FastMath repmul

Average Error: 0.2 → 0.2

Time: 3.2s

Precision: 64

Math

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

↓

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

C

double f(double d1) {
        double r1877177 = d1;
        double r1877178 = r1877177 * r1877177;
        double r1877179 = r1877178 * r1877177;
        double r1877180 = r1877179 * r1877177;
        return r1877180;
}

↓

double f(double d1) {
        double r1877181 = d1;
        double r1877182 = r1877181 * r1877181;
        double r1877183 = r1877182 * r1877181;
        double r1877184 = r1877183 * r1877181;
        return r1877184;
}

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 2019107 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))