Average Error: 0.1 → 0.1
Time: 2.0m
Precision: 64
\[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]
↓
\[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]
\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1
↓
\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1
double f(double d1) {
        double r3699111 = d1;
        double r3699112 = r3699111 * r3699111;
        double r3699113 = r3699112 * r3699111;
        double r3699114 = r3699113 * r3699111;
        return r3699114;
}
↓
double f(double d1) {
        double r3699115 = d1;
        double r3699116 = r3699115 * r3699115;
        double r3699117 = r3699116 * r3699115;
        double r3699118 = r3699117 * r3699115;
        return r3699118;
}

Error

Bits error versus d1

Derivation

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Reproduce

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