Average Error: 15.6 → 15.6
Time: 26.0s
Precision: 64
\[\mathsf{log1p}\left({x}^{2}\right)\]
\[\mathsf{log1p}\left(x \cdot x\right)\]
\mathsf{log1p}\left({x}^{2}\right)
\mathsf{log1p}\left(x \cdot x\right)
double f(double x) {
        double r13428644 = x;
        double r13428645 = 2.0;
        double r13428646 = pow(r13428644, r13428645);
        double r13428647 = log1p(r13428646);
        return r13428647;
}

double f(double x) {
        double r13428648 = x;
        double r13428649 = r13428648 * r13428648;
        double r13428650 = log1p(r13428649);
        return r13428650;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.6

    \[\mathsf{log1p}\left({x}^{2}\right)\]
  2. Simplified15.6

    \[\leadsto \color{blue}{\mathsf{log1p}\left(x \cdot x\right)}\]
  3. Final simplification15.6

    \[\leadsto \mathsf{log1p}\left(x \cdot x\right)\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "log1p(x^2)"
  (log1p (pow x 2)))