Average Error: 5.6 → 0
Time: 5.1s
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 r116217 = a;
        double r116218 = log(r116217);
        double r116219 = b;
        double r116220 = log(r116219);
        double r116221 = r116218 + r116220;
        double r116222 = exp(r116221);
        return r116222;
}
↓
double f(double a, double b) {
        double r116223 = a;
        double r116224 = b;
        double r116225 = r116223 * r116224;
        return r116225;
}

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 2019298 
(FPCore (a b)
  :name "Exp of sum of logs"
  :precision binary64

  :herbie-target
  (* a b)

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