Average Error: 0.1 → 0
Time: 4.4s
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 r31808940 = d1;
        double r31808941 = r31808940 * r31808940;
        double r31808942 = r31808941 * r31808940;
        double r31808943 = r31808942 * r31808940;
        return r31808943;
}
↓
double f(double d1) {
        double r31808944 = d1;
        double r31808945 = 4.0;
        double r31808946 = pow(r31808944, r31808945);
        return r31808946;
}

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. Taylor expanded around -inf 0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"

  :herbie-target
  (pow d1 4)

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