Average Error: 15.1 → 0.3
Time: 7.1s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b \cdot r}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b \cdot r}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r17533 = r;
        double r17534 = b;
        double r17535 = sin(r17534);
        double r17536 = a;
        double r17537 = r17536 + r17534;
        double r17538 = cos(r17537);
        double r17539 = r17535 / r17538;
        double r17540 = r17533 * r17539;
        return r17540;
}
↓
double f(double r, double a, double b) {
        double r17541 = b;
        double r17542 = sin(r17541);
        double r17543 = r;
        double r17544 = r17542 * r17543;
        double r17545 = a;
        double r17546 = cos(r17545);
        double r17547 = cos(r17541);
        double r17548 = r17546 * r17547;
        double r17549 = sin(r17545);
        double r17550 = r17549 * r17542;
        double r17551 = r17548 - r17550;
        double r17552 = r17544 / r17551;
        return r17552;
}

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 15.1

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 div-inv0.4

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

  7. Applied un-div-inv0.3

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

  8. Applied associate-*r/0.3

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

  9. Simplified0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))