Average Error: 14.9 → 0.4
Time: 7.3s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r18337 = r;
        double r18338 = b;
        double r18339 = sin(r18338);
        double r18340 = a;
        double r18341 = r18340 + r18338;
        double r18342 = cos(r18341);
        double r18343 = r18339 / r18342;
        double r18344 = r18337 * r18343;
        return r18344;
}
↓
double f(double r, double a, double b) {
        double r18345 = r;
        double r18346 = b;
        double r18347 = sin(r18346);
        double r18348 = r18345 * r18347;
        double r18349 = 1.0;
        double r18350 = a;
        double r18351 = cos(r18350);
        double r18352 = cos(r18346);
        double r18353 = r18351 * r18352;
        double r18354 = sin(r18350);
        double r18355 = r18354 * r18347;
        double r18356 = r18353 - r18355;
        double r18357 = r18349 / r18356;
        double r18358 = r18348 * r18357;
        return r18358;
}

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

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 div-inv0.4

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

  6. Applied associate-*r*0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2020081 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))