Average Error: 15.0 → 0.4
Time: 8.5s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot \left(r \cdot \sin b\right)\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot \left(r \cdot \sin b\right)
double f(double r, double a, double b) {
        double r18298 = r;
        double r18299 = b;
        double r18300 = sin(r18299);
        double r18301 = a;
        double r18302 = r18301 + r18299;
        double r18303 = cos(r18302);
        double r18304 = r18300 / r18303;
        double r18305 = r18298 * r18304;
        return r18305;
}
↓
double f(double r, double a, double b) {
        double r18306 = 1.0;
        double r18307 = a;
        double r18308 = cos(r18307);
        double r18309 = b;
        double r18310 = cos(r18309);
        double r18311 = r18308 * r18310;
        double r18312 = sin(r18307);
        double r18313 = sin(r18309);
        double r18314 = r18312 * r18313;
        double r18315 = r18311 - r18314;
        double r18316 = r18306 / r18315;
        double r18317 = r;
        double r18318 = r18317 * r18313;
        double r18319 = r18316 * r18318;
        return r18319;
}

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. Using strategy rm

  9. Applied div-inv0.4

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

  10. Applied *-un-lft-identity0.4

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

  11. Applied times-frac0.5

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

  12. Simplified0.4

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

  13. Final simplification0.4

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

Reproduce

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