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 r32327759 = a;
        double r32327760 = log(r32327759);
        double r32327761 = b;
        double r32327762 = log(r32327761);
        double r32327763 = r32327760 + r32327762;
        double r32327764 = exp(r32327763);
        return r32327764;
}
↓
double f(double a, double b) {
        double r32327765 = a;
        double r32327766 = b;
        double r32327767 = r32327765 * r32327766;
        return r32327767;
}

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 2019119 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"

  :herbie-target
  (* a b)

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