Average Error: 5.7 → 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 r25528688 = a;
        double r25528689 = log(r25528688);
        double r25528690 = b;
        double r25528691 = log(r25528690);
        double r25528692 = r25528689 + r25528691;
        double r25528693 = exp(r25528692);
        return r25528693;
}
↓
double f(double a, double b) {
        double r25528694 = a;
        double r25528695 = b;
        double r25528696 = r25528694 * r25528695;
        return r25528696;
}

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 2019104 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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