Average Error: 14.9 → 0.4
Time: 6.3s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \left(\sin b \cdot \frac{1}{\cos b \cdot \cos a - \sin a \cdot \sin b}\right)\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \left(\sin b \cdot \frac{1}{\cos b \cdot \cos a - \sin a \cdot \sin b}\right)
double f(double r, double a, double b) {
        double r16837 = r;
        double r16838 = b;
        double r16839 = sin(r16838);
        double r16840 = a;
        double r16841 = r16840 + r16838;
        double r16842 = cos(r16841);
        double r16843 = r16839 / r16842;
        double r16844 = r16837 * r16843;
        return r16844;
}
↓
double f(double r, double a, double b) {
        double r16845 = r;
        double r16846 = b;
        double r16847 = sin(r16846);
        double r16848 = 1.0;
        double r16849 = cos(r16846);
        double r16850 = a;
        double r16851 = cos(r16850);
        double r16852 = r16849 * r16851;
        double r16853 = sin(r16850);
        double r16854 = r16853 * r16847;
        double r16855 = r16852 - r16854;
        double r16856 = r16848 / r16855;
        double r16857 = r16847 * r16856;
        double r16858 = r16845 * r16857;
        return r16858;
}

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. Using strategy rm

  7. Applied div-inv0.4

    \[\leadsto r \cdot \color{blue}{\left(\sin b \cdot \frac{1}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}\right)}\]

  8. Simplified0.4

    \[\leadsto r \cdot \left(\sin b \cdot \color{blue}{\frac{1}{\cos b \cdot \cos a - \sin a \cdot \sin b}}\right)\]

  9. Final simplification0.4

    \[\leadsto r \cdot \left(\sin b \cdot \frac{1}{\cos b \cdot \cos a - \sin a \cdot \sin b}\right)\]

Reproduce

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