Average Error: 15.3 → 0.3
Time: 13.3s
Precision: binary64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\sin b \cdot \frac{r}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\sin b \cdot \frac{r}{\cos a \cdot \cos b - \sin b \cdot \sin a}
(FPCore (r a b) :precision binary64 (* r (/ (sin b) (cos (+ a b)))))
↓
(FPCore (r a b)
 :precision binary64
 (* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin 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 sin(b) * (r / ((cos(a) * cos(b)) - (sin(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 15.3

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

  3. Applied cos-sum_binary64_5530.3

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

  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. Using strategy rm

  7. Applied associate-*r/_binary64_3610.3

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

  8. Simplified0.3

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

  10. Applied *-un-lft-identity_binary64_4190.3

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

  11. Applied times-frac_binary64_4250.3

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

  12. Simplified0.3

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

  13. Simplified0.3

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

  14. Final simplification0.3

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

Reproduce

herbie shell --seed 2021046 
(FPCore (r a b)
  :name "rsin B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))