FastMath repmul

Average Error: 0.2 → 0.2

Time: 3.2s

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 r2450184 = d1;
        double r2450185 = r2450184 * r2450184;
        double r2450186 = r2450185 * r2450184;
        double r2450187 = r2450186 * r2450184;
        return r2450187;
}

↓

double f(double d1) {
        double r2450188 = d1;
        double r2450189 = r2450188 * r2450188;
        double r2450190 = r2450189 * r2450189;
        return r2450190;
}

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 2019124 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))