Average Error: 5.7 → 0
Time: 4.0s
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 r113478 = a;
        double r113479 = log(r113478);
        double r113480 = b;
        double r113481 = log(r113480);
        double r113482 = r113479 + r113481;
        double r113483 = exp(r113482);
        return r113483;
}
↓
double f(double a, double b) {
        double r113484 = b;
        double r113485 = a;
        double r113486 = r113484 * r113485;
        return r113486;
}

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 2019304 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"
  :precision binary64

  :herbie-target
  (* a b)

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