Average Error: 14.8 → 0.3
Time: 35.1s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot r\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot r
double f(double r, double a, double b) {
        double r1203234 = r;
        double r1203235 = b;
        double r1203236 = sin(r1203235);
        double r1203237 = r1203234 * r1203236;
        double r1203238 = a;
        double r1203239 = r1203238 + r1203235;
        double r1203240 = cos(r1203239);
        double r1203241 = r1203237 / r1203240;
        return r1203241;
}
↓
double f(double r, double a, double b) {
        double r1203242 = b;
        double r1203243 = sin(r1203242);
        double r1203244 = a;
        double r1203245 = cos(r1203244);
        double r1203246 = cos(r1203242);
        double r1203247 = r1203245 * r1203246;
        double r1203248 = sin(r1203244);
        double r1203249 = r1203248 * r1203243;
        double r1203250 = r1203247 - r1203249;
        double r1203251 = r1203243 / r1203250;
        double r1203252 = r;
        double r1203253 = r1203251 * r1203252;
        return r1203253;
}

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 14.8

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 *-commutative0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019112 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))