Average Error: 5.7 → 0
Time: 4.1s
Precision: 64
\[e^{\log a + \log b}\]
↓
\[a \cdot b\]
e^{\log a + \log b}
↓
a \cdot b
double f(double a, double b) {
        double r5521714 = a;
        double r5521715 = log(r5521714);
        double r5521716 = b;
        double r5521717 = log(r5521716);
        double r5521718 = r5521715 + r5521717;
        double r5521719 = exp(r5521718);
        return r5521719;
}
↓
double f(double a, double b) {
        double r5521720 = a;
        double r5521721 = b;
        double r5521722 = r5521720 * r5521721;
        return r5521722;
}

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

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

  3. Final simplification0

    \[\leadsto a \cdot b\]

Reproduce

herbie shell --seed 2019130 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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