Average Error: 15.4 → 0.3
Time: 6.9s
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 r17432 = r;
        double r17433 = b;
        double r17434 = sin(r17433);
        double r17435 = a;
        double r17436 = r17435 + r17433;
        double r17437 = cos(r17436);
        double r17438 = r17434 / r17437;
        double r17439 = r17432 * r17438;
        return r17439;
}
↓
double f(double r, double a, double b) {
        double r17440 = r;
        double r17441 = b;
        double r17442 = sin(r17441);
        double r17443 = r17440 * r17442;
        double r17444 = a;
        double r17445 = cos(r17444);
        double r17446 = cos(r17441);
        double r17447 = r17445 * r17446;
        double r17448 = sin(r17444);
        double r17449 = r17448 * r17442;
        double r17450 = r17447 - r17449;
        double r17451 = r17443 / r17450;
        return r17451;
}

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 15.4

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 2020025 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))