Average Error: 0.1 → 0
Time: 41.8s
Precision: 64
\[\left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right) \cdot d1\right) \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right)\right) \cdot d1\]
↓
\[{d1}^{10}\]
double f(double d1) {
        double r29273360 = d1;
        double r29273361 = r29273360 * r29273360;
        double r29273362 = r29273360 * r29273361;
        double r29273363 = r29273362 * r29273360;
        double r29273364 = r29273363 * r29273360;
        double r29273365 = r29273364 * r29273361;
        double r29273366 = r29273365 * r29273360;
        double r29273367 = r29273360 * r29273366;
        double r29273368 = r29273367 * r29273360;
        return r29273368;
}
↓
double f(double d1) {
        double r29273369 = d1;
        double r29273370 = 10.0;
        double r29273371 = pow(r29273369, r29273370);
        return r29273371;
}


\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}^{10}

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. Using strategy rm

  3. Applied pow10.1

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

  4. Applied pow10.1

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

  5. Applied pow10.1

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

  6. Applied pow-prod-up0.1

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

  7. Applied pow10.1

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

  8. Applied pow10.1

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

  9. Applied pow-plus0.1

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

  10. Applied pow10.1

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

  11. Applied pow-prod-up0.1

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

  12. Applied pow-prod-up0.1

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

  13. Applied pow-plus0.1

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

  14. Applied pow-prod-up0.1

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

  15. Applied pow-prod-up0.1

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

  16. Simplified0.1

    \[\leadsto \left(d1 \cdot {d1}^{\color{blue}{8}}\right) \cdot d1\]
  17. Using strategy rm

  18. Applied pow10.1

    \[\leadsto \left(d1 \cdot {d1}^{8}\right) \cdot \color{blue}{{d1}^{1}}\]

  19. Applied pow10.1

    \[\leadsto \left(\color{blue}{{d1}^{1}} \cdot {d1}^{8}\right) \cdot {d1}^{1}\]

  20. Applied pow-prod-up0.0

    \[\leadsto \color{blue}{{d1}^{\left(1 + 8\right)}} \cdot {d1}^{1}\]

  21. Applied pow-prod-up0

    \[\leadsto \color{blue}{{d1}^{\left(\left(1 + 8\right) + 1\right)}}\]

  22. Simplified0

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

  23. Final simplification0

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

Reproduce

herbie shell --seed 2019101 
(FPCore (d1)
  :name "FastMath test5"

  :herbie-target
  (pow d1 10)

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