Average Error: 5.6 → 0
Time: 3.9s
Precision: 64
\[e^{\log a + \log b}\]
↓
\[b \cdot a\]
e^{\log a + \log b}
↓
b \cdot a
double f(double a, double b) {
        double r2537643 = a;
        double r2537644 = log(r2537643);
        double r2537645 = b;
        double r2537646 = log(r2537645);
        double r2537647 = r2537644 + r2537646;
        double r2537648 = exp(r2537647);
        return r2537648;
}
↓
double f(double a, double b) {
        double r2537649 = b;
        double r2537650 = a;
        double r2537651 = r2537649 * r2537650;
        return r2537651;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.6
Target0
Herbie0
\[a \cdot b\]

Derivation

  1. Initial program 5.6

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

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto b \cdot a\]

Reproduce

herbie shell --seed 2019154 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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