Average Error: 5.6 → 0
Time: 4.6s
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 r96688 = a;
        double r96689 = log(r96688);
        double r96690 = b;
        double r96691 = log(r96690);
        double r96692 = r96689 + r96691;
        double r96693 = exp(r96692);
        return r96693;
}
↓
double f(double a, double b) {
        double r96694 = b;
        double r96695 = a;
        double r96696 = r96694 * r96695;
        return r96696;
}

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 2019195 
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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