Average Error: 5.7 → 0
Time: 3.5s
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 r3903639 = a;
        double r3903640 = log(r3903639);
        double r3903641 = b;
        double r3903642 = log(r3903641);
        double r3903643 = r3903640 + r3903642;
        double r3903644 = exp(r3903643);
        return r3903644;
}
↓
double f(double a, double b) {
        double r3903645 = b;
        double r3903646 = a;
        double r3903647 = r3903645 * r3903646;
        return r3903647;
}

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 2019168 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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