FastMath repmul

Average Error: 0.1 → 0.2

Time: 27.9s

Precision: 64

Math

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

↓

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

C

double f(double d1) {
        double r1468817 = d1;
        double r1468818 = r1468817 * r1468817;
        double r1468819 = r1468818 * r1468817;
        double r1468820 = r1468819 * r1468817;
        return r1468820;
}

↓

double f(double d1) {
        double r1468821 = d1;
        double r1468822 = r1468821 * r1468821;
        double r1468823 = r1468822 * r1468822;
        return r1468823;
}

Error

Bits error versus d1

Derivation

1. Initial program 0.1

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

2. Simplified 0.2

   \[\leadsto \color{blue}{\left(d1 \cdot d1\right) \cdot \left(d1 \cdot d1\right)}\]

3. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019151 
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))