FastMath repmul

Average Error: 0.2 → 0.2

Time: 6.3s

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 r1382214 = d1;
        double r1382215 = r1382214 * r1382214;
        double r1382216 = r1382215 * r1382214;
        double r1382217 = r1382216 * r1382214;
        return r1382217;
}

↓

double f(double d1) {
        double r1382218 = d1;
        double r1382219 = r1382218 * r1382218;
        double r1382220 = r1382219 * r1382218;
        double r1382221 = r1382220 * r1382218;
        return r1382221;
}

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 2019156 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))