Average Error: 0.1 → 0
Time: 10.4s
Precision: 64
Internal Precision: 576
\[\left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right) \cdot d1\right) \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right)\right) \cdot d1\]
↓
\[{d1}^{\left(3 + 7\right)}\]

Error

Bits error versus d1

Target

Original0.1
Target0
Herbie0
\[{d1}^{10}\]

Derivation

  1. Initial program 0.1

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

  2. Taylor expanded around inf 0.1

    \[\leadsto \left(d1 \cdot \left(\color{blue}{{d1}^{7}} \cdot d1\right)\right) \cdot d1\]

  3. Applied simplify0.1

    \[\leadsto \color{blue}{{d1}^{3} \cdot {d1}^{7}}\]
  4. Using strategy rm

  5. Applied pow-prod-up0

    \[\leadsto \color{blue}{{d1}^{\left(3 + 7\right)}}\]

Runtime

Time bar (total: 10.4s)Debug logProfile

herbie shell --seed '#(1071373924 2949776965 1885069702 3247780810 90874544 2263903749)' +o rules:numerics
(FPCore (d1)
  :name "FastMath test5"

  :herbie-target
  (pow d1 10)

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