Average Error: 5.7 → 0
Time: 3.8s
Precision: 64
\[e^{\log a + \log b}\]
↓
\[a \cdot b\]
e^{\log a + \log b}
↓
a \cdot b
double f(double a, double b) {
        double r6427562 = a;
        double r6427563 = log(r6427562);
        double r6427564 = b;
        double r6427565 = log(r6427564);
        double r6427566 = r6427563 + r6427565;
        double r6427567 = exp(r6427566);
        return r6427567;
}
↓
double f(double a, double b) {
        double r6427568 = a;
        double r6427569 = b;
        double r6427570 = r6427568 * r6427569;
        return r6427570;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.7
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 2019192 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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