Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, G

Average Error: 0.0 → 0.0

Time: 2.1s

Precision: binary64

Cost: 192

Math

\[x - \frac{1}{3} \]

↓

\[x + -0.3333333333333333 \]

FPCore

(FPCore (x) :precision binary64 (- x (/ 1.0 3.0)))

↓

(FPCore (x) :precision binary64 (+ x -0.3333333333333333))

C

double code(double x) {
	return x - (1.0 / 3.0);
}

↓

double code(double x) {
	return x + -0.3333333333333333;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = x - (1.0d0 / 3.0d0)
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = x + (-0.3333333333333333d0)
end function

Java

public static double code(double x) {
	return x - (1.0 / 3.0);
}

↓

public static double code(double x) {
	return x + -0.3333333333333333;
}

Python

def code(x):
	return x - (1.0 / 3.0)

↓

def code(x):
	return x + -0.3333333333333333

Julia

function code(x)
	return Float64(x - Float64(1.0 / 3.0))
end

↓

function code(x)
	return Float64(x + -0.3333333333333333)
end

MATLAB

function tmp = code(x)
	tmp = x - (1.0 / 3.0);
end

↓

function tmp = code(x)
	tmp = x + -0.3333333333333333;
end

Wolfram

code[x_] := N[(x - N[(1.0 / 3.0), $MachinePrecision]), $MachinePrecision]

↓

code[x_] := N[(x + -0.3333333333333333), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[x - \frac{1}{3} \]

2. Simplified 0.0

   \[\leadsto \color{blue}{x + -0.3333333333333333} \]
   Proof
   (+.f64 x -1/3): 0 points increase in error, 0 points decrease in error
   (+.f64 x (Rewrite<= metadata-eval (neg.f64 1/3))): 0 points increase in error, 0 points decrease in error
   (+.f64 x (neg.f64 (Rewrite<= metadata-eval (/.f64 1 3)))): 0 points increase in error, 0 points decrease in error
   (Rewrite<= sub-neg_binary64 (-.f64 x (/.f64 1 3))): 0 points increase in error, 0 points decrease in error

3. Final simplification 0.0

   \[\leadsto x + -0.3333333333333333 \]

Alternatives

Alternative 1
Error	1.3
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -0.602516291185853:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.021398597363671983:\\ \;\;\;\;-0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 2
Error	31.8
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022297 
(FPCore (x)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, G"
  :precision binary64
  (- x (/ 1.0 3.0)))