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. Final simplification 100.0%

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

Alternative 2: 73.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-63}:\\ \;\;\;\;-\frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.25e+16) 1.0 (if (<= x 1.2e-63) (- (/ y x)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.25e+16) {
		tmp = 1.0;
	} else if (x <= 1.2e-63) {
		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 <= (-1.25d+16)) then
        tmp = 1.0d0
    else if (x <= 1.2d-63) 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 <= -1.25e+16) {
		tmp = 1.0;
	} else if (x <= 1.2e-63) {
		tmp = -(y / x);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.25e+16:
		tmp = 1.0
	elif x <= 1.2e-63:
		tmp = -(y / x)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.25e+16)
		tmp = 1.0;
	elseif (x <= 1.2e-63)
		tmp = Float64(-Float64(y / x));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.25e+16)
		tmp = 1.0;
	elseif (x <= 1.2e-63)
		tmp = -(y / x);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.25e+16], 1.0, If[LessEqual[x, 1.2e-63], (-N[(y / x), $MachinePrecision]), 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.25e16 or 1.2e-63 < 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. Taylor expanded in y around 0 75.2%

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

   if -1.25e16 < x < 1.2e-63

   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. Taylor expanded in y around inf 79.6%

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

      1. mul-1-neg 79.6%

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

      2. distribute-frac-neg 79.6%

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

   6. Simplified 79.6%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-63}:\\ \;\;\;\;-\frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 50.1% 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. Taylor expanded in y around 0 47.6%

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

5. Final simplification 47.6%

   \[\leadsto 1 \]

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 2023268 
(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))