Average Error: 15.5 → 0.4
Time: 25.2s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos a}{\frac{\sin b}{\cos b}} - \sin a}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos a}{\frac{\sin b}{\cos b}} - \sin a}
double f(double r, double a, double b) {
        double r1089398 = r;
        double r1089399 = b;
        double r1089400 = sin(r1089399);
        double r1089401 = r1089398 * r1089400;
        double r1089402 = a;
        double r1089403 = r1089402 + r1089399;
        double r1089404 = cos(r1089403);
        double r1089405 = r1089401 / r1089404;
        return r1089405;
}
↓
double f(double r, double a, double b) {
        double r1089406 = r;
        double r1089407 = a;
        double r1089408 = cos(r1089407);
        double r1089409 = b;
        double r1089410 = sin(r1089409);
        double r1089411 = cos(r1089409);
        double r1089412 = r1089410 / r1089411;
        double r1089413 = r1089408 / r1089412;
        double r1089414 = sin(r1089407);
        double r1089415 = r1089413 - r1089414;
        double r1089416 = r1089406 / r1089415;
        return r1089416;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.5

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 *-un-lft-identity0.3

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

  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 *-un-lft-identity0.3

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

  10. Applied associate-*l*0.3

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

  11. Simplified0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))