Average Error: 14.8 → 0.3
Time: 42.7s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r1199546 = r;
        double r1199547 = b;
        double r1199548 = sin(r1199547);
        double r1199549 = r1199546 * r1199548;
        double r1199550 = a;
        double r1199551 = r1199550 + r1199547;
        double r1199552 = cos(r1199551);
        double r1199553 = r1199549 / r1199552;
        return r1199553;
}
↓
double f(double r, double a, double b) {
        double r1199554 = r;
        double r1199555 = b;
        double r1199556 = sin(r1199555);
        double r1199557 = r1199554 * r1199556;
        double r1199558 = a;
        double r1199559 = cos(r1199558);
        double r1199560 = cos(r1199555);
        double r1199561 = r1199559 * r1199560;
        double r1199562 = sin(r1199558);
        double r1199563 = r1199562 * r1199556;
        double r1199564 = r1199561 - r1199563;
        double r1199565 = r1199557 / r1199564;
        return r1199565;
}

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 add-cbrt-cube0.4

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\sin a \cdot \sin b\right)}}}\]

  6. Taylor expanded around inf 0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))