Average Error: 14.9 → 0.4
Time: 7.1s
Precision: binary64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\left(\sin b \cdot r\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\left(\sin b \cdot r\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin b \cdot \sin a}
double code(double r, double a, double b) {
	return ((double) (r * (((double) sin(b)) / ((double) cos(((double) (a + b)))))));
}
↓
double code(double r, double a, double b) {
	return ((double) (((double) (((double) sin(b)) * r)) * (1.0 / ((double) (((double) (((double) cos(a)) * ((double) cos(b)))) - ((double) (((double) sin(b)) * ((double) 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 Error: 14.9 bits

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

  3. Applied cos-sumError: 0.3 bits

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

  5. Applied div-invError: 0.4 bits

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

  6. Applied associate-*r*Error: 0.4 bits

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

  7. SimplifiedError: 0.4 bits

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

  8. Final simplificationError: 0.4 bits

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

Reproduce

herbie shell --seed 2020200 
(FPCore (r a b)
  :name "rsin B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))