Average Error: 15.5 → 0.3
Time: 20.3s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot \sin b\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot \sin b
double f(double r, double a, double b) {
        double r913261 = r;
        double r913262 = b;
        double r913263 = sin(r913262);
        double r913264 = a;
        double r913265 = r913264 + r913262;
        double r913266 = cos(r913265);
        double r913267 = r913263 / r913266;
        double r913268 = r913261 * r913267;
        return r913268;
}
↓
double f(double r, double a, double b) {
        double r913269 = r;
        double r913270 = a;
        double r913271 = cos(r913270);
        double r913272 = b;
        double r913273 = cos(r913272);
        double r913274 = r913271 * r913273;
        double r913275 = sin(r913272);
        double r913276 = sin(r913270);
        double r913277 = r913275 * r913276;
        double r913278 = r913274 - r913277;
        double r913279 = r913269 / r913278;
        double r913280 = r913279 * r913275;
        return r913280;
}

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 15.5

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Taylor expanded around inf 0.3

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

  6. Applied *-un-lft-identity0.3

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

  7. Applied times-frac0.3

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

  8. Simplified0.3

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

  9. Final simplification0.3

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

Reproduce

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