Average Error: 14.8 → 0.4
Time: 18.3s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\frac{\cos a \cdot \cos b + \left(-\sin a \cdot \sin b\right)}{r}}\]
r \cdot \frac{\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 r25511 = r;
        double r25512 = b;
        double r25513 = sin(r25512);
        double r25514 = a;
        double r25515 = r25514 + r25512;
        double r25516 = cos(r25515);
        double r25517 = r25513 / r25516;
        double r25518 = r25511 * r25517;
        return r25518;
}
↓
double f(double r, double a, double b) {
        double r25519 = b;
        double r25520 = sin(r25519);
        double r25521 = a;
        double r25522 = cos(r25521);
        double r25523 = cos(r25519);
        double r25524 = r25522 * r25523;
        double r25525 = sin(r25521);
        double r25526 = r25525 * r25520;
        double r25527 = -r25526;
        double r25528 = r25524 + r25527;
        double r25529 = r;
        double r25530 = r25528 / r25529;
        double r25531 = r25520 / r25530;
        return r25531;
}

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 14.8

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 add-cbrt-cube0.4

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \color{blue}{\sqrt[3]{\left(\sin b \cdot \sin b\right) \cdot \sin b}}}\]

  6. Applied add-cbrt-cube0.4

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{\left(\sin a \cdot \sin a\right) \cdot \sin a}} \cdot \sqrt[3]{\left(\sin b \cdot \sin b\right) \cdot \sin b}}\]

  7. Applied cbrt-unprod0.4

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{\left(\left(\sin a \cdot \sin a\right) \cdot \sin a\right) \cdot \left(\left(\sin b \cdot \sin b\right) \cdot \sin b\right)}}}\]

  8. Simplified0.4

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{\color{blue}{{\left(\sin a \cdot \sin b\right)}^{3}}}}\]
  9. Using strategy rm

  10. Applied associate-*r/0.4

    \[\leadsto \color{blue}{\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin a \cdot \sin b\right)}^{3}}}}\]

  11. 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 2019297 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))