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;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

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
  3. Applied add-log-exp0.1

    \[\leadsto \cos^{-1} \color{blue}{\left(\log \left(e^{\frac{\sin x}{\sin y}}\right)\right)}\]
  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))))