Average Error: 5.8 → 0
Time: 3.2s
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 r187949 = a;
        double r187950 = log(r187949);
        double r187951 = b;
        double r187952 = log(r187951);
        double r187953 = r187950 + r187952;
        double r187954 = exp(r187953);
        return r187954;
}
↓
double f(double a, double b) {
        double r187955 = a;
        double r187956 = b;
        double r187957 = r187955 * r187956;
        return r187957;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.8
Target0
Herbie0
\[a \cdot b\]

Derivation

  1. Initial program 5.8

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

  3. Applied exp-sum5.5

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

  4. Simplified4.8

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

  5. Simplified0

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

  6. Final simplification0

    \[\leadsto a \cdot b\]

Reproduce

herbie shell --seed 2019322 
(FPCore (a b)
  :name "Exp of sum of logs"
  :precision binary64

  :herbie-target
  (* a b)

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