FastMath repmul

Average Error: 0.2 → 0.2

Time: 2.1s

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 r3397230 = d1;
        double r3397231 = r3397230 * r3397230;
        double r3397232 = r3397231 * r3397230;
        double r3397233 = r3397232 * r3397230;
        return r3397233;
}

↓

double f(double d1) {
        double r3397234 = d1;
        double r3397235 = r3397234 * r3397234;
        double r3397236 = r3397235 * r3397235;
        return r3397236;
}

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 2019134 
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))