Average Error: 0.1 → 0
Time: 4.7s
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 r8505370 = d1;
        double r8505371 = r8505370 * r8505370;
        double r8505372 = r8505371 * r8505370;
        double r8505373 = r8505372 * r8505370;
        return r8505373;
}
↓
double f(double d1) {
        double r8505374 = d1;
        double r8505375 = 4.0;
        double r8505376 = pow(r8505374, r8505375);
        return r8505376;
}

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

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

  4. Applied pow10.1

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

  5. Applied pow10.1

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

  6. Applied pow10.1

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

  7. Applied pow-prod-up0.1

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

  8. Applied pow-prod-up0.1

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

  9. Applied pow-prod-up0

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

  10. Simplified0

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

  11. Final simplification0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"

  :herbie-target
  (pow d1 4.0)

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