Average Error: 0.1 → 0.1
Time: 20.2s
Precision: 64
$\cos^{-1} \left(\frac{\sin x}{\sin y}\right)$
$\cos^{-1} \left(\log \left(e^{\frac{\sin x}{\sin y}}\right)\right)$
\cos^{-1} \left(\frac{\sin x}{\sin y}\right)
\cos^{-1} \left(\log \left(e^{\frac{\sin x}{\sin y}}\right)\right)
double f(double x, double y) {
double r1419935 = x;
double r1419936 = sin(r1419935);
double r1419937 = y;
double r1419938 = sin(r1419937);
double r1419939 = r1419936 / r1419938;
double r1419940 = acos(r1419939);
return r1419940;
}


double f(double x, double y) {
double r1419941 = x;
double r1419942 = sin(r1419941);
double r1419943 = y;
double r1419944 = sin(r1419943);
double r1419945 = r1419942 / r1419944;
double r1419946 = exp(r1419945);
double r1419947 = log(r1419946);
double r1419948 = acos(r1419947);
return r1419948;
}



Try it out

Results

 In Out
Enter valid numbers for all inputs

Derivation

1. Initial program 0.1

$\cos^{-1} \left(\frac{\sin x}{\sin y}\right)$
2. Using strategy rm

$\leadsto \cos^{-1} \color{blue}{\left(\log \left(e^{\frac{\sin x}{\sin y}}\right)\right)}$
4. Final simplification0.1

$\leadsto \cos^{-1} \left(\log \left(e^{\frac{\sin x}{\sin y}}\right)\right)$

Reproduce

herbie shell --seed 1
(FPCore (x y)
:name "acos(sin(x)/sin(y))"
:precision binary64
(acos (/ (sin x) (sin y))))