Average Error: 5.7 → 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 r63383 = a;
        double r63384 = log(r63383);
        double r63385 = b;
        double r63386 = log(r63385);
        double r63387 = r63384 + r63386;
        double r63388 = exp(r63387);
        return r63388;
}
↓
double f(double a, double b) {
        double r63389 = a;
        double r63390 = b;
        double r63391 = r63389 * r63390;
        return r63391;
}

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 2019194 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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