Average Error: 14.9 → 0.3
Time: 22.3s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin a \cdot \sin b}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos b \cdot \cos a - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r462344 = r;
        double r462345 = b;
        double r462346 = sin(r462345);
        double r462347 = r462344 * r462346;
        double r462348 = a;
        double r462349 = r462348 + r462345;
        double r462350 = cos(r462349);
        double r462351 = r462347 / r462350;
        return r462351;
}
↓
double f(double r, double a, double b) {
        double r462352 = r;
        double r462353 = b;
        double r462354 = sin(r462353);
        double r462355 = cos(r462353);
        double r462356 = a;
        double r462357 = cos(r462356);
        double r462358 = r462355 * r462357;
        double r462359 = sin(r462356);
        double r462360 = r462359 * r462354;
        double r462361 = r462358 - r462360;
        double r462362 = r462354 / r462361;
        double r462363 = r462352 * r462362;
        return r462363;
}

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 14.9

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 div-inv0.4

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

  7. Applied associate-*l*0.4

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019152 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))