Average Error: 5.7 → 0
Time: 2.6s
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 r106673 = a;
        double r106674 = log(r106673);
        double r106675 = b;
        double r106676 = log(r106675);
        double r106677 = r106674 + r106676;
        double r106678 = exp(r106677);
        return r106678;
}
↓
double f(double a, double b) {
        double r106679 = b;
        double r106680 = a;
        double r106681 = r106679 * r106680;
        return r106681;
}

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

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

  3. Final simplification0

    \[\leadsto b \cdot a\]

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"
  :precision binary64

  :herbie-target
  (* a b)

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