Average Error: 15.3 → 0.3
Time: 27.7s
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 r25379 = r;
        double r25380 = b;
        double r25381 = sin(r25380);
        double r25382 = a;
        double r25383 = r25382 + r25380;
        double r25384 = cos(r25383);
        double r25385 = r25381 / r25384;
        double r25386 = r25379 * r25385;
        return r25386;
}
↓
double f(double r, double a, double b) {
        double r25387 = r;
        double r25388 = b;
        double r25389 = sin(r25388);
        double r25390 = r25387 * r25389;
        double r25391 = a;
        double r25392 = cos(r25391);
        double r25393 = cos(r25388);
        double r25394 = r25392 * r25393;
        double r25395 = sin(r25391);
        double r25396 = r25395 * r25389;
        double r25397 = r25394 - r25396;
        double r25398 = r25390 / r25397;
        return r25398;
}

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)))))