Average Error: 0.1 → 0
Time: 11.6s
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 r3326329 = d1;
        double r3326330 = r3326329 * r3326329;
        double r3326331 = r3326329 * r3326330;
        double r3326332 = r3326331 * r3326329;
        double r3326333 = r3326332 * r3326329;
        double r3326334 = r3326333 * r3326330;
        double r3326335 = r3326334 * r3326329;
        double r3326336 = r3326329 * r3326335;
        double r3326337 = r3326336 * r3326329;
        return r3326337;
}
↓
double f(double d1) {
        double r3326338 = d1;
        double r3326339 = 10.0;
        double r3326340 = pow(r3326338, r3326339);
        return r3326340;
}

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. Taylor expanded around inf 0.1

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

  4. Applied pow10.1

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

  5. Applied pow10.1

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

  6. Applied pow-prod-up0.1

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

  7. Applied pow10.1

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

  8. Applied pow-prod-up0.0

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

  9. Applied pow-prod-up0

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

  10. Simplified0

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

  11. Final simplification0

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

Reproduce

herbie shell --seed 2019151 +o rules:numerics
(FPCore (d1)
  :name "FastMath test5"

  :herbie-target
  (pow d1 10)

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