Average Error: 14.9 → 0.3
Time: 9.1s
Precision: binary64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)} \]
↓
\[\frac{\sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot r \]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot r

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

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

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

  2. Applied cos-sum_binary640.3

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

  3. Applied div-inv_binary640.4

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

  4. Applied associate-*l*_binary640.4

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

  5. Taylor expanded in r around 0 0.3

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

  6. Simplified0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2021329 
(FPCore (r a b)
  :name "rsin A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))