Average Error: 0.1 → 0
Time: 4.4s
Precision: 64
\[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]
↓
\[{d1}^{4}\]
double f(double d1) {
        double r52820210 = d1;
        double r52820211 = r52820210 * r52820210;
        double r52820212 = r52820211 * r52820210;
        double r52820213 = r52820212 * r52820210;
        return r52820213;
}
↓
double f(double d1) {
        double r52820214 = d1;
        double r52820215 = 4.0;
        double r52820216 = pow(r52820214, r52820215);
        return r52820216;
}


\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1
↓
{d1}^{4}

Error

Bits error versus d1

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

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

  4. Applied pow10.1

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

  5. Applied pow-plus0.1

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

  6. Applied pow-plus0.1

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

  7. Applied pow-prod-up0

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

  8. Simplified0

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

  9. Final simplification0

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

Reproduce

herbie shell --seed 2019101 
(FPCore (d1)
  :name "FastMath repmul"

  :herbie-target
  (pow d1 4)

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