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 r3909233 = a;
        double r3909234 = log(r3909233);
        double r3909235 = b;
        double r3909236 = log(r3909235);
        double r3909237 = r3909234 + r3909236;
        double r3909238 = exp(r3909237);
        return r3909238;
}
↓
double f(double a, double b) {
        double r3909239 = a;
        double r3909240 = b;
        double r3909241 = r3909239 * r3909240;
        return r3909241;
}

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 2019149 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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