Average Error: 0.3 → 0
Time: 754.0ms
Precision: 64
\[d \cdot 10 + d \cdot 20\]
↓
\[d \cdot 30\]
double f(double d) {
        double r27256838 = d;
        double r27256839 = 10.0;
        double r27256840 = r27256838 * r27256839;
        double r27256841 = 20.0;
        double r27256842 = r27256838 * r27256841;
        double r27256843 = r27256840 + r27256842;
        return r27256843;
}
↓
double f(double d) {
        double r27256844 = d;
        double r27256845 = 30.0;
        double r27256846 = r27256844 * r27256845;
        return r27256846;
}


d \cdot 10 + d \cdot 20
↓
d \cdot 30

Error

Bits error versus d

Target

Original0.3
Target0
Herbie0
\[d \cdot 30\]

Derivation

  1. Initial program 0.3

    \[d \cdot 10 + d \cdot 20\]

  2. Simplified0

    \[\leadsto \color{blue}{d \cdot 30}\]

  3. Final simplification0

    \[\leadsto d \cdot 30\]

Reproduce

herbie shell --seed 2019101 +o rules:numerics
(FPCore (d)
  :name "FastMath test1"

  :herbie-target
  (* d 30)

  (+ (* d 10) (* d 20)))