Error

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Target

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. Using strategy rm

3. Applied pow20.1

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

4. Applied cube-unmult0.1

   \[\leadsto \left(d1 \cdot \left(\left(\left(\left(\color{blue}{{d1}^{3}} \cdot d1\right) \cdot d1\right) \cdot {d1}^{2}\right) \cdot d1\right)\right) \cdot d1\]

5. Applied pow-plus0.1

   \[\leadsto \left(d1 \cdot \left(\left(\left(\color{blue}{{d1}^{\left(3 + 1\right)}} \cdot d1\right) \cdot {d1}^{2}\right) \cdot d1\right)\right) \cdot d1\]

6. Applied pow-plus0.1

   \[\leadsto \left(d1 \cdot \left(\left(\color{blue}{{d1}^{\left(\left(3 + 1\right) + 1\right)}} \cdot {d1}^{2}\right) \cdot d1\right)\right) \cdot d1\]

7. Applied pow-prod-up0.1

   \[\leadsto \left(d1 \cdot \left(\color{blue}{{d1}^{\left(\left(\left(3 + 1\right) + 1\right) + 2\right)}} \cdot d1\right)\right) \cdot d1\]

8. Applied pow-plus0.1

   \[\leadsto \left(d1 \cdot \color{blue}{{d1}^{\left(\left(\left(\left(3 + 1\right) + 1\right) + 2\right) + 1\right)}}\right) \cdot d1\]

9. Taylor expanded around 0 0

   \[\leadsto \color{blue}{{d1}^{10}}\]

10. Final simplification0

    \[\leadsto {d1}^{10}\]

Runtime

Time bar (total: 10.8s)Debug logProfile

herbie shell --seed 2018217 +o rules:numerics
(FPCore (d1)
  :name "FastMath test5"

  :herbie-target
  (pow d1 10)

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