Average Error: 0.2 → 0.2
Time: 1.8m
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 r5073383 = d1;
        double r5073384 = r5073383 * r5073383;
        double r5073385 = r5073384 * r5073383;
        double r5073386 = r5073385 * r5073383;
        return r5073386;
}
↓
double f(double d1) {
        double r5073387 = d1;
        double r5073388 = r5073387 * r5073387;
        double r5073389 = r5073388 * r5073387;
        double r5073390 = r5073389 * r5073387;
        return r5073390;
}

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 2019158 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))