Average Error: 0.1 → 0.1
Time: 15.9s
Precision: 64
\[\sqrt{\sin x + \cos x}\]
\[\sqrt{\log \left(e^{\sin x + \cos x}\right)}\]
\sqrt{\sin x + \cos x}
\sqrt{\log \left(e^{\sin x + \cos x}\right)}
double f(double x) {
        double r1086976 = x;
        double r1086977 = sin(r1086976);
        double r1086978 = cos(r1086976);
        double r1086979 = r1086977 + r1086978;
        double r1086980 = sqrt(r1086979);
        return r1086980;
}

double f(double x) {
        double r1086981 = x;
        double r1086982 = sin(r1086981);
        double r1086983 = cos(r1086981);
        double r1086984 = r1086982 + r1086983;
        double r1086985 = exp(r1086984);
        double r1086986 = log(r1086985);
        double r1086987 = sqrt(r1086986);
        return r1086987;
}

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

    \[\sqrt{\sin x + \cos x}\]
  2. Using strategy rm
  3. Applied add-log-exp0.2

    \[\leadsto \sqrt{\sin x + \color{blue}{\log \left(e^{\cos x}\right)}}\]
  4. Applied add-log-exp0.2

    \[\leadsto \sqrt{\color{blue}{\log \left(e^{\sin x}\right)} + \log \left(e^{\cos x}\right)}\]
  5. Applied sum-log0.2

    \[\leadsto \sqrt{\color{blue}{\log \left(e^{\sin x} \cdot e^{\cos x}\right)}}\]
  6. Simplified0.1

    \[\leadsto \sqrt{\log \color{blue}{\left(e^{\sin x + \cos x}\right)}}\]
  7. Final simplification0.1

    \[\leadsto \sqrt{\log \left(e^{\sin x + \cos x}\right)}\]

Reproduce

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