Data.Colour.CIE:cieLABView from colour-2.3.3, A

Average Error: 0.1 → 0.1

Time: 4.9s

Precision: binary64

Cost: 320

Math

\[\frac{841}{108} \cdot x + \frac{4}{29} \]

↓

\[7.787037037037037 \cdot x + 0.13793103448275862 \]

FPCore

(FPCore (x) :precision binary64 (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))

↓

(FPCore (x)
 :precision binary64
 (+ (* 7.787037037037037 x) 0.13793103448275862))

C

double code(double x) {
	return ((841.0 / 108.0) * x) + (4.0 / 29.0);
}

↓

double code(double x) {
	return (7.787037037037037 * x) + 0.13793103448275862;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((841.0d0 / 108.0d0) * x) + (4.0d0 / 29.0d0)
end function

↓

real(8) function code(x)
    real(8), intent (in) :: x
    code = (7.787037037037037d0 * x) + 0.13793103448275862d0
end function

Java

public static double code(double x) {
	return ((841.0 / 108.0) * x) + (4.0 / 29.0);
}

↓

public static double code(double x) {
	return (7.787037037037037 * x) + 0.13793103448275862;
}

Python

def code(x):
	return ((841.0 / 108.0) * x) + (4.0 / 29.0)

↓

def code(x):
	return (7.787037037037037 * x) + 0.13793103448275862

Julia

function code(x)
	return Float64(Float64(Float64(841.0 / 108.0) * x) + Float64(4.0 / 29.0))
end

↓

function code(x)
	return Float64(Float64(7.787037037037037 * x) + 0.13793103448275862)
end

MATLAB

function tmp = code(x)
	tmp = ((841.0 / 108.0) * x) + (4.0 / 29.0);
end

↓

function tmp = code(x)
	tmp = (7.787037037037037 * x) + 0.13793103448275862;
end

Wolfram

code[x_] := N[(N[(N[(841.0 / 108.0), $MachinePrecision] * x), $MachinePrecision] + N[(4.0 / 29.0), $MachinePrecision]), $MachinePrecision]

↓

code[x_] := N[(N[(7.787037037037037 * x), $MachinePrecision] + 0.13793103448275862), $MachinePrecision]

Derivation

1. Initial program 0.1

   \[\frac{841}{108} \cdot x + \frac{4}{29} \]

2. Simplified 0.1

   \[\leadsto \color{blue}{\mathsf{fma}\left(7.787037037037037, x, 0.13793103448275862\right)} \]
   Proof
   (fma.f64 841/108 x 4/29): 0 points increase in error, 0 points decrease in error
   (fma.f64 (Rewrite<= metadata-eval (/.f64 841 108)) x 4/29): 0 points increase in error, 0 points decrease in error
   (fma.f64 (/.f64 841 108) x (Rewrite<= metadata-eval (/.f64 4 29))): 0 points increase in error, 0 points decrease in error
   (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 841 108) x) (/.f64 4 29))): 2 points increase in error, 2 points decrease in error

3. Applied egg-rr 0.1

   \[\leadsto \color{blue}{7.787037037037037 \cdot x + 0.13793103448275862} \]

4. Final simplification 0.1

   \[\leadsto 7.787037037037037 \cdot x + 0.13793103448275862 \]

Alternatives

Alternative 1
Error	1.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -0.050911373029014544:\\ \;\;\;\;\frac{x}{0.12841854934601665}\\ \mathbf{elif}\;x \leq 9.346374982514411 \cdot 10^{-7}:\\ \;\;\;\;0.13793103448275862\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{0.12841854934601665}\\ \end{array} \]

Alternative 2
Error	1.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -0.050911373029014544:\\ \;\;\;\;7.787037037037037 \cdot x\\ \mathbf{elif}\;x \leq 9.346374982514411 \cdot 10^{-7}:\\ \;\;\;\;0.13793103448275862\\ \mathbf{else}:\\ \;\;\;\;7.787037037037037 \cdot x\\ \end{array} \]

Alternative 3
Error	31.4
Cost	64

\[0.13793103448275862 \]

Reproduce

herbie shell --seed 2022294 
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))