FastMath repmul

Average Error: 0.2 → 0.2

Time: 33.1s

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 r3980517 = d1;
        double r3980518 = r3980517 * r3980517;
        double r3980519 = r3980518 * r3980517;
        double r3980520 = r3980519 * r3980517;
        return r3980520;
}

↓

double f(double d1) {
        double r3980521 = d1;
        double r3980522 = r3980521 * r3980521;
        double r3980523 = r3980522 * r3980521;
        double r3980524 = r3980523 * r3980521;
        return r3980524;
}

Error

Bits error versus d1

Derivation

1. Initial program 0.2

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

2. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019158 
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))