Average Error: 0.1 → 0.1
Time: 55.8s
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 r2715082 = d1;
        double r2715083 = r2715082 * r2715082;
        double r2715084 = r2715083 * r2715082;
        double r2715085 = r2715084 * r2715082;
        return r2715085;
}
↓
double f(double d1) {
        double r2715086 = d1;
        double r2715087 = r2715086 * r2715086;
        double r2715088 = r2715087 * r2715086;
        double r2715089 = r2715088 * r2715086;
        return r2715089;
}

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