Average Error: 5.7 → 0
Time: 4.1s
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 r5279390 = a;
        double r5279391 = log(r5279390);
        double r5279392 = b;
        double r5279393 = log(r5279392);
        double r5279394 = r5279391 + r5279393;
        double r5279395 = exp(r5279394);
        return r5279395;
}
↓
double f(double a, double b) {
        double r5279396 = a;
        double r5279397 = b;
        double r5279398 = r5279396 * r5279397;
        return r5279398;
}

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 2019172 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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