Average Error: 0.1 → 0
Time: 33.5s
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 r48812805 = d1;
        double r48812806 = r48812805 * r48812805;
        double r48812807 = r48812805 * r48812806;
        double r48812808 = r48812807 * r48812805;
        double r48812809 = r48812808 * r48812805;
        double r48812810 = r48812809 * r48812806;
        double r48812811 = r48812810 * r48812805;
        double r48812812 = r48812805 * r48812811;
        double r48812813 = r48812812 * r48812805;
        return r48812813;
}

double f(double d1) {
        double r48812814 = d1;
        double r48812815 = 10.0;
        double r48812816 = pow(r48812814, r48812815);
        return r48812816;
}

\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

    \[\leadsto \left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right) \cdot d1\right) \cdot \left(d1 \cdot \color{blue}{{d1}^{1}}\right)\right) \cdot d1\right)\right) \cdot d1\]
  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-sqr0.1

    \[\leadsto \left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right) \cdot d1\right) \cdot \color{blue}{{d1}^{\left(2 \cdot 1\right)}}\right) \cdot d1\right)\right) \cdot d1\]
  6. Applied pow10.1

    \[\leadsto \left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot \color{blue}{{d1}^{1}}\right) \cdot d1\right) \cdot {d1}^{\left(2 \cdot 1\right)}\right) \cdot d1\right)\right) \cdot d1\]
  7. Applied cube-unmult0.1

    \[\leadsto \left(d1 \cdot \left(\left(\left(\left(\color{blue}{{d1}^{3}} \cdot {d1}^{1}\right) \cdot d1\right) \cdot {d1}^{\left(2 \cdot 1\right)}\right) \cdot d1\right)\right) \cdot d1\]
  8. Applied pow-prod-up0.1

    \[\leadsto \left(d1 \cdot \left(\left(\left(\color{blue}{{d1}^{\left(3 + 1\right)}} \cdot d1\right) \cdot {d1}^{\left(2 \cdot 1\right)}\right) \cdot d1\right)\right) \cdot d1\]
  9. Applied pow-plus0.1

    \[\leadsto \left(d1 \cdot \left(\left(\color{blue}{{d1}^{\left(\left(3 + 1\right) + 1\right)}} \cdot {d1}^{\left(2 \cdot 1\right)}\right) \cdot d1\right)\right) \cdot d1\]
  10. Applied pow-prod-up0.1

    \[\leadsto \left(d1 \cdot \left(\color{blue}{{d1}^{\left(\left(\left(3 + 1\right) + 1\right) + 2 \cdot 1\right)}} \cdot d1\right)\right) \cdot d1\]
  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 pow-prod-up0.1

    \[\leadsto \left(d1 \cdot \color{blue}{{d1}^{\left(7 + 1\right)}}\right) \cdot {d1}^{1}\]
  16. Applied pow10.1

    \[\leadsto \left(\color{blue}{{d1}^{1}} \cdot {d1}^{\left(7 + 1\right)}\right) \cdot {d1}^{1}\]
  17. Applied pow-prod-up0.0

    \[\leadsto \color{blue}{{d1}^{\left(1 + \left(7 + 1\right)\right)}} \cdot {d1}^{1}\]
  18. Applied pow-prod-up0

    \[\leadsto \color{blue}{{d1}^{\left(\left(1 + \left(7 + 1\right)\right) + 1\right)}}\]
  19. Simplified0

    \[\leadsto {d1}^{\color{blue}{10}}\]
  20. Final simplification0

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

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (d1)
  :name "FastMath test5"

  :herbie-target
  (pow d1 10)

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