Average Error: 0.2 → 0.3
Time: 1.5m
Precision: 64
Internal Precision: 384
\[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]
↓
\[\left(x - \frac{16.0}{116.0}\right) \cdot \left(3.0 \cdot y\right)\]

Error

Bits error versus x

Bits error versus y

Target

Original0.2
Target0.2
Herbie0.3
\[y \cdot \left(x \cdot 3.0 - 0.41379310344827586\right)\]

Derivation

  1. Initial program 0.2

    \[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]
  2. Using strategy rm

  3. Applied associate-*l*0.3

    \[\leadsto \color{blue}{\left(x - \frac{16.0}{116.0}\right) \cdot \left(3.0 \cdot y\right)}\]
  4. Removed slow pow expressions.

Runtime

Time bar (total: 1.5m)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit +o reduce:binary-search
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"

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

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