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

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

Alternatives: 3

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x - y}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) x))

C

double code(double x, double y) {
	return (x - y) / x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / x
end function

Java

public static double code(double x, double y) {
	return (x - y) / x;
}

Python

def code(x, y):
	return (x - y) / x

Julia

function code(x, y)
	return Float64(Float64(x - y) / x)
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / x;
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / x), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x - y}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (- x y) x))

C

double code(double x, double y) {
	return (x - y) / x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x - y) / x
end function

Java

public static double code(double x, double y) {
	return (x - y) / x;
}

Python

def code(x, y):
	return (x - y) / x

Julia

function code(x, y)
	return Float64(Float64(x - y) / x)
end

MATLAB

function tmp = code(x, y)
	tmp = (x - y) / x;
end

Wolfram

code[x_, y_] := N[(N[(x - y), $MachinePrecision] / x), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 - \frac{y}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- 1.0 (/ y x)))

C

double code(double x, double y) {
	return 1.0 - (y / x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 - (y / x)
end function

Java

public static double code(double x, double y) {
	return 1.0 - (y / x);
}

Python

def code(x, y):
	return 1.0 - (y / x)

Julia

function code(x, y)
	return Float64(1.0 - Float64(y / x))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 - (y / x);
end

Wolfram

code[x_, y_] := N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x - y}{x} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift--.f64 N/A

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

   3. div-sub N/A

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

   4. *-inverses N/A

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

   5. lower--.f64 N/A

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

   6. lower-/.f64 100.0

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

4. Applied rewrites 100.0%

   \[\leadsto \color{blue}{1 - \frac{y}{x}} \]
5. Add Preprocessing

Alternative 2: 97.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{x}\\ t_1 := \frac{-y}{x}\\ \mathbf{if}\;t\_0 \leq -2000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) x)) (t_1 (/ (- y) x)))
   (if (<= t_0 -2000.0) t_1 (if (<= t_0 2.0) 1.0 t_1))))

C

double code(double x, double y) {
	double t_0 = (x - y) / x;
	double t_1 = -y / x;
	double tmp;
	if (t_0 <= -2000.0) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	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 = (x - y) / x
    t_1 = -y / x
    if (t_0 <= (-2000.0d0)) then
        tmp = t_1
    else if (t_0 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x - y) / x;
	double t_1 = -y / x;
	double tmp;
	if (t_0 <= -2000.0) {
		tmp = t_1;
	} else if (t_0 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) / x
	t_1 = -y / x
	tmp = 0
	if t_0 <= -2000.0:
		tmp = t_1
	elif t_0 <= 2.0:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / x)
	t_1 = Float64(Float64(-y) / x)
	tmp = 0.0
	if (t_0 <= -2000.0)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) / x;
	t_1 = -y / x;
	tmp = 0.0;
	if (t_0 <= -2000.0)
		tmp = t_1;
	elseif (t_0 <= 2.0)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / x), $MachinePrecision]}, Block[{t$95$1 = N[((-y) / x), $MachinePrecision]}, If[LessEqual[t$95$0, -2000.0], t$95$1, If[LessEqual[t$95$0, 2.0], 1.0, t$95$1]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 x y) x) < -2e3 or 2 < (/.f64 (-.f64 x y) x)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

         \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(y\right)}}{x} \]

      2. lower-neg.f64 97.9

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

   5. Applied rewrites 97.9%

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

   if -2e3 < (/.f64 (-.f64 x y) x) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.2%

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

Alternative 3: 49.8% accurate, 15.0× 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%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{1} \]
4. Step-by-step derivation

5. Applied rewrites 49.3%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Developer Target 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 - \frac{y}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- 1.0 (/ y x)))

C

double code(double x, double y) {
	return 1.0 - (y / x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 - (y / x)
end function

Java

public static double code(double x, double y) {
	return 1.0 - (y / x);
}

Python

def code(x, y):
	return 1.0 - (y / x)

Julia

function code(x, y)
	return Float64(1.0 - Float64(y / x))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 - (y / x);
end

Wolfram

code[x_, y_] := N[(1.0 - N[(y / x), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024232 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, E"
  :precision binary64

  :alt
  (! :herbie-platform default (- 1 (/ y x)))

  (/ (- x y) x))