Average Error: 5.7 → 0
Time: 4.3s
Precision: 64
\[e^{\log a + \log b}\]
↓
\[a \cdot b\]
double f(double a, double b) {
        double r19784746 = a;
        double r19784747 = log(r19784746);
        double r19784748 = b;
        double r19784749 = log(r19784748);
        double r19784750 = r19784747 + r19784749;
        double r19784751 = exp(r19784750);
        return r19784751;
}
↓
double f(double a, double b) {
        double r19784752 = a;
        double r19784753 = b;
        double r19784754 = r19784752 * r19784753;
        return r19784754;
}


e^{\log a + \log b}
↓
a \cdot b

Error

Bits error versus a

Bits error versus b

Target

Original5.7
Target0
Herbie0
\[a \cdot b\]

Derivation

  1. Initial program 5.7

    \[e^{\log a + \log b}\]

  2. Simplified0

    \[\leadsto \color{blue}{a \cdot b}\]

  3. Final simplification0

    \[\leadsto a \cdot b\]

Reproduce

herbie shell --seed 2019102 
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

  (exp (+ (log a) (log b))))