Average Error: 0.1 → 0.1
Time: 9.4s
Precision: 64
Internal precision: 128
\[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]
⬇
\[\left(x \cdot 3.0 - 0.41379310344827586\right) \cdot y\]

Error

Bits error versus x

Bits error versus y

Target

Original0.1
Comparison0.1
Herbie0.1
\[ y \cdot \left(x \cdot 3.0 - 0.41379310344827586\right) \]

Derivation

  1. Initial program 0.1

    \[\left(\left(x - \frac{16.0}{116.0}\right) \cdot 3.0\right) \cdot y\]

  2. Applied taylor 0.1

    \[\leadsto 3.0 \cdot \left(y \cdot x\right) - 0.41379310344827586 \cdot y\]

  3. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{3.0 \cdot \left(y \cdot x\right) - 0.41379310344827586 \cdot y}\]

  4. Applied simplify 0.1

    \[\leadsto \color{blue}{\left(x \cdot 3.0 - 0.41379310344827586\right) \cdot y}\]
  5. Removed slow pow expressions

Runtime

Time bar (total: 9.4s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(1786898679 631303472 1913215086 3200019177 513096340 262810080)'
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"

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

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