Average Error: 5.7 → 0
Time: 3.2s
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 r6407918 = a;
        double r6407919 = log(r6407918);
        double r6407920 = b;
        double r6407921 = log(r6407920);
        double r6407922 = r6407919 + r6407921;
        double r6407923 = exp(r6407922);
        return r6407923;
}
↓
double f(double a, double b) {
        double r6407924 = b;
        double r6407925 = a;
        double r6407926 = r6407924 * r6407925;
        return r6407926;
}

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 2019171 
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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