Average Error: 0.1 → 0
Time: 5.5s
Precision: 64
\[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]
↓
\[{d1}^{4}\]
\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1
↓
{d1}^{4}
double f(double d1) {
        double r9520508 = d1;
        double r9520509 = r9520508 * r9520508;
        double r9520510 = r9520509 * r9520508;
        double r9520511 = r9520510 * r9520508;
        return r9520511;
}
↓
double f(double d1) {
        double r9520512 = d1;
        double r9520513 = 4.0;
        double r9520514 = pow(r9520512, r9520513);
        return r9520514;
}

Error

Bits error versus d1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0
Herbie0
\[{d1}^{4}\]

Derivation

  1. Initial program 0.1

    \[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]
  2. Using strategy rm

  3. Applied pow10.1

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

  4. Applied pow10.1

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

  5. Applied pow-plus0.1

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

  6. Applied pow-prod-up0.1

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

  7. Applied pow-plus0

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

  8. Simplified0

    \[\leadsto {d1}^{\color{blue}{4}}\]

  9. Final simplification0

    \[\leadsto {d1}^{4}\]

Reproduce

herbie shell --seed 2019132 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"

  :herbie-target
  (pow d1 4)

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