Average Error: 5.8 → 0
Time: 4.4s
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 r5687479 = a;
        double r5687480 = log(r5687479);
        double r5687481 = b;
        double r5687482 = log(r5687481);
        double r5687483 = r5687480 + r5687482;
        double r5687484 = exp(r5687483);
        return r5687484;
}
↓
double f(double a, double b) {
        double r5687485 = a;
        double r5687486 = b;
        double r5687487 = r5687485 * r5687486;
        return r5687487;
}

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

  :herbie-target
  (* a b)

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