Average Error: 15.1 → 0.4
Time: 6.5s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos b \cdot \cos a - \log \left(e^{\sin a \cdot \sin b}\right)}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \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 r16885 = r;
        double r16886 = b;
        double r16887 = sin(r16886);
        double r16888 = a;
        double r16889 = r16888 + r16886;
        double r16890 = cos(r16889);
        double r16891 = r16887 / r16890;
        double r16892 = r16885 * r16891;
        return r16892;
}
↓
double f(double r, double a, double b) {
        double r16893 = r;
        double r16894 = b;
        double r16895 = sin(r16894);
        double r16896 = r16893 * r16895;
        double r16897 = cos(r16894);
        double r16898 = a;
        double r16899 = cos(r16898);
        double r16900 = r16897 * r16899;
        double r16901 = sin(r16898);
        double r16902 = r16901 * r16895;
        double r16903 = exp(r16902);
        double r16904 = log(r16903);
        double r16905 = r16900 - r16904;
        double r16906 = r16896 / r16905;
        return r16906;
}

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 15.1

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Taylor expanded around inf 0.3

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

  8. Applied add-log-exp0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2020060 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))