Average Error: 15.2 → 0.4
Time: 8.7s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot \left(r \cdot \sin b\right)\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot \left(r \cdot \sin b\right)
double f(double r, double a, double b) {
        double r25422 = r;
        double r25423 = b;
        double r25424 = sin(r25423);
        double r25425 = r25422 * r25424;
        double r25426 = a;
        double r25427 = r25426 + r25423;
        double r25428 = cos(r25427);
        double r25429 = r25425 / r25428;
        return r25429;
}
↓
double f(double r, double a, double b) {
        double r25430 = 1.0;
        double r25431 = a;
        double r25432 = cos(r25431);
        double r25433 = b;
        double r25434 = cos(r25433);
        double r25435 = r25432 * r25434;
        double r25436 = sin(r25431);
        double r25437 = sin(r25433);
        double r25438 = r25436 * r25437;
        double r25439 = r25435 - r25438;
        double r25440 = r25430 / r25439;
        double r25441 = r;
        double r25442 = r25441 * r25437;
        double r25443 = r25440 * r25442;
        return r25443;
}

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 15.2

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 associate-/l*0.4

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

  7. Applied div-inv0.5

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

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

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

  9. Applied times-frac0.5

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

  10. Simplified0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2019318 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))