Average Error: 0.2 → 0.2
Time: 2.6s
Precision: 64
\[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]
↓
\[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]
\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1
↓
\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1
double f(double d1) {
        double r3110015 = d1;
        double r3110016 = r3110015 * r3110015;
        double r3110017 = r3110016 * r3110015;
        double r3110018 = r3110017 * r3110015;
        return r3110018;
}
↓
double f(double d1) {
        double r3110019 = d1;
        double r3110020 = r3110019 * r3110019;
        double r3110021 = r3110020 * r3110019;
        double r3110022 = r3110021 * r3110019;
        return r3110022;
}

Error

Bits error versus d1

Derivation

  1. Initial program 0.2

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))