FastMath repmul

Average Error: 0.2 → 0.2

Time: 7.2s

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 r1266960 = d1;
        double r1266961 = r1266960 * r1266960;
        double r1266962 = r1266961 * r1266960;
        double r1266963 = r1266962 * r1266960;
        return r1266963;
}

↓

double f(double d1) {
        double r1266964 = d1;
        double r1266965 = r1266964 * r1266964;
        double r1266966 = r1266965 * r1266964;
        double r1266967 = r1266966 * r1266964;
        return r1266967;
}

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