Average Error: 0.1 → 0.0
Time: 12.4s
Precision: 64
\[e^{x + 5} - \sqrt{x}\]
\[\left(\sqrt{e^{5}} \cdot e^{x}\right) \cdot \sqrt{e^{5}} - \sqrt{x}\]
e^{x + 5} - \sqrt{x}
\left(\sqrt{e^{5}} \cdot e^{x}\right) \cdot \sqrt{e^{5}} - \sqrt{x}
double f(double x) {
        double r1351618 = x;
        double r1351619 = 5.0;
        double r1351620 = r1351618 + r1351619;
        double r1351621 = exp(r1351620);
        double r1351622 = sqrt(r1351618);
        double r1351623 = r1351621 - r1351622;
        return r1351623;
}

double f(double x) {
        double r1351624 = 5.0;
        double r1351625 = exp(r1351624);
        double r1351626 = sqrt(r1351625);
        double r1351627 = x;
        double r1351628 = exp(r1351627);
        double r1351629 = r1351626 * r1351628;
        double r1351630 = r1351629 * r1351626;
        double r1351631 = sqrt(r1351627);
        double r1351632 = r1351630 - r1351631;
        return r1351632;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[e^{x + 5} - \sqrt{x}\]
  2. Using strategy rm
  3. Applied exp-sum0.0

    \[\leadsto \color{blue}{e^{x} \cdot e^{5}} - \sqrt{x}\]
  4. Using strategy rm
  5. Applied add-sqr-sqrt0.0

    \[\leadsto e^{x} \cdot \color{blue}{\left(\sqrt{e^{5}} \cdot \sqrt{e^{5}}\right)} - \sqrt{x}\]
  6. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(e^{x} \cdot \sqrt{e^{5}}\right) \cdot \sqrt{e^{5}}} - \sqrt{x}\]
  7. Simplified0.0

    \[\leadsto \color{blue}{\left(\sqrt{e^{5}} \cdot e^{x}\right)} \cdot \sqrt{e^{5}} - \sqrt{x}\]
  8. Final simplification0.0

    \[\leadsto \left(\sqrt{e^{5}} \cdot e^{x}\right) \cdot \sqrt{e^{5}} - \sqrt{x}\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "exp(x + 5) - sqrt(x)"
  :precision binary64
  (- (exp (+ x 5)) (sqrt x)))