FastMath repmul

Average Error: 0.2 → 0.2

Time: 27.8s

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 r1974314 = d1;
        double r1974315 = r1974314 * r1974314;
        double r1974316 = r1974315 * r1974314;
        double r1974317 = r1974316 * r1974314;
        return r1974317;
}

↓

double f(double d1) {
        double r1974318 = d1;
        double r1974319 = r1974318 * r1974318;
        double r1974320 = r1974319 * r1974319;
        return r1974320;
}

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 
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))