Average Error: 5.8 → 0
Time: 6.3s
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 r5587917 = a;
        double r5587918 = log(r5587917);
        double r5587919 = b;
        double r5587920 = log(r5587919);
        double r5587921 = r5587918 + r5587920;
        double r5587922 = exp(r5587921);
        return r5587922;
}
↓
double f(double a, double b) {
        double r5587923 = b;
        double r5587924 = a;
        double r5587925 = r5587923 * r5587924;
        return r5587925;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.8
Target0
Herbie0
\[a \cdot b\]

Derivation

  1. Initial program 5.8

    \[e^{\log a + \log b}\]

  2. Simplified0

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

  3. Final simplification0

    \[\leadsto b \cdot a\]

Reproduce

herbie shell --seed 2019165 
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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