Average Error: 0.1 → 0
Time: 8.8s
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 r7593787 = d1;
        double r7593788 = r7593787 * r7593787;
        double r7593789 = r7593788 * r7593787;
        double r7593790 = r7593789 * r7593787;
        return r7593790;
}
↓
double f(double d1) {
        double r7593791 = d1;
        double r7593792 = 4.0;
        double r7593793 = pow(r7593791, r7593792);
        return r7593793;
}

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 pow20.1

    \[\leadsto \left(\color{blue}{{d1}^{2}} \cdot d1\right) \cdot d1\]

  4. Applied pow-plus0.1

    \[\leadsto \color{blue}{{d1}^{\left(2 + 1\right)}} \cdot d1\]

  5. Applied pow-plus0

    \[\leadsto \color{blue}{{d1}^{\left(\left(2 + 1\right) + 1\right)}}\]

  6. Simplified0

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

  7. Final simplification0

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

Reproduce

herbie shell --seed 2019149 
(FPCore (d1)
  :name "FastMath repmul"

  :herbie-target
  (pow d1 4)

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