Average Error: 5.7 → 0
Time: 3.5s
Precision: 64
\[e^{\log a + \log b}\]
↓
\[b \cdot a\]
e^{\log a + \log b}
↓
b \cdot a
double f(double a, double b) {
        double r4826175 = a;
        double r4826176 = log(r4826175);
        double r4826177 = b;
        double r4826178 = log(r4826177);
        double r4826179 = r4826176 + r4826178;
        double r4826180 = exp(r4826179);
        return r4826180;
}
↓
double f(double a, double b) {
        double r4826181 = b;
        double r4826182 = a;
        double r4826183 = r4826181 * r4826182;
        return r4826183;
}

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

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

  3. Final simplification0

    \[\leadsto b \cdot a\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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