Average Error: 14.9 → 0.3
Time: 13.7s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r16582 = r;
        double r16583 = b;
        double r16584 = sin(r16583);
        double r16585 = r16582 * r16584;
        double r16586 = a;
        double r16587 = r16586 + r16583;
        double r16588 = cos(r16587);
        double r16589 = r16585 / r16588;
        return r16589;
}
↓
double f(double r, double a, double b) {
        double r16590 = r;
        double r16591 = b;
        double r16592 = sin(r16591);
        double r16593 = a;
        double r16594 = cos(r16593);
        double r16595 = cos(r16591);
        double r16596 = r16594 * r16595;
        double r16597 = sin(r16593);
        double r16598 = r16597 * r16592;
        double r16599 = r16596 - r16598;
        double r16600 = r16592 / r16599;
        double r16601 = r16590 * r16600;
        return r16601;
}

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

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  2. Using strategy rm

  3. Applied cos-sum0.3

    \[\leadsto \frac{r \cdot \sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity0.3

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

  6. Applied times-frac0.3

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019350 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))