Average Error: 15.3 → 0.3
Time: 28.9s
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 r25386 = r;
        double r25387 = b;
        double r25388 = sin(r25387);
        double r25389 = a;
        double r25390 = r25389 + r25387;
        double r25391 = cos(r25390);
        double r25392 = r25388 / r25391;
        double r25393 = r25386 * r25392;
        return r25393;
}
↓
double f(double r, double a, double b) {
        double r25394 = r;
        double r25395 = b;
        double r25396 = sin(r25395);
        double r25397 = r25394 * r25396;
        double r25398 = a;
        double r25399 = cos(r25398);
        double r25400 = cos(r25395);
        double r25401 = r25399 * r25400;
        double r25402 = sin(r25398);
        double r25403 = r25402 * r25396;
        double r25404 = r25401 - r25403;
        double r25405 = r25397 / r25404;
        return r25405;
}

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 15.3

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

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))