Average Error: 15.4 → 0.3
Time: 8.0s
Precision: binary64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot \sin b\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot \sin b
double code(double r, double a, double b) {
	return ((double) (r * ((double) (((double) sin(b)) / ((double) cos(((double) (a + b))))))));
}
↓
double code(double r, double a, double b) {
	return ((double) (((double) (r / ((double) (((double) (((double) cos(a)) * ((double) cos(b)))) - ((double) (((double) sin(a)) * ((double) sin(b)))))))) * ((double) sin(b))));
}

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 15.4

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 clear-num0.4

    \[\leadsto r \cdot \color{blue}{\frac{1}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}}\]
  6. Using strategy rm

  7. Applied associate-/r/0.4

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

  8. Applied associate-*r*0.4

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

  9. Simplified0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2020147 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))