Average Error: 0.1 → 0
Time: 7.0s
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 r162502 = d1;
        double r162503 = r162502 * r162502;
        double r162504 = r162502 * r162503;
        double r162505 = r162504 * r162502;
        double r162506 = r162505 * r162502;
        double r162507 = r162506 * r162503;
        double r162508 = r162507 * r162502;
        double r162509 = r162502 * r162508;
        double r162510 = r162509 * r162502;
        return r162510;
}
↓
double f(double d1) {
        double r162511 = d1;
        double r162512 = 10.0;
        double r162513 = pow(r162511, r162512);
        return r162513;
}

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. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (d1)
  :name "FastMath test5"
  :precision binary64

  :herbie-target
  (pow d1 10)

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