Average Error: 15.0 → 0.4
Time: 10.8s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}
double f(double r, double a, double b) {
        double r18497 = r;
        double r18498 = b;
        double r18499 = sin(r18498);
        double r18500 = a;
        double r18501 = r18500 + r18498;
        double r18502 = cos(r18501);
        double r18503 = r18499 / r18502;
        double r18504 = r18497 * r18503;
        return r18504;
}
↓
double f(double r, double a, double b) {
        double r18505 = r;
        double r18506 = b;
        double r18507 = sin(r18506);
        double r18508 = a;
        double r18509 = cos(r18508);
        double r18510 = cos(r18506);
        double r18511 = r18509 * r18510;
        double r18512 = sin(r18508);
        double r18513 = r18512 * r18507;
        double r18514 = exp(r18513);
        double r18515 = log(r18514);
        double r18516 = r18511 - r18515;
        double r18517 = r18507 / r18516;
        double r18518 = r18505 * r18517;
        return r18518;
}

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 15.0

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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-log-exp0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2020047 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))