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

Percentage Accurate: 100.0% → 100.0%

Time: 2.7s

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. Step-by-step derivation

   1. div-sub 100.0%

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

   2. *-inverses 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

   \[\leadsto 1 - \frac{y}{x} \]
6. Add Preprocessing

Alternative 2: 73.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+108}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+98} \lor \neg \left(x \leq -1.75 \cdot 10^{-9}\right) \land x \leq 8.8 \cdot 10^{-116}:\\ \;\;\;\;\frac{y}{-x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.2e+108)
   1.0
   (if (or (<= x -1.6e+98) (and (not (<= x -1.75e-9)) (<= x 8.8e-116)))
     (/ y (- x))
     1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.2e+108) {
		tmp = 1.0;
	} else if ((x <= -1.6e+98) || (!(x <= -1.75e-9) && (x <= 8.8e-116))) {
		tmp = 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 (x <= (-9.2d+108)) then
        tmp = 1.0d0
    else if ((x <= (-1.6d+98)) .or. (.not. (x <= (-1.75d-9))) .and. (x <= 8.8d-116)) then
        tmp = y / -x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -9.2e+108) {
		tmp = 1.0;
	} else if ((x <= -1.6e+98) || (!(x <= -1.75e-9) && (x <= 8.8e-116))) {
		tmp = y / -x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.2e+108:
		tmp = 1.0
	elif (x <= -1.6e+98) or (not (x <= -1.75e-9) and (x <= 8.8e-116)):
		tmp = y / -x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.2e+108)
		tmp = 1.0;
	elseif ((x <= -1.6e+98) || (!(x <= -1.75e-9) && (x <= 8.8e-116)))
		tmp = Float64(y / Float64(-x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9.2e+108)
		tmp = 1.0;
	elseif ((x <= -1.6e+98) || (~((x <= -1.75e-9)) && (x <= 8.8e-116)))
		tmp = y / -x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.2e+108], 1.0, If[Or[LessEqual[x, -1.6e+98], And[N[Not[LessEqual[x, -1.75e-9]], $MachinePrecision], LessEqual[x, 8.8e-116]]], N[(y / (-x)), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -9.1999999999999996e108 or -1.6000000000000001e98 < x < -1.75e-9 or 8.8000000000000004e-116 < x

   1. Initial program 100.0%

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

      1. div-sub 100.0%

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

      2. *-inverses 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 78.1%

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

   if -9.1999999999999996e108 < x < -1.6000000000000001e98 or -1.75e-9 < x < 8.8000000000000004e-116

   1. Initial program 100.0%

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

      1. div-sub 100.0%

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

      2. *-inverses 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 86.8%

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

      1. associate-*r/ 86.8%

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

      2. neg-mul-1 86.8%

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

   7. Simplified 86.8%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+108}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+98} \lor \neg \left(x \leq -1.75 \cdot 10^{-9}\right) \land x \leq 8.8 \cdot 10^{-116}:\\ \;\;\;\;\frac{y}{-x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.1% accurate, 5.0× 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. Step-by-step derivation

   1. div-sub 100.0%

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

   2. *-inverses 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around 0 48.0%

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

6. Final simplification 48.0%

   \[\leadsto 1 \]
7. Add Preprocessing

Developer target: 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 2024078 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, E"
  :precision binary64

  :alt
  (- 1.0 (/ y x))

  (/ (- x y) x))