Average Error: 15.1 → 0.3
Time: 21.4s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
r \cdot \frac{\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 r451229 = r;
        double r451230 = b;
        double r451231 = sin(r451230);
        double r451232 = a;
        double r451233 = r451232 + r451230;
        double r451234 = cos(r451233);
        double r451235 = r451231 / r451234;
        double r451236 = r451229 * r451235;
        return r451236;
}
↓
double f(double r, double a, double b) {
        double r451237 = r;
        double r451238 = b;
        double r451239 = sin(r451238);
        double r451240 = r451237 * r451239;
        double r451241 = a;
        double r451242 = cos(r451241);
        double r451243 = cos(r451238);
        double r451244 = r451242 * r451243;
        double r451245 = sin(r451241);
        double r451246 = r451245 * r451239;
        double r451247 = r451244 - r451246;
        double r451248 = r451240 / r451247;
        return r451248;
}

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 15.1

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

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))