Average Error: 14.9 → 0.3
Time: 5.8s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{-\left(\cos a \cdot \cos b - \sin a \cdot \sin b\right)} \cdot \left(-\sin b\right)\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{-\left(\cos a \cdot \cos b - \sin a \cdot \sin b\right)} \cdot \left(-\sin b\right)
double code(double r, double a, double b) {
	return (r * (sin(b) / cos((a + b))));
}
↓
double code(double r, double a, double b) {
	return ((r / -((cos(a) * cos(b)) - (sin(a) * sin(b)))) * -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 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 clear-num0.4

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

  6. Applied un-div-inv0.4

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

  8. Applied frac-2neg0.4

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

  9. Applied associate-/r/0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2020078 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))