Average Error: 0.2 → 0.2
Time: 12.1s
Precision: 64
\[\tan^{-1} \left(e^{\frac{1}{\sin x}}\right)\]
\[\tan^{-1} \left(e^{\frac{1}{\sin x}}\right)\]
\tan^{-1} \left(e^{\frac{1}{\sin x}}\right)
\tan^{-1} \left(e^{\frac{1}{\sin x}}\right)
double f(double x) {
        double r21153904 = 1.0;
        double r21153905 = x;
        double r21153906 = sin(r21153905);
        double r21153907 = r21153904 / r21153906;
        double r21153908 = exp(r21153907);
        double r21153909 = atan(r21153908);
        return r21153909;
}

double f(double x) {
        double r21153910 = 1.0;
        double r21153911 = x;
        double r21153912 = sin(r21153911);
        double r21153913 = r21153910 / r21153912;
        double r21153914 = exp(r21153913);
        double r21153915 = atan(r21153914);
        return r21153915;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\tan^{-1} \left(e^{\frac{1}{\sin x}}\right)\]
  2. Using strategy rm
  3. Applied add-exp-log0.3

    \[\leadsto \color{blue}{e^{\log \left(\tan^{-1} \left(e^{\frac{1}{\sin x}}\right)\right)}}\]
  4. Using strategy rm
  5. Applied rem-exp-log0.2

    \[\leadsto \color{blue}{\tan^{-1} \left(e^{\frac{1}{\sin x}}\right)}\]
  6. Final simplification0.2

    \[\leadsto \tan^{-1} \left(e^{\frac{1}{\sin x}}\right)\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "atan(exp(1/sin(x)))"
  (atan (exp (/ 1.0 (sin x)))))