Average Error: 14.6 → 0.3
Time: 27.2s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}
double f(double r, double a, double b) {
        double r769484 = r;
        double r769485 = b;
        double r769486 = sin(r769485);
        double r769487 = a;
        double r769488 = r769487 + r769485;
        double r769489 = cos(r769488);
        double r769490 = r769486 / r769489;
        double r769491 = r769484 * r769490;
        return r769491;
}
↓
double f(double r, double a, double b) {
        double r769492 = r;
        double r769493 = b;
        double r769494 = sin(r769493);
        double r769495 = r769492 * r769494;
        double r769496 = a;
        double r769497 = cos(r769496);
        double r769498 = cos(r769493);
        double r769499 = r769497 * r769498;
        double r769500 = sin(r769496);
        double r769501 = r769494 * r769500;
        double r769502 = r769499 - r769501;
        double r769503 = r769495 / r769502;
        return r769503;
}

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 14.6

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

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

  6. Applied associate-*r*0.4

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

  8. Applied associate-*r/0.3

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

  9. Simplified0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019134 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))