Average Error: 15.3 → 0.4
Time: 6.5s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos b \cdot \cos a - \log \left(e^{\sin a \cdot \sin b}\right)}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos b \cdot \cos a - \log \left(e^{\sin a \cdot \sin b}\right)}
double f(double r, double a, double b) {
        double r16833 = r;
        double r16834 = b;
        double r16835 = sin(r16834);
        double r16836 = r16833 * r16835;
        double r16837 = a;
        double r16838 = r16837 + r16834;
        double r16839 = cos(r16838);
        double r16840 = r16836 / r16839;
        return r16840;
}
↓
double f(double r, double a, double b) {
        double r16841 = r;
        double r16842 = b;
        double r16843 = sin(r16842);
        double r16844 = cos(r16842);
        double r16845 = a;
        double r16846 = cos(r16845);
        double r16847 = r16844 * r16846;
        double r16848 = sin(r16845);
        double r16849 = r16848 * r16843;
        double r16850 = exp(r16849);
        double r16851 = log(r16850);
        double r16852 = r16847 - r16851;
        double r16853 = r16843 / r16852;
        double r16854 = r16841 * r16853;
        return r16854;
}

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 15.3

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

  3. Applied cos-sum0.3

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

  5. Applied *-un-lft-identity0.3

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

  6. Applied times-frac0.3

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

  7. Simplified0.3

    \[\leadsto \color{blue}{r} \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]

  8. Simplified0.3

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

  10. Applied add-log-exp0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2020034 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))