Average Error: 0.1 → 0.1
Time: 10.4s
Precision: 64
\[\sqrt{\sqrt{x} + \log x}\]
\[\sqrt{\left(\sqrt{x} + \log \left(\sqrt{x}\right)\right) + \log \left(\sqrt{x}\right)}\]
\sqrt{\sqrt{x} + \log x}
\sqrt{\left(\sqrt{x} + \log \left(\sqrt{x}\right)\right) + \log \left(\sqrt{x}\right)}
double f(double x) {
        double r1453562 = x;
        double r1453563 = sqrt(r1453562);
        double r1453564 = log(r1453562);
        double r1453565 = r1453563 + r1453564;
        double r1453566 = sqrt(r1453565);
        return r1453566;
}

double f(double x) {
        double r1453567 = x;
        double r1453568 = sqrt(r1453567);
        double r1453569 = log(r1453568);
        double r1453570 = r1453568 + r1453569;
        double r1453571 = r1453570 + r1453569;
        double r1453572 = sqrt(r1453571);
        return r1453572;
}

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

    \[\sqrt{\sqrt{x} + \log x}\]
  2. Using strategy rm
  3. Applied add-sqr-sqrt0.1

    \[\leadsto \sqrt{\sqrt{x} + \log \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)}}\]
  4. Applied log-prod0.1

    \[\leadsto \sqrt{\sqrt{x} + \color{blue}{\left(\log \left(\sqrt{x}\right) + \log \left(\sqrt{x}\right)\right)}}\]
  5. Applied associate-+r+0.1

    \[\leadsto \sqrt{\color{blue}{\left(\sqrt{x} + \log \left(\sqrt{x}\right)\right) + \log \left(\sqrt{x}\right)}}\]
  6. Final simplification0.1

    \[\leadsto \sqrt{\left(\sqrt{x} + \log \left(\sqrt{x}\right)\right) + \log \left(\sqrt{x}\right)}\]

Reproduce

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