Average Error: 15.3 → 0.4
Time: 6.5s
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 r18198 = r;
        double r18199 = b;
        double r18200 = sin(r18199);
        double r18201 = a;
        double r18202 = r18201 + r18199;
        double r18203 = cos(r18202);
        double r18204 = r18200 / r18203;
        double r18205 = r18198 * r18204;
        return r18205;
}
↓
double f(double r, double a, double b) {
        double r18206 = r;
        double r18207 = a;
        double r18208 = cos(r18207);
        double r18209 = b;
        double r18210 = cos(r18209);
        double r18211 = r18208 * r18210;
        double r18212 = sin(r18207);
        double r18213 = sin(r18209);
        double r18214 = r18212 * r18213;
        double r18215 = r18211 - r18214;
        double r18216 = r18215 / r18213;
        double r18217 = r18206 / r18216;
        return r18217;
}

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 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 2020024 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))