Average Error: 15.1 → 0.4
Time: 31.8s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\left(\frac{1}{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot \sin b\right) \cdot r\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\left(\frac{1}{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot \sin b\right) \cdot r
double f(double r, double a, double b) {
        double r769666 = r;
        double r769667 = b;
        double r769668 = sin(r769667);
        double r769669 = r769666 * r769668;
        double r769670 = a;
        double r769671 = r769670 + r769667;
        double r769672 = cos(r769671);
        double r769673 = r769669 / r769672;
        return r769673;
}
↓
double f(double r, double a, double b) {
        double r769674 = 1.0;
        double r769675 = a;
        double r769676 = cos(r769675);
        double r769677 = b;
        double r769678 = cos(r769677);
        double r769679 = r769676 * r769678;
        double r769680 = sin(r769677);
        double r769681 = sin(r769675);
        double r769682 = r769680 * r769681;
        double r769683 = r769679 - r769682;
        double r769684 = r769674 / r769683;
        double r769685 = r769684 * r769680;
        double r769686 = r;
        double r769687 = r769685 * r769686;
        return r769687;
}

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

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

  9. Applied div-inv0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019146 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))