Average Error: 14.9 → 0.4
Time: 6.6s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}
double f(double r, double a, double b) {
        double r17786 = r;
        double r17787 = b;
        double r17788 = sin(r17787);
        double r17789 = a;
        double r17790 = r17789 + r17787;
        double r17791 = cos(r17790);
        double r17792 = r17788 / r17791;
        double r17793 = r17786 * r17792;
        return r17793;
}
↓
double f(double r, double a, double b) {
        double r17794 = r;
        double r17795 = b;
        double r17796 = sin(r17795);
        double r17797 = a;
        double r17798 = cos(r17797);
        double r17799 = cos(r17795);
        double r17800 = r17798 * r17799;
        double r17801 = sin(r17797);
        double r17802 = r17801 * r17796;
        double r17803 = exp(r17802);
        double r17804 = log(r17803);
        double r17805 = r17800 - r17804;
        double r17806 = r17796 / r17805;
        double r17807 = r17794 * r17806;
        return r17807;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.9

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  2. Using strategy rm

  3. Applied cos-sum0.3

    \[\leadsto r \cdot \frac{\sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
  4. Using strategy rm

  5. Applied add-log-exp0.4

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{\log \left(e^{\sin a \cdot \sin b}\right)}}\]

  6. Final simplification0.4

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}\]

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))