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

Percentage Accurate: 100.0% → 100.0%

Time: 2.0s

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: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-162} \lor \neg \left(x \leq 1.2 \cdot 10^{-134}\right) \land x \leq 62000000:\\ \;\;\;\;\frac{-y}{x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.35e-7)
   1.0
   (if (or (<= x 2.05e-162) (and (not (<= x 1.2e-134)) (<= x 62000000.0)))
     (/ (- y) x)
     1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.35e-7) {
		tmp = 1.0;
	} else if ((x <= 2.05e-162) || (!(x <= 1.2e-134) && (x <= 62000000.0))) {
		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 (x <= (-1.35d-7)) then
        tmp = 1.0d0
    else if ((x <= 2.05d-162) .or. (.not. (x <= 1.2d-134)) .and. (x <= 62000000.0d0)) 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 (x <= -1.35e-7) {
		tmp = 1.0;
	} else if ((x <= 2.05e-162) || (!(x <= 1.2e-134) && (x <= 62000000.0))) {
		tmp = -y / x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.35e-7:
		tmp = 1.0
	elif (x <= 2.05e-162) or (not (x <= 1.2e-134) and (x <= 62000000.0)):
		tmp = -y / x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.35e-7)
		tmp = 1.0;
	elseif ((x <= 2.05e-162) || (!(x <= 1.2e-134) && (x <= 62000000.0)))
		tmp = Float64(Float64(-y) / x);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.35e-7)
		tmp = 1.0;
	elseif ((x <= 2.05e-162) || (~((x <= 1.2e-134)) && (x <= 62000000.0)))
		tmp = -y / x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.35e-7], 1.0, If[Or[LessEqual[x, 2.05e-162], And[N[Not[LessEqual[x, 1.2e-134]], $MachinePrecision], LessEqual[x, 62000000.0]]], N[((-y) / x), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.35000000000000004e-7 or 2.0500000000000001e-162 < x < 1.20000000000000005e-134 or 6.2e7 < x

   1. Initial program 99.9%

      \[\frac{x - y}{x} \]
   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 78.0%

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

   if -1.35000000000000004e-7 < x < 2.0500000000000001e-162 or 1.20000000000000005e-134 < x < 6.2e7

   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 80.9%

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

      1. mul-1-neg 80.9%

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

      2. distribute-frac-neg 80.9%

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

   6. Simplified 80.9%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-7}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-162} \lor \neg \left(x \leq 1.2 \cdot 10^{-134}\right) \land x \leq 62000000:\\ \;\;\;\;\frac{-y}{x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 49.4% 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 52.3%

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

5. Final simplification 52.3%

   \[\leadsto 1 \]

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 2023308 
(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))