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 r18250618 = a;
        double r18250619 = log(r18250618);
        double r18250620 = b;
        double r18250621 = log(r18250620);
        double r18250622 = r18250619 + r18250621;
        double r18250623 = exp(r18250622);
        return r18250623;
}
↓
double f(double a, double b) {
        double r18250624 = a;
        double r18250625 = b;
        double r18250626 = r18250624 * r18250625;
        return r18250626;
}


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 2019101 
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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