Average Error: 0.1 → 0
Time: 11.0s
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 r8566378 = d1;
        double r8566379 = r8566378 * r8566378;
        double r8566380 = r8566379 * r8566378;
        double r8566381 = r8566380 * r8566378;
        return r8566381;
}
↓
double f(double d1) {
        double r8566382 = d1;
        double r8566383 = 4.0;
        double r8566384 = pow(r8566382, r8566383);
        return r8566384;
}

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 2019134 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"

  :herbie-target
  (pow d1 4)

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