Average Error: 5.7 → 0
Time: 3.9s
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 r83656 = a;
        double r83657 = log(r83656);
        double r83658 = b;
        double r83659 = log(r83658);
        double r83660 = r83657 + r83659;
        double r83661 = exp(r83660);
        return r83661;
}
↓
double f(double a, double b) {
        double r83662 = b;
        double r83663 = a;
        double r83664 = r83662 * r83663;
        return r83664;
}

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 2019306 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"
  :precision binary64

  :herbie-target
  (* a b)

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