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

Average Error: 0.1 → 0.1

Time: 4.4s

Precision: binary64

Cost: 320

Math

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

↓

\[0.13793103448275862 + 7.787037037037037 \cdot x \]

FPCore

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

↓

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

C

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

↓

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

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 = 0.13793103448275862d0 + (7.787037037037037d0 * x)
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 0.13793103448275862 + (7.787037037037037 * x);
}

Python

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

↓

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

Julia

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

↓

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

MATLAB

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

↓

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

Wolfram

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

↓

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

Derivation

1. Initial program 0.1

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

2. Taylor expanded in x around 0 0.1

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

3. Final simplification 0.1

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

Alternatives

Alternative 1
Error	1.5
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq -4.405786177188472:\\ \;\;\;\;7.787037037037037 \cdot x\\ \mathbf{elif}\;x \leq 7.324045184595973 \cdot 10^{-6}:\\ \;\;\;\;0.13793103448275862\\ \mathbf{else}:\\ \;\;\;\;7.787037037037037 \cdot x\\ \end{array} \]

Alternative 2
Error	31.8
Cost	64

\[0.13793103448275862 \]

Reproduce

herbie shell --seed 2022228 
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))