Error

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 pow10.1

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

4. Applied pow10.1

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

5. Applied pow-prod-up0.1

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

6. Applied pow10.1

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

7. Applied cube-unmult0.1

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

8. Applied pow-prod-up0.1

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

9. Applied pow-plus0.1

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

10. Applied pow-prod-up0.1

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

11. Simplified0.1

    \[\leadsto \left(d1 \cdot \left({d1}^{\color{blue}{7}} \cdot d1\right)\right) \cdot d1\]
12. Using strategy rm

13. Applied pow10.1

    \[\leadsto \left(d1 \cdot \left({d1}^{7} \cdot d1\right)\right) \cdot \color{blue}{{d1}^{1}}\]

14. Applied pow10.1

    \[\leadsto \left(d1 \cdot \left({d1}^{7} \cdot \color{blue}{{d1}^{1}}\right)\right) \cdot {d1}^{1}\]

15. Applied pow10.1

    \[\leadsto \left(d1 \cdot \left({\color{blue}{\left({d1}^{1}\right)}}^{7} \cdot {d1}^{1}\right)\right) \cdot {d1}^{1}\]

16. Applied pow-pow0.1

    \[\leadsto \left(d1 \cdot \left(\color{blue}{{d1}^{\left(1 \cdot 7\right)}} \cdot {d1}^{1}\right)\right) \cdot {d1}^{1}\]

17. Applied pow-prod-up0.1

    \[\leadsto \left(d1 \cdot \color{blue}{{d1}^{\left(1 \cdot 7 + 1\right)}}\right) \cdot {d1}^{1}\]

18. Applied pow10.1

    \[\leadsto \left(\color{blue}{{d1}^{1}} \cdot {d1}^{\left(1 \cdot 7 + 1\right)}\right) \cdot {d1}^{1}\]

19. Applied pow-prod-up0.0

    \[\leadsto \color{blue}{{d1}^{\left(1 + \left(1 \cdot 7 + 1\right)\right)}} \cdot {d1}^{1}\]

20. Applied pow-prod-up0

    \[\leadsto \color{blue}{{d1}^{\left(\left(1 + \left(1 \cdot 7 + 1\right)\right) + 1\right)}}\]

21. Simplified0

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

22. Final simplification0

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

Reproduce

herbie shell --seed 2019072 +o rules:numerics
(FPCore (d1)
  :name "FastMath test5"

  :herbie-target
  (pow d1 10)

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