Average Error: 5.6 → 0
Time: 4.0s
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 r81566 = a;
        double r81567 = log(r81566);
        double r81568 = b;
        double r81569 = log(r81568);
        double r81570 = r81567 + r81569;
        double r81571 = exp(r81570);
        return r81571;
}
↓
double f(double a, double b) {
        double r81572 = b;
        double r81573 = a;
        double r81574 = r81572 * r81573;
        return r81574;
}

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

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

  3. Final simplification0

    \[\leadsto b \cdot a\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"
  :precision binary64

  :herbie-target
  (* a b)

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