Average Error: 15.0 → 0.4
Time: 6.5s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{1}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{1}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}
double f(double r, double a, double b) {
        double r17656 = r;
        double r17657 = b;
        double r17658 = sin(r17657);
        double r17659 = a;
        double r17660 = r17659 + r17657;
        double r17661 = cos(r17660);
        double r17662 = r17658 / r17661;
        double r17663 = r17656 * r17662;
        return r17663;
}
↓
double f(double r, double a, double b) {
        double r17664 = r;
        double r17665 = 1.0;
        double r17666 = a;
        double r17667 = cos(r17666);
        double r17668 = b;
        double r17669 = cos(r17668);
        double r17670 = r17667 * r17669;
        double r17671 = sin(r17666);
        double r17672 = sin(r17668);
        double r17673 = r17671 * r17672;
        double r17674 = r17670 - r17673;
        double r17675 = r17674 / r17672;
        double r17676 = r17665 / r17675;
        double r17677 = r17664 * r17676;
        return r17677;
}

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 15.0

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 clear-num0.4

    \[\leadsto r \cdot \color{blue}{\frac{1}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}}\]

  6. Final simplification0.4

    \[\leadsto r \cdot \frac{1}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}\]

Reproduce

herbie shell --seed 2020049 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))