FastMath repmul

Average Error: 0.1 → 0.1

Time: 2.9s

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 r4179524 = d1;
        double r4179525 = r4179524 * r4179524;
        double r4179526 = r4179525 * r4179524;
        double r4179527 = r4179526 * r4179524;
        return r4179527;
}

↓

double f(double d1) {
        double r4179528 = d1;
        double r4179529 = r4179528 * r4179528;
        double r4179530 = r4179529 * r4179528;
        double r4179531 = r4179530 * r4179528;
        return r4179531;
}

Error

Bits error versus d1

Derivation

1. Initial program 0.1

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

2. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019125 
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))