Data.Colour.CIE:lightness from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 1.8s

Alternatives: 3

Speedup: 1.3×

Specification

Math

\[\begin{array}{l} \\ x \cdot 116 - 16 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- (* x 116.0) 16.0))

C

double code(double x) {
	return (x * 116.0) - 16.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * 116.0d0) - 16.0d0
end function

Java

public static double code(double x) {
	return (x * 116.0) - 16.0;
}

Python

def code(x):
	return (x * 116.0) - 16.0

Julia

function code(x)
	return Float64(Float64(x * 116.0) - 16.0)
end

MATLAB

function tmp = code(x)
	tmp = (x * 116.0) - 16.0;
end

Wolfram

code[x_] := N[(N[(x * 116.0), $MachinePrecision] - 16.0), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 116 - 16 \end{array} \]

FPCore

(FPCore (x) :precision binary64 (- (* x 116.0) 16.0))

C

double code(double x) {
	return (x * 116.0) - 16.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * 116.0d0) - 16.0d0
end function

Java

public static double code(double x) {
	return (x * 116.0) - 16.0;
}

Python

def code(x):
	return (x * 116.0) - 16.0

Julia

function code(x)
	return Float64(Float64(x * 116.0) - 16.0)
end

MATLAB

function tmp = code(x)
	tmp = (x * 116.0) - 16.0;
end

Wolfram

code[x_] := N[(N[(x * 116.0), $MachinePrecision] - 16.0), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(116, x, -16\right) \end{array} \]

FPCore

(FPCore (x) :precision binary64 (fma 116.0 x -16.0))

C

double code(double x) {
	return fma(116.0, x, -16.0);
}

Julia

function code(x)
	return fma(116.0, x, -16.0)
end

Wolfram

code[x_] := N[(116.0 * x + -16.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x \cdot 116 - 16 \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{116 \cdot x - 16} \]
4. Step-by-step derivation

   1. metadata-eval N/A

      \[\leadsto 116 \cdot x - \color{blue}{16 \cdot 1} \]

   2. metadata-eval N/A

      \[\leadsto 116 \cdot x - \color{blue}{\left(\mathsf{neg}\left(-16\right)\right)} \cdot 1 \]

   3. metadata-eval N/A

      \[\leadsto 116 \cdot x - \left(\mathsf{neg}\left(\color{blue}{\left(\mathsf{neg}\left(16\right)\right)}\right)\right) \cdot 1 \]

   4. lft-mult-inverse N/A

      \[\leadsto 116 \cdot x - \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(16\right)\right)\right)\right) \cdot \color{blue}{\left(\frac{1}{x} \cdot x\right)} \]

   5. fp-cancel-sign-sub-inv N/A

      \[\leadsto \color{blue}{116 \cdot x + \left(\mathsf{neg}\left(16\right)\right) \cdot \left(\frac{1}{x} \cdot x\right)} \]

   6. lft-mult-inverse N/A

      \[\leadsto 116 \cdot x + \left(\mathsf{neg}\left(16\right)\right) \cdot \color{blue}{1} \]

   7. metadata-eval N/A

      \[\leadsto 116 \cdot x + \color{blue}{-16} \cdot 1 \]

   8. metadata-eval N/A

      \[\leadsto 116 \cdot x + \color{blue}{-16} \]

   9. metadata-eval N/A

      \[\leadsto 116 \cdot x + \color{blue}{\left(\mathsf{neg}\left(16\right)\right)} \]

   10. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(116, x, \mathsf{neg}\left(16\right)\right)} \]

   11. metadata-eval 100.0

       \[\leadsto \mathsf{fma}\left(116, x, \color{blue}{-16}\right) \]

5. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(116, x, -16\right)} \]
6. Add Preprocessing

Alternative 2: 97.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 116 \leq -5 \cdot 10^{+15} \lor \neg \left(x \cdot 116 \leq 5 \cdot 10^{-6}\right):\\ \;\;\;\;116 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-16\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= (* x 116.0) -5e+15) (not (<= (* x 116.0) 5e-6)))
   (* 116.0 x)
   -16.0))

C

double code(double x) {
	double tmp;
	if (((x * 116.0) <= -5e+15) || !((x * 116.0) <= 5e-6)) {
		tmp = 116.0 * x;
	} else {
		tmp = -16.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (((x * 116.0d0) <= (-5d+15)) .or. (.not. ((x * 116.0d0) <= 5d-6))) then
        tmp = 116.0d0 * x
    else
        tmp = -16.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (((x * 116.0) <= -5e+15) || !((x * 116.0) <= 5e-6)) {
		tmp = 116.0 * x;
	} else {
		tmp = -16.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if ((x * 116.0) <= -5e+15) or not ((x * 116.0) <= 5e-6):
		tmp = 116.0 * x
	else:
		tmp = -16.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((Float64(x * 116.0) <= -5e+15) || !(Float64(x * 116.0) <= 5e-6))
		tmp = Float64(116.0 * x);
	else
		tmp = -16.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (((x * 116.0) <= -5e+15) || ~(((x * 116.0) <= 5e-6)))
		tmp = 116.0 * x;
	else
		tmp = -16.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[N[(x * 116.0), $MachinePrecision], -5e+15], N[Not[LessEqual[N[(x * 116.0), $MachinePrecision], 5e-6]], $MachinePrecision]], N[(116.0 * x), $MachinePrecision], -16.0]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 116 binary64)) < -5e15 or 5.00000000000000041e-6 < (*.f64 x #s(literal 116 binary64))

   1. Initial program 100.0%

      \[x \cdot 116 - 16 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-16} \]
   4. Step-by-step derivation

   5. Applied rewrites 3.0%

      \[\leadsto \color{blue}{-16} \]

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{116 \cdot x} \]
   7. Step-by-step derivation

      1. lower-*.f64 99.2

         \[\leadsto \color{blue}{116 \cdot x} \]

   8. Applied rewrites 99.2%

      \[\leadsto \color{blue}{116 \cdot x} \]

   if -5e15 < (*.f64 x #s(literal 116 binary64)) < 5.00000000000000041e-6

   1. Initial program 100.0%

      \[x \cdot 116 - 16 \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-16} \]
   4. Step-by-step derivation

   5. Applied rewrites 97.6%

      \[\leadsto \color{blue}{-16} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 116 \leq -5 \cdot 10^{+15} \lor \neg \left(x \cdot 116 \leq 5 \cdot 10^{-6}\right):\\ \;\;\;\;116 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-16\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.8% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ -16 \end{array} \]

FPCore

(FPCore (x) :precision binary64 -16.0)

C

double code(double x) {
	return -16.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = -16.0d0
end function

Java

public static double code(double x) {
	return -16.0;
}

Python

def code(x):
	return -16.0

Julia

function code(x)
	return -16.0
end

MATLAB

function tmp = code(x)
	tmp = -16.0;
end

Wolfram

code[x_] := -16.0

Derivation

1. Initial program 100.0%

   \[x \cdot 116 - 16 \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-16} \]
4. Step-by-step derivation

5. Applied rewrites 49.2%

   \[\leadsto \color{blue}{-16} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024320 
(FPCore (x)
  :name "Data.Colour.CIE:lightness from colour-2.3.3"
  :precision binary64
  (- (* x 116.0) 16.0))