FastMath repmul

Average Error: 0.1 → 0.1

Time: 2.7s

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 r1555222 = d1;
        double r1555223 = r1555222 * r1555222;
        double r1555224 = r1555223 * r1555222;
        double r1555225 = r1555224 * r1555222;
        return r1555225;
}

↓

double f(double d1) {
        double r1555226 = d1;
        double r1555227 = r1555226 * r1555226;
        double r1555228 = r1555227 * r1555226;
        double r1555229 = r1555228 * r1555226;
        return r1555229;
}

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 2019125 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))