FastMath repmul

Average Error: 0.2 → 0.2

Time: 2.4s

Precision: 64

Math

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

↓

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

C

double f(double d1) {
        double r6476797 = d1;
        double r6476798 = r6476797 * r6476797;
        double r6476799 = r6476798 * r6476797;
        double r6476800 = r6476799 * r6476797;
        return r6476800;
}

↓

double f(double d1) {
        double r6476801 = d1;
        double r6476802 = r6476801 * r6476801;
        double r6476803 = r6476802 * r6476801;
        double r6476804 = r6476803 * r6476801;
        return r6476804;
}

Error

Bits error versus d1

Derivation

1. Initial program 0.2

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

2. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019135 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))