Average Error: 14.9 → 0.3
Time: 16.3s
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 r16660 = r;
        double r16661 = b;
        double r16662 = sin(r16661);
        double r16663 = a;
        double r16664 = r16663 + r16661;
        double r16665 = cos(r16664);
        double r16666 = r16662 / r16665;
        double r16667 = r16660 * r16666;
        return r16667;
}
↓
double f(double r, double a, double b) {
        double r16668 = r;
        double r16669 = b;
        double r16670 = sin(r16669);
        double r16671 = r16668 * r16670;
        double r16672 = a;
        double r16673 = cos(r16672);
        double r16674 = cos(r16669);
        double r16675 = r16673 * r16674;
        double r16676 = sin(r16672);
        double r16677 = r16676 * r16670;
        double r16678 = r16675 - r16677;
        double r16679 = r16671 / r16678;
        return r16679;
}

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 14.9

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 2019350 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))