Average Error: 5.6 → 0
Time: 4.3s
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 r5997462 = a;
        double r5997463 = log(r5997462);
        double r5997464 = b;
        double r5997465 = log(r5997464);
        double r5997466 = r5997463 + r5997465;
        double r5997467 = exp(r5997466);
        return r5997467;
}
↓
double f(double a, double b) {
        double r5997468 = a;
        double r5997469 = b;
        double r5997470 = r5997468 * r5997469;
        return r5997470;
}

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 2019132 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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