
		tmp = -1.0;
	elseif ((y <= 2.4e+45) || (!(y <= 3.2e+101) && (y <= 2.6e+142)))
		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 <= -2.7e-120)
		tmp = -1.0;
	elseif ((y <= 2.4e+45) || (~((y <= 3.2e+101)) && (y <= 2.6e+142)))
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.7e-120], -1.0, If[Or[LessEqual[y, 2.4e+45], And[N[Not[LessEqual[y, 3.2e+101]], $MachinePrecision], LessEqual[y, 2.6e+142]]], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6999999999999999e-120 or 2.39999999999999989e45 < y < 3.20000000000000005e101 or 2.60000000000000021e142 < 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 -2.6999999999999999e-120 < y < 2.39999999999999989e45 or 3.20000000000000005e101 < y < 2.60000000000000021e142

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 77.5%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-120}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+45} \lor \neg \left(y \leq 3.2 \cdot 10^{+101}\right) \land y \leq 2.6 \cdot 10^{+142}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot \frac{x}{y} + -1\\ t_1 := 1 + -2 \cdot \frac{y}{x}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{-120}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+101}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+142}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (* 2.0 (/ x y)) -1.0)) (t_1 (+ 1.0 (* -2.0 (/ y x)))))
   (if (<= y -2.7e-120)
     t_0
     (if (<= y 6.5e+38)
       t_1
       (if (<= y 3.4e+101) -1.0 (if (<= y 2.6e+142) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = (2.0 * (x / y)) + -1.0;
	double t_1 = 1.0 + (-2.0 * (y / x));
	double tmp;
	if (y <= -2.7e-120) {
		tmp = t_0;
	} else if (y <= 6.5e+38) {
		tmp = t_1;
	} else if (y <= 3.4e+101) {
		tmp = -1.0;
	} else if (y <= 2.6e+142) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (2.0d0 * (x / y)) + (-1.0d0)
    t_1 = 1.0d0 + ((-2.0d0) * (y / x))
    if (y <= (-2.7d-120)) then
        tmp = t_0
    else if (y <= 6.5d+38) then
        tmp = t_1
    else if (y <= 3.4d+101) then
        tmp = -1.0d0
    else if (y <= 2.6d+142) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (2.0 * (x / y)) + -1.0;
	double t_1 = 1.0 + (-2.0 * (y / x));
	double tmp;
	if (y <= -2.7e-120) {
		tmp = t_0;
	} else if (y <= 6.5e+38) {
		tmp = t_1;
	} else if (y <= 3.4e+101) {
		tmp = -1.0;
	} else if (y <= 2.6e+142) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (2.0 * (x / y)) + -1.0
	t_1 = 1.0 + (-2.0 * (y / x))
	tmp = 0
	if y <= -2.7e-120:
		tmp = t_0
	elif y <= 6.5e+38:
		tmp = t_1
	elif y <= 3.4e+101:
		tmp = -1.0
	elif y <= 2.6e+142:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(2.0 * Float64(x / y)) + -1.0)
	t_1 = Float64(1.0 + Float64(-2.0 * Float64(y / x)))
	tmp = 0.0
	if (y <= -2.7e-120)
		tmp = t_0;
	elseif (y <= 6.5e+38)
		tmp = t_1;
	elseif (y <= 3.4e+101)
		tmp = -1.0;
	elseif (y <= 2.6e+142)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (2.0 * (x / y)) + -1.0;
	t_1 = 1.0 + (-2.0 * (y / x));
	tmp = 0.0;
	if (y <= -2.7e-120)
		tmp = t_0;
	elseif (y <= 6.5e+38)
		tmp = t_1;
	elseif (y <= 3.4e+101)
		tmp = -1.0;
	elseif (y <= 2.6e+142)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.7e-120], t$95$0, If[LessEqual[y, 6.5e+38], t$95$1, If[LessEqual[y, 3.4e+101], -1.0, If[LessEqual[y, 2.6e+142], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.6999999999999999e-120 or 2.60000000000000021e142 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 80.0%

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

   if -2.6999999999999999e-120 < y < 6.5e38 or 3.40000000000000017e101 < y < 2.60000000000000021e142

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 77.5%

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

   if 6.5e38 < y < 3.40000000000000017e101

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 78.1%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-120}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+38}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+101}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+142}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \frac{x}{y} + -1\\ \end{array} \]

Alternative 4: 71.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-120}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+40}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+102}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+142}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.7e-120)
   -1.0
   (if (<= y 5.8e+40)
     1.0
     (if (<= y 4.4e+102) -1.0 (if (<= y 3.8e+142) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.7e-120) {
		tmp = -1.0;
	} else if (y <= 5.8e+40) {
		tmp = 1.0;
	} else if (y <= 4.4e+102) {
		tmp = -1.0;
	} else if (y <= 3.8e+142) {
		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 <= (-2.7d-120)) then
        tmp = -1.0d0
    else if (y <= 5.8d+40) then
        tmp = 1.0d0
    else if (y <= 4.4d+102) then
        tmp = -1.0d0
    else if (y <= 3.8d+142) 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 <= -2.7e-120) {
		tmp = -1.0;
	} else if (y <= 5.8e+40) {
		tmp = 1.0;
	} else if (y <= 4.4e+102) {
		tmp = -1.0;
	} else if (y <= 3.8e+142) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.7e-120:
		tmp = -1.0
	elif y <= 5.8e+40:
		tmp = 1.0
	elif y <= 4.4e+102:
		tmp = -1.0
	elif y <= 3.8e+142:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.7e-120)
		tmp = -1.0;
	elseif (y <= 5.8e+40)
		tmp = 1.0;
	elseif (y <= 4.4e+102)
		tmp = -1.0;
	elseif (y <= 3.8e+142)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.7e-120)
		tmp = -1.0;
	elseif (y <= 5.8e+40)
		tmp = 1.0;
	elseif (y <= 4.4e+102)
		tmp = -1.0;
	elseif (y <= 3.8e+142)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.7e-120], -1.0, If[LessEqual[y, 5.8e+40], 1.0, If[LessEqual[y, 4.4e+102], -1.0, If[LessEqual[y, 3.8e+142], 1.0, -1.0]]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6999999999999999e-120 or 5.80000000000000035e40 < y < 4.40000000000000015e102 or 3.7999999999999999e142 < 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 -2.6999999999999999e-120 < y < 5.80000000000000035e40 or 4.40000000000000015e102 < y < 3.7999999999999999e142

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 75.9%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-120}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+40}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+102}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+142}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

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 100.0%

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

2. Final simplification 100.0%

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

Alternative 6: 50.0% 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. Taylor expanded in x around 0 53.9%

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

3. Final simplification 53.9%

   \[\leadsto -1 \]

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 2023310 
(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)))