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

Percentage Accurate: 100.0% → 100.0%

Time: 1.8s

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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+128} \lor \neg \left(y \leq -1.35 \cdot 10^{+76}\right) \land \left(y \leq -2.7 \cdot 10^{+14} \lor \neg \left(y \leq 1200000000000\right)\right):\\ \;\;\;\;\frac{-y}{x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -6.5e+128)
         (and (not (<= y -1.35e+76))
              (or (<= y -2.7e+14) (not (<= y 1200000000000.0)))))
   (/ (- y) x)
   1.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -6.5e+128) || (!(y <= -1.35e+76) && ((y <= -2.7e+14) || !(y <= 1200000000000.0)))) {
		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 ((y <= (-6.5d+128)) .or. (.not. (y <= (-1.35d+76))) .and. (y <= (-2.7d+14)) .or. (.not. (y <= 1200000000000.0d0))) 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 ((y <= -6.5e+128) || (!(y <= -1.35e+76) && ((y <= -2.7e+14) || !(y <= 1200000000000.0)))) {
		tmp = -y / x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -6.5e+128) or (not (y <= -1.35e+76) and ((y <= -2.7e+14) or not (y <= 1200000000000.0))):
		tmp = -y / x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -6.5e+128) || (!(y <= -1.35e+76) && ((y <= -2.7e+14) || !(y <= 1200000000000.0))))
		tmp = Float64(Float64(-y) / x);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -6.5e+128) || (~((y <= -1.35e+76)) && ((y <= -2.7e+14) || ~((y <= 1200000000000.0)))))
		tmp = -y / x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -6.5e+128], And[N[Not[LessEqual[y, -1.35e+76]], $MachinePrecision], Or[LessEqual[y, -2.7e+14], N[Not[LessEqual[y, 1200000000000.0]], $MachinePrecision]]]], N[((-y) / x), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if y < -6.5000000000000003e128 or -1.34999999999999995e76 < y < -2.7e14 or 1.2e12 < y

   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 82.4%

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

      1. mul-1-neg 82.4%

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

      2. distribute-frac-neg 82.4%

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

   7. Simplified 82.4%

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

   if -6.5000000000000003e128 < y < -1.34999999999999995e76 or -2.7e14 < y < 1.2e12

   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 79.6%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+128} \lor \neg \left(y \leq -1.35 \cdot 10^{+76}\right) \land \left(y \leq -2.7 \cdot 10^{+14} \lor \neg \left(y \leq 1200000000000\right)\right):\\ \;\;\;\;\frac{-y}{x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.2% 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 56.6%

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

6. Final simplification 56.6%

   \[\leadsto 1 \]
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 2024026 
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- 1.0 (/ y x))

  (/ (- x y) x))