Average Error: 0.1 → 0.2
Time: 3.3s
Precision: 64
\[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]
↓
\[\left(d1 \cdot d1\right) \cdot \left(d1 \cdot d1\right)\]
\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1
↓
\left(d1 \cdot d1\right) \cdot \left(d1 \cdot d1\right)
double f(double d1) {
        double r2425237 = d1;
        double r2425238 = r2425237 * r2425237;
        double r2425239 = r2425238 * r2425237;
        double r2425240 = r2425239 * r2425237;
        return r2425240;
}
↓
double f(double d1) {
        double r2425241 = d1;
        double r2425242 = r2425241 * r2425241;
        double r2425243 = r2425242 * r2425242;
        return r2425243;
}

Error

Bits error versus d1

Derivation

  1. Initial program 0.1

    \[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]

  2. Simplified0.2

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

  3. Final simplification0.2

    \[\leadsto \left(d1 \cdot d1\right) \cdot \left(d1 \cdot d1\right)\]

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))