Average Error: 15.3 → 0.4
Time: 6.6s
Precision: binary64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \log \left({\left(e^{\sin a}\right)}^{\left(\sin b\right)}\right)}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos a \cdot \cos b - \log \left({\left(e^{\sin a}\right)}^{\left(\sin b\right)}\right)}
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) (r * (((double) sin(b)) / ((double) (((double) (((double) cos(a)) * ((double) cos(b)))) - ((double) log(((double) pow(((double) exp(((double) sin(a)))), ((double) sin(b)))))))))));
}

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-sum0.3

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

  5. Applied add-log-exp0.4

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

  6. Simplified0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2020182 
(FPCore (r a b)
  :name "rsin B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))