Average Error: 14.8 → 0.3
Time: 36.9s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin b \cdot \sin a}
double f(double r, double a, double b) {
        double r1210493 = r;
        double r1210494 = b;
        double r1210495 = sin(r1210494);
        double r1210496 = a;
        double r1210497 = r1210496 + r1210494;
        double r1210498 = cos(r1210497);
        double r1210499 = r1210495 / r1210498;
        double r1210500 = r1210493 * r1210499;
        return r1210500;
}
↓
double f(double r, double a, double b) {
        double r1210501 = r;
        double r1210502 = b;
        double r1210503 = sin(r1210502);
        double r1210504 = r1210501 * r1210503;
        double r1210505 = a;
        double r1210506 = cos(r1210505);
        double r1210507 = cos(r1210502);
        double r1210508 = r1210506 * r1210507;
        double r1210509 = sin(r1210505);
        double r1210510 = r1210503 * r1210509;
        double r1210511 = r1210508 - r1210510;
        double r1210512 = r1210504 / r1210511;
        return r1210512;
}

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 associate-*r/0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019112 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))