Average Error: 15.0 → 0.4
Time: 6.6s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}
double f(double r, double a, double b) {
        double r17443 = r;
        double r17444 = b;
        double r17445 = sin(r17444);
        double r17446 = a;
        double r17447 = r17446 + r17444;
        double r17448 = cos(r17447);
        double r17449 = r17445 / r17448;
        double r17450 = r17443 * r17449;
        return r17450;
}
↓
double f(double r, double a, double b) {
        double r17451 = r;
        double r17452 = a;
        double r17453 = cos(r17452);
        double r17454 = b;
        double r17455 = cos(r17454);
        double r17456 = r17453 * r17455;
        double r17457 = sin(r17452);
        double r17458 = sin(r17454);
        double r17459 = r17457 * r17458;
        double r17460 = r17456 - r17459;
        double r17461 = r17460 / r17458;
        double r17462 = r17451 / r17461;
        return r17462;
}

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 15.0

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 associate-*r/0.3

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

  7. Applied associate-/l*0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))