Average Error: 5.7 → 0
Time: 2.2s
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 r145119 = a;
        double r145120 = log(r145119);
        double r145121 = b;
        double r145122 = log(r145121);
        double r145123 = r145120 + r145122;
        double r145124 = exp(r145123);
        return r145124;
}
↓
double f(double a, double b) {
        double r145125 = a;
        double r145126 = b;
        double r145127 = r145125 * r145126;
        return r145127;
}

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. 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 2020021 +o rules:numerics
(FPCore (a b)
  :name "Exp of sum of logs"
  :precision binary64

  :herbie-target
  (* a b)

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