Average Error: 14.9 → 0.4
Time: 16.4s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\frac{\cos a \cdot \cos b + \left(-\sin a \cdot \sin b\right)}{r}}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b}{\frac{\cos a \cdot \cos b + \left(-\sin a \cdot \sin b\right)}{r}}
double f(double r, double a, double b) {
        double r25565 = r;
        double r25566 = b;
        double r25567 = sin(r25566);
        double r25568 = r25565 * r25567;
        double r25569 = a;
        double r25570 = r25569 + r25566;
        double r25571 = cos(r25570);
        double r25572 = r25568 / r25571;
        return r25572;
}
↓
double f(double r, double a, double b) {
        double r25573 = b;
        double r25574 = sin(r25573);
        double r25575 = a;
        double r25576 = cos(r25575);
        double r25577 = cos(r25573);
        double r25578 = r25576 * r25577;
        double r25579 = sin(r25575);
        double r25580 = r25579 * r25574;
        double r25581 = -r25580;
        double r25582 = r25578 + r25581;
        double r25583 = r;
        double r25584 = r25582 / r25583;
        double r25585 = r25574 / r25584;
        return r25585;
}

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 add-log-exp0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019303 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))