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;
}

# Try it out

Results

 In Out
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

$\leadsto \color{blue}{e^{\log \left(\tan^{-1} \left(e^{\frac{1}{\sin x}}\right)\right)}}$
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)))))