Average Error: 5.8 → 0
Time: 4.2s
Precision: 64
\[e^{\log a + \log b}\]
↓
\[b \cdot a\]
e^{\log a + \log b}
↓
b \cdot a
double f(double a, double b) {
        double r87235 = a;
        double r87236 = log(r87235);
        double r87237 = b;
        double r87238 = log(r87237);
        double r87239 = r87236 + r87238;
        double r87240 = exp(r87239);
        return r87240;
}
↓
double f(double a, double b) {
        double r87241 = b;
        double r87242 = a;
        double r87243 = r87241 * r87242;
        return r87243;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.8
Target0
Herbie0
\[a \cdot b\]

Derivation

  1. Initial program 5.8

    \[e^{\log a + \log b}\]

  2. Simplified0

    \[\leadsto \color{blue}{b \cdot a}\]

  3. Final simplification0

    \[\leadsto b \cdot a\]

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"
  :precision binary64

  :herbie-target
  (* a b)

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