Average Error: 0.1 → 0
Time: 34.9s
Precision: 64
\[\left(d1 \cdot \left(\left(\left(\left(\left(d1 \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right) \cdot d1\right) \cdot \left(d1 \cdot d1\right)\right) \cdot d1\right)\right) \cdot d1\]
↓
\[{d1}^{10}\]
\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 r51712448 = d1;
        double r51712449 = r51712448 * r51712448;
        double r51712450 = r51712448 * r51712449;
        double r51712451 = r51712450 * r51712448;
        double r51712452 = r51712451 * r51712448;
        double r51712453 = r51712452 * r51712449;
        double r51712454 = r51712453 * r51712448;
        double r51712455 = r51712448 * r51712454;
        double r51712456 = r51712455 * r51712448;
        return r51712456;
}
↓
double f(double d1) {
        double r51712457 = d1;
        double r51712458 = 10.0;
        double r51712459 = pow(r51712457, r51712458);
        return r51712459;
}

Error

Bits error versus d1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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

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

  4. Applied pow-plus0.1

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

  5. Applied cube-unmult0.1

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

  6. Applied pow-plus0.1

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

  7. Applied pow-plus0.1

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

  8. Applied pow-prod-up0.1

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

  9. Simplified0.1

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

  10. Taylor expanded around inf 0

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

  11. Final simplification0

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

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(FPCore (d1)
  :name "FastMath test5"

  :herbie-target
  (pow d1 10)

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