Average Error: 5.7 → 0
Time: 8.4s
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 r116942 = a;
        double r116943 = log(r116942);
        double r116944 = b;
        double r116945 = log(r116944);
        double r116946 = r116943 + r116945;
        double r116947 = exp(r116946);
        return r116947;
}
↓
double f(double a, double b) {
        double r116948 = b;
        double r116949 = a;
        double r116950 = r116948 * r116949;
        return r116950;
}

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. Taylor expanded around -inf 64.0

    \[\leadsto \color{blue}{e^{2 \cdot \log -1 - \left(\log \left(\frac{-1}{b}\right) + \log \left(\frac{-1}{a}\right)\right)}}\]

  3. Simplified0

    \[\leadsto \color{blue}{1 \cdot \left(b \cdot a\right)}\]

  4. Final simplification0

    \[\leadsto b \cdot a\]

Reproduce

herbie shell --seed 2019291 
(FPCore (a b)
  :name "Exp of sum of logs"
  :precision binary64

  :herbie-target
  (* a b)

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