Average Error: 0.1 → 0
Time: 3.5s
Precision: 64
Internal precision: 128
\[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]
⬇
\[{d1}^{4}\]

Error

Bits error versus d1

Target

Original0.1
Comparison0
Herbie0
\[ {d1}^{4} \]

Derivation

  1. Initial program 0.1

    \[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]

  2. Applied simplify 0.2

    \[\leadsto \color{blue}{{\left({d1}^2\right)}^2}\]

  3. Applied taylor 0

    \[\leadsto {d1}^{4}\]

  4. Taylor expanded around 0 0

    \[\leadsto \color{blue}{{d1}^{4}}\]
  5. Removed slow pow expressions

Runtime

Time bar (total: 3.5s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(1834863469 1442491745 3286196109 779910222 4249740604 2432667276)'
(FPCore (d1)
  :name "FastMath repmul"

  :target
  (pow d1 4)

  (* (* (* d1 d1) d1) d1))