Average Error: 5.8 → 0
Time: 4.3s
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 r7141517 = a;
        double r7141518 = log(r7141517);
        double r7141519 = b;
        double r7141520 = log(r7141519);
        double r7141521 = r7141518 + r7141520;
        double r7141522 = exp(r7141521);
        return r7141522;
}
↓
double f(double a, double b) {
        double r7141523 = a;
        double r7141524 = b;
        double r7141525 = r7141523 * r7141524;
        return r7141525;
}

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

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

  3. Final simplification0

    \[\leadsto a \cdot b\]

Reproduce

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

  :herbie-target
  (* a b)

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