Average Error: 5.6 → 0
Time: 4.0s
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 r4528410 = a;
        double r4528411 = log(r4528410);
        double r4528412 = b;
        double r4528413 = log(r4528412);
        double r4528414 = r4528411 + r4528413;
        double r4528415 = exp(r4528414);
        return r4528415;
}
↓
double f(double a, double b) {
        double r4528416 = a;
        double r4528417 = b;
        double r4528418 = r4528416 * r4528417;
        return r4528418;
}

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 
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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