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

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

Alternatives: 4

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. Final simplification 100.0%

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

Alternative 2: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+135}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+80} \lor \neg \left(y \leq -1.65 \cdot 10^{+45}\right) \land y \leq 4 \cdot 10^{+32}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.9e+135)
   -1.0
   (if (or (<= y -6.5e+80) (and (not (<= y -1.65e+45)) (<= y 4e+32)))
     (+ 1.0 (* -2.0 (/ y x)))
     -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.9e+135) {
		tmp = -1.0;
	} else if ((y <= -6.5e+80) || (!(y <= -1.65e+45) && (y <= 4e+32))) {
		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 <= (-4.9d+135)) then
        tmp = -1.0d0
    else if ((y <= (-6.5d+80)) .or. (.not. (y <= (-1.65d+45))) .and. (y <= 4d+32)) 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 <= -4.9e+135) {
		tmp = -1.0;
	} else if ((y <= -6.5e+80) || (!(y <= -1.65e+45) && (y <= 4e+32))) {
		tmp = 1.0 + (-2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.9e+135:
		tmp = -1.0
	elif (y <= -6.5e+80) or (not (y <= -1.65e+45) and (y <= 4e+32)):
		tmp = 1.0 + (-2.0 * (y / x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.9e+135)
		tmp = -1.0;
	elseif ((y <= -6.5e+80) || (!(y <= -1.65e+45) && (y <= 4e+32)))
		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 <= -4.9e+135)
		tmp = -1.0;
	elseif ((y <= -6.5e+80) || (~((y <= -1.65e+45)) && (y <= 4e+32)))
		tmp = 1.0 + (-2.0 * (y / x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.9e+135], -1.0, If[Or[LessEqual[y, -6.5e+80], And[N[Not[LessEqual[y, -1.65e+45]], $MachinePrecision], LessEqual[y, 4e+32]]], N[(1.0 + N[(-2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9000000000000001e135 or -6.4999999999999998e80 < y < -1.65e45 or 4.00000000000000021e32 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 79.0%

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

   if -4.9000000000000001e135 < y < -6.4999999999999998e80 or -1.65e45 < y < 4.00000000000000021e32

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.0%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+135}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+80} \lor \neg \left(y \leq -1.65 \cdot 10^{+45}\right) \land y \leq 4 \cdot 10^{+32}:\\ \;\;\;\;1 + -2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3: 73.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+135}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+128}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+45}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+30}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.2e+135)
   -1.0
   (if (<= y -4.1e+128)
     1.0
     (if (<= y -3.2e+45) -1.0 (if (<= y 7e+30) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.2e+135) {
		tmp = -1.0;
	} else if (y <= -4.1e+128) {
		tmp = 1.0;
	} else if (y <= -3.2e+45) {
		tmp = -1.0;
	} else if (y <= 7e+30) {
		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 <= (-3.2d+135)) then
        tmp = -1.0d0
    else if (y <= (-4.1d+128)) then
        tmp = 1.0d0
    else if (y <= (-3.2d+45)) then
        tmp = -1.0d0
    else if (y <= 7d+30) 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 <= -3.2e+135) {
		tmp = -1.0;
	} else if (y <= -4.1e+128) {
		tmp = 1.0;
	} else if (y <= -3.2e+45) {
		tmp = -1.0;
	} else if (y <= 7e+30) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.2e+135:
		tmp = -1.0
	elif y <= -4.1e+128:
		tmp = 1.0
	elif y <= -3.2e+45:
		tmp = -1.0
	elif y <= 7e+30:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.2e+135)
		tmp = -1.0;
	elseif (y <= -4.1e+128)
		tmp = 1.0;
	elseif (y <= -3.2e+45)
		tmp = -1.0;
	elseif (y <= 7e+30)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.2e+135)
		tmp = -1.0;
	elseif (y <= -4.1e+128)
		tmp = 1.0;
	elseif (y <= -3.2e+45)
		tmp = -1.0;
	elseif (y <= 7e+30)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.2e+135], -1.0, If[LessEqual[y, -4.1e+128], 1.0, If[LessEqual[y, -3.2e+45], -1.0, If[LessEqual[y, 7e+30], 1.0, -1.0]]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999975e135 or -4.10000000000000012e128 < y < -3.2000000000000003e45 or 7.00000000000000042e30 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 77.3%

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

   if -3.19999999999999975e135 < y < -4.10000000000000012e128 or -3.2000000000000003e45 < y < 7.00000000000000042e30

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 75.8%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+135}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+128}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{+45}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+30}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 4: 50.6% 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 43.3%

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

3. Final simplification 43.3%

   \[\leadsto -1 \]

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 2023318 
(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)))