Average Error: 5.6 → 0
Time: 1.9s
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 r161760 = a;
        double r161761 = log(r161760);
        double r161762 = b;
        double r161763 = log(r161762);
        double r161764 = r161761 + r161763;
        double r161765 = exp(r161764);
        return r161765;
}
↓
double f(double a, double b) {
        double r161766 = a;
        double r161767 = b;
        double r161768 = r161766 * r161767;
        return r161768;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.6
Target0
Herbie0
\[a \cdot b\]

Derivation

  1. Initial program 5.6

    \[e^{\log a + \log b}\]
  2. Using strategy rm

  3. Applied exp-sum5.4

    \[\leadsto \color{blue}{e^{\log a} \cdot e^{\log b}}\]

  4. Simplified4.7

    \[\leadsto \color{blue}{a} \cdot e^{\log b}\]

  5. Simplified0

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

  6. Final simplification0

    \[\leadsto a \cdot b\]

Reproduce

herbie shell --seed 2020056 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"
  :precision binary64

  :herbie-target
  (* a b)

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