FastMath repmul

Average Error: 0.1 → 0.1

Time: 2.3s

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 r1497875 = d1;
        double r1497876 = r1497875 * r1497875;
        double r1497877 = r1497876 * r1497875;
        double r1497878 = r1497877 * r1497875;
        return r1497878;
}

↓

double f(double d1) {
        double r1497879 = d1;
        double r1497880 = r1497879 * r1497879;
        double r1497881 = r1497880 * r1497879;
        double r1497882 = r1497881 * r1497879;
        return r1497882;
}

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 2019120 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))