Average Error: 15.0 → 0.4
Time: 23.7s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos b \cdot \cos a}{\sin b} - \sin a}\]
r \cdot \frac{\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 r24034 = r;
        double r24035 = b;
        double r24036 = sin(r24035);
        double r24037 = a;
        double r24038 = r24037 + r24035;
        double r24039 = cos(r24038);
        double r24040 = r24036 / r24039;
        double r24041 = r24034 * r24040;
        return r24041;
}
↓
double f(double r, double a, double b) {
        double r24042 = r;
        double r24043 = b;
        double r24044 = cos(r24043);
        double r24045 = a;
        double r24046 = cos(r24045);
        double r24047 = r24044 * r24046;
        double r24048 = sin(r24043);
        double r24049 = r24047 / r24048;
        double r24050 = sin(r24045);
        double r24051 = r24049 - r24050;
        double r24052 = r24042 / r24051;
        return r24052;
}

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 15.0

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

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

  6. Applied pow10.3

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

  7. Applied pow10.3

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

  8. Applied pow-prod-down0.3

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

  9. Simplified0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019199 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))