Average Error: 15.3 → 0.4
Time: 21.0s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{1}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}} \cdot r\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{1}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}} \cdot r
double f(double r, double a, double b) {
        double r1010703 = r;
        double r1010704 = b;
        double r1010705 = sin(r1010704);
        double r1010706 = a;
        double r1010707 = r1010706 + r1010704;
        double r1010708 = cos(r1010707);
        double r1010709 = r1010705 / r1010708;
        double r1010710 = r1010703 * r1010709;
        return r1010710;
}
↓
double f(double r, double a, double b) {
        double r1010711 = 1.0;
        double r1010712 = a;
        double r1010713 = cos(r1010712);
        double r1010714 = b;
        double r1010715 = cos(r1010714);
        double r1010716 = r1010713 * r1010715;
        double r1010717 = sin(r1010712);
        double r1010718 = sin(r1010714);
        double r1010719 = r1010717 * r1010718;
        double r1010720 = r1010716 - r1010719;
        double r1010721 = r1010720 / r1010718;
        double r1010722 = r1010711 / r1010721;
        double r1010723 = r;
        double r1010724 = r1010722 * r1010723;
        return r1010724;
}

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 15.3

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 associate-*r/0.3

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

  7. Applied associate-/l*0.4

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

  9. Applied div-inv0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019179 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))