Average Error: 14.8 → 0.3
Time: 37.6s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}
double f(double r, double a, double b) {
        double r1287339 = r;
        double r1287340 = b;
        double r1287341 = sin(r1287340);
        double r1287342 = a;
        double r1287343 = r1287342 + r1287340;
        double r1287344 = cos(r1287343);
        double r1287345 = r1287341 / r1287344;
        double r1287346 = r1287339 * r1287345;
        return r1287346;
}
↓
double f(double r, double a, double b) {
        double r1287347 = r;
        double r1287348 = b;
        double r1287349 = sin(r1287348);
        double r1287350 = r1287347 * r1287349;
        double r1287351 = a;
        double r1287352 = cos(r1287351);
        double r1287353 = cos(r1287348);
        double r1287354 = r1287352 * r1287353;
        double r1287355 = sin(r1287351);
        double r1287356 = r1287349 * r1287355;
        double r1287357 = r1287354 - r1287356;
        double r1287358 = r1287350 / r1287357;
        return r1287358;
}

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

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Using strategy rm

  5. Applied associate-*r/0.3

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

  6. Final simplification0.3

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

Reproduce

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