Average Error: 15.2 → 0.3
Time: 10.2s
Precision: binary64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
↓
\[r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin b \cdot \sin a} \]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin b \cdot \sin a}

(FPCore (r a b) :precision binary64 (/ (* r (sin b)) (cos (+ a b))))
↓
(FPCore (r a b)
 :precision binary64
 (* r (/ (sin b) (- (* (cos b) (cos a)) (* (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 r * (sin(b) / ((cos(b) * cos(a)) - (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 15.2

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

  3. Applied cos-sum_binary640.3

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

  4. Simplified0.3

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

  5. Simplified0.3

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

  7. Applied flip--_binary640.4

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

  8. Simplified0.4

    \[\leadsto \frac{r \cdot \sin b}{\frac{\color{blue}{{\cos a}^{2} \cdot {\cos b}^{2} - {\sin a}^{2} \cdot {\sin b}^{2}}}{\cos b \cdot \cos a + \sin b \cdot \sin a}} \]

  9. Simplified0.4

    \[\leadsto \frac{r \cdot \sin b}{\frac{{\cos a}^{2} \cdot {\cos b}^{2} - {\sin a}^{2} \cdot {\sin b}^{2}}{\color{blue}{\cos a \cdot \cos b + \sin b \cdot \sin a}}} \]
  10. Using strategy rm

  11. Applied flip-+_binary640.4

    \[\leadsto \frac{r \cdot \sin b}{\frac{{\cos a}^{2} \cdot {\cos b}^{2} - {\sin a}^{2} \cdot {\sin b}^{2}}{\color{blue}{\frac{\left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right) - \left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)}{\cos a \cdot \cos b - \sin b \cdot \sin a}}}} \]

  12. Applied associate-/r/_binary640.4

    \[\leadsto \frac{r \cdot \sin b}{\color{blue}{\frac{{\cos a}^{2} \cdot {\cos b}^{2} - {\sin a}^{2} \cdot {\sin b}^{2}}{\left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right) - \left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)} \cdot \left(\cos a \cdot \cos b - \sin b \cdot \sin a\right)}} \]

  13. Applied times-frac_binary640.4

    \[\leadsto \color{blue}{\frac{r}{\frac{{\cos a}^{2} \cdot {\cos b}^{2} - {\sin a}^{2} \cdot {\sin b}^{2}}{\left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right) - \left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)}} \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}} \]

  14. Simplified0.3

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

  15. Simplified0.3

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

  16. Final simplification0.3

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

Reproduce

herbie shell --seed 2021196 
(FPCore (r a b)
  :name "rsin A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))