Average Error: 14.8 → 0.4
Time: 23.3s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos b \cdot \cos a}{\sin b} - \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos b \cdot \cos a}{\sin b} - \sin a}
double f(double r, double a, double b) {
        double r1140401 = r;
        double r1140402 = b;
        double r1140403 = sin(r1140402);
        double r1140404 = a;
        double r1140405 = r1140404 + r1140402;
        double r1140406 = cos(r1140405);
        double r1140407 = r1140403 / r1140406;
        double r1140408 = r1140401 * r1140407;
        return r1140408;
}
↓
double f(double r, double a, double b) {
        double r1140409 = r;
        double r1140410 = b;
        double r1140411 = cos(r1140410);
        double r1140412 = a;
        double r1140413 = cos(r1140412);
        double r1140414 = r1140411 * r1140413;
        double r1140415 = sin(r1140410);
        double r1140416 = r1140414 / r1140415;
        double r1140417 = sin(r1140412);
        double r1140418 = r1140416 - r1140417;
        double r1140419 = r1140409 / r1140418;
        return r1140419;
}

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 14.8

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

  9. Applied div-sub0.4

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

  10. Simplified0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))