FastMath repmul

Average Error: 0.2 → 0.2

Time: 6.7s

Precision: 64

Math

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

↓

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

C

double f(double d1) {
        double r1814264 = d1;
        double r1814265 = r1814264 * r1814264;
        double r1814266 = r1814265 * r1814264;
        double r1814267 = r1814266 * r1814264;
        return r1814267;
}

↓

double f(double d1) {
        double r1814268 = d1;
        double r1814269 = r1814268 * r1814268;
        double r1814270 = r1814269 * r1814269;
        return r1814270;
}

Error

Bits error versus d1

Derivation

1. Initial program 0.2

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

2. Simplified 0.2

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

3. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))