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

Average Error: 0.33% → 0.33%

Time: 5.7s

Precision: binary64

Cost: 448

Math

\[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]

↓

\[\left(3 \cdot x + -0.41379310344827586\right) \cdot y \]

FPCore

(FPCore (x y) :precision binary64 (* (* (- x (/ 16.0 116.0)) 3.0) y))

↓

(FPCore (x y) :precision binary64 (* (+ (* 3.0 x) -0.41379310344827586) y))

C

double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

↓

double code(double x, double y) {
	return ((3.0 * x) + -0.41379310344827586) * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x - (16.0d0 / 116.0d0)) * 3.0d0) * y
end function

↓

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((3.0d0 * x) + (-0.41379310344827586d0)) * y
end function

Java

public static double code(double x, double y) {
	return ((x - (16.0 / 116.0)) * 3.0) * y;
}

↓

public static double code(double x, double y) {
	return ((3.0 * x) + -0.41379310344827586) * y;
}

Python

def code(x, y):
	return ((x - (16.0 / 116.0)) * 3.0) * y

↓

def code(x, y):
	return ((3.0 * x) + -0.41379310344827586) * y

Julia

function code(x, y)
	return Float64(Float64(Float64(x - Float64(16.0 / 116.0)) * 3.0) * y)
end

↓

function code(x, y)
	return Float64(Float64(Float64(3.0 * x) + -0.41379310344827586) * y)
end

MATLAB

function tmp = code(x, y)
	tmp = ((x - (16.0 / 116.0)) * 3.0) * y;
end

↓

function tmp = code(x, y)
	tmp = ((3.0 * x) + -0.41379310344827586) * y;
end

Wolfram

code[x_, y_] := N[(N[(N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision] * y), $MachinePrecision]

↓

code[x_, y_] := N[(N[(N[(3.0 * x), $MachinePrecision] + -0.41379310344827586), $MachinePrecision] * y), $MachinePrecision]

Target

Original	0.33%
Target	0.33%
Herbie	0.33%

\[y \cdot \left(x \cdot 3 - 0.41379310344827586\right) \]

Derivation

1. Initial program 0.33

   \[\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y \]

2. Taylor expanded in x around 0 0.33

   \[\leadsto \color{blue}{\left(3 \cdot x - 0.41379310344827586\right)} \cdot y \]

3. Final simplification 0.33

   \[\leadsto \left(3 \cdot x + -0.41379310344827586\right) \cdot y \]

Alternatives

Alternative 1
Error	2.56%
Cost	585

\[\begin{array}{l} \mathbf{if}\;x \leq -0.136 \lor \neg \left(x \leq 0.14\right):\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.41379310344827586\\ \end{array} \]

Alternative 2
Error	2.55%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -0.136:\\ \;\;\;\;x \cdot \left(3 \cdot y\right)\\ \mathbf{elif}\;x \leq 0.14:\\ \;\;\;\;y \cdot -0.41379310344827586\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 3
Error	2.6%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -0.136:\\ \;\;\;\;\left(3 \cdot x\right) \cdot y\\ \mathbf{elif}\;x \leq 0.14:\\ \;\;\;\;y \cdot -0.41379310344827586\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 4
Error	0.49%
Cost	448

\[3 \cdot \left(y \cdot \left(x + -0.13793103448275862\right)\right) \]

Alternative 5
Error	0.33%
Cost	448

\[y \cdot \left(3 \cdot \left(x + -0.13793103448275862\right)\right) \]

Alternative 6
Error	41.74%
Cost	192

\[y \cdot -0.41379310344827586 \]

Reproduce

herbie shell --seed 2023115 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (* y (- (* x 3.0) 0.41379310344827586))

  (* (* (- x (/ 16.0 116.0)) 3.0) y))