Average Error: 15.3 → 0.4
Time: 55.3s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\left(\frac{1}{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot \sin b\right) \cdot r\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\left(\frac{1}{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot \sin b\right) \cdot r
double f(double r, double a, double b) {
        double r2413357 = r;
        double r2413358 = b;
        double r2413359 = sin(r2413358);
        double r2413360 = r2413357 * r2413359;
        double r2413361 = a;
        double r2413362 = r2413361 + r2413358;
        double r2413363 = cos(r2413362);
        double r2413364 = r2413360 / r2413363;
        return r2413364;
}
↓
double f(double r, double a, double b) {
        double r2413365 = 1.0;
        double r2413366 = a;
        double r2413367 = cos(r2413366);
        double r2413368 = b;
        double r2413369 = cos(r2413368);
        double r2413370 = r2413367 * r2413369;
        double r2413371 = sin(r2413368);
        double r2413372 = sin(r2413366);
        double r2413373 = r2413371 * r2413372;
        double r2413374 = r2413370 - r2413373;
        double r2413375 = r2413365 / r2413374;
        double r2413376 = r2413375 * r2413371;
        double r2413377 = r;
        double r2413378 = r2413376 * r2413377;
        return r2413378;
}

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

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

  3. Applied cos-sum0.4

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

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

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

  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 div-inv0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019128 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))