FastMath repmul

Average Error: 0.1 → 0.1

Time: 56.2s

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 r2670070 = d1;
        double r2670071 = r2670070 * r2670070;
        double r2670072 = r2670071 * r2670070;
        double r2670073 = r2670072 * r2670070;
        return r2670073;
}

↓

double f(double d1) {
        double r2670074 = d1;
        double r2670075 = r2670074 * r2670074;
        double r2670076 = r2670075 * r2670074;
        double r2670077 = r2670076 * r2670074;
        return r2670077;
}

Error

Bits error versus d1

Derivation

1. Initial program 0.1

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

2. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019162 
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))