Average Error: 15.4 → 0.4
Time: 19.3s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{1}{\frac{\cos b}{\frac{\sin b}{\cos a}} - \sin a} \cdot r\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{1}{\frac{\cos b}{\frac{\sin b}{\cos a}} - \sin a} \cdot r
double f(double r, double a, double b) {
        double r26414 = r;
        double r26415 = b;
        double r26416 = sin(r26415);
        double r26417 = r26414 * r26416;
        double r26418 = a;
        double r26419 = r26418 + r26415;
        double r26420 = cos(r26419);
        double r26421 = r26417 / r26420;
        return r26421;
}
↓
double f(double r, double a, double b) {
        double r26422 = 1.0;
        double r26423 = b;
        double r26424 = cos(r26423);
        double r26425 = sin(r26423);
        double r26426 = a;
        double r26427 = cos(r26426);
        double r26428 = r26425 / r26427;
        double r26429 = r26424 / r26428;
        double r26430 = sin(r26426);
        double r26431 = r26429 - r26430;
        double r26432 = r26422 / r26431;
        double r26433 = r;
        double r26434 = r26432 * r26433;
        return r26434;
}

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 15.4

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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. Simplified0.3

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

  6. Applied associate-/l*0.4

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

  7. Simplified0.4

    \[\leadsto \frac{r}{\color{blue}{\frac{\cos b}{\frac{\sin b}{\cos a}} - \frac{\sin a}{1}}}\]
  8. Using strategy rm

  9. Applied div-inv0.4

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

  10. Simplified0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2019196 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))