Average Error: 5.7 → 0
Time: 4.5s
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 r5033271 = a;
        double r5033272 = log(r5033271);
        double r5033273 = b;
        double r5033274 = log(r5033273);
        double r5033275 = r5033272 + r5033274;
        double r5033276 = exp(r5033275);
        return r5033276;
}
↓
double f(double a, double b) {
        double r5033277 = a;
        double r5033278 = b;
        double r5033279 = r5033277 * r5033278;
        return r5033279;
}

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 2019143 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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