Average Error: 14.8 → 0.3
Time: 23.0s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot r\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot r
double f(double r, double a, double b) {
        double r1156398 = r;
        double r1156399 = b;
        double r1156400 = sin(r1156399);
        double r1156401 = r1156398 * r1156400;
        double r1156402 = a;
        double r1156403 = r1156402 + r1156399;
        double r1156404 = cos(r1156403);
        double r1156405 = r1156401 / r1156404;
        return r1156405;
}
↓
double f(double r, double a, double b) {
        double r1156406 = b;
        double r1156407 = sin(r1156406);
        double r1156408 = a;
        double r1156409 = cos(r1156408);
        double r1156410 = cos(r1156406);
        double r1156411 = r1156409 * r1156410;
        double r1156412 = sin(r1156408);
        double r1156413 = r1156412 * r1156407;
        double r1156414 = r1156411 - r1156413;
        double r1156415 = r1156407 / r1156414;
        double r1156416 = r;
        double r1156417 = r1156415 * r1156416;
        return r1156417;
}

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

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

  3. Applied cos-sum0.3

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

  5. Applied *-un-lft-identity0.3

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

  6. Applied times-frac0.3

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

  7. Simplified0.3

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

  9. Applied *-commutative0.3

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

  10. Final simplification0.3

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

Reproduce

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