Average Error: 5.6 → 0
Time: 4.5s
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 r4909332 = a;
        double r4909333 = log(r4909332);
        double r4909334 = b;
        double r4909335 = log(r4909334);
        double r4909336 = r4909333 + r4909335;
        double r4909337 = exp(r4909336);
        return r4909337;
}
↓
double f(double a, double b) {
        double r4909338 = a;
        double r4909339 = b;
        double r4909340 = r4909338 * r4909339;
        return r4909340;
}

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

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

  3. Final simplification0

    \[\leadsto a \cdot b\]

Reproduce

herbie shell --seed 2019133 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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