FastMath repmul

Average Error: 0.1 → 0.1

Time: 19.9s

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 r1758778 = d1;
        double r1758779 = r1758778 * r1758778;
        double r1758780 = r1758779 * r1758778;
        double r1758781 = r1758780 * r1758778;
        return r1758781;
}

↓

double f(double d1) {
        double r1758782 = d1;
        double r1758783 = r1758782 * r1758782;
        double r1758784 = r1758783 * r1758782;
        double r1758785 = r1758784 * r1758782;
        return r1758785;
}

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 2019163 +o rules:numerics
(FPCore (d1)
  :name "FastMath repmul"
  (*.p16 (*.p16 (*.p16 d1 d1) d1) d1))