Average Error: 14.8 → 0.4
Time: 10.8s
Precision: binary64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos a}{\tan b} - \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos a}{\tan b} - \sin a}
(FPCore (r a b) :precision binary64 (* r (/ (sin b) (cos (+ a b)))))
↓
(FPCore (r a b) :precision binary64 (/ r (- (/ (cos a) (tan b)) (sin a))))
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) / tan(b)) - sin(a));
}

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 14.8

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

  3. Applied cos-sum_binary640.3

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

  4. Simplified0.3

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

  5. Simplified0.3

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

  6. Taylor expanded around 0 0.3

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

  7. Simplified0.4

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

  9. Applied quot-tan_binary640.4

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

  10. Final simplification0.4

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

Alternatives

Reproduce

herbie shell --seed 2021118 
(FPCore (r a b)
  :name "rsin B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))