Average Error: 15.5 → 0.4
Time: 48.2s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos b \cdot \cos a}{\sin b} - \sin a}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos b \cdot \cos a}{\sin b} - \sin a}
double f(double r, double a, double b) {
        double r933400 = r;
        double r933401 = b;
        double r933402 = sin(r933401);
        double r933403 = r933400 * r933402;
        double r933404 = a;
        double r933405 = r933404 + r933401;
        double r933406 = cos(r933405);
        double r933407 = r933403 / r933406;
        return r933407;
}
↓
double f(double r, double a, double b) {
        double r933408 = r;
        double r933409 = b;
        double r933410 = cos(r933409);
        double r933411 = a;
        double r933412 = cos(r933411);
        double r933413 = r933410 * r933412;
        double r933414 = sin(r933409);
        double r933415 = r933413 / r933414;
        double r933416 = sin(r933411);
        double r933417 = r933415 - r933416;
        double r933418 = r933408 / r933417;
        return r933418;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

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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

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2019165 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))