Average Error: 15.3 → 0.4
Time: 39.1s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\cos a \cdot \cos b - \mathsf{log1p}\left(\left(\mathsf{expm1}\left(\left(\sin a \cdot \sin b\right)\right)\right)\right)} \cdot r\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b}{\cos a \cdot \cos b - \mathsf{log1p}\left(\left(\mathsf{expm1}\left(\left(\sin a \cdot \sin b\right)\right)\right)\right)} \cdot r
double f(double r, double a, double b) {
        double r1437428 = r;
        double r1437429 = b;
        double r1437430 = sin(r1437429);
        double r1437431 = a;
        double r1437432 = r1437431 + r1437429;
        double r1437433 = cos(r1437432);
        double r1437434 = r1437430 / r1437433;
        double r1437435 = r1437428 * r1437434;
        return r1437435;
}
↓
double f(double r, double a, double b) {
        double r1437436 = b;
        double r1437437 = sin(r1437436);
        double r1437438 = a;
        double r1437439 = cos(r1437438);
        double r1437440 = cos(r1437436);
        double r1437441 = r1437439 * r1437440;
        double r1437442 = sin(r1437438);
        double r1437443 = r1437442 * r1437437;
        double r1437444 = expm1(r1437443);
        double r1437445 = log1p(r1437444);
        double r1437446 = r1437441 - r1437445;
        double r1437447 = r1437437 / r1437446;
        double r1437448 = r;
        double r1437449 = r1437447 * r1437448;
        return r1437449;
}

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 log1p-expm1-u0.4

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{\mathsf{log1p}\left(\left(\mathsf{expm1}\left(\left(\sin a \cdot \sin b\right)\right)\right)\right)}}\]

  6. Final simplification0.4

    \[\leadsto \frac{\sin b}{\cos a \cdot \cos b - \mathsf{log1p}\left(\left(\mathsf{expm1}\left(\left(\sin a \cdot \sin b\right)\right)\right)\right)} \cdot r\]

Reproduce

herbie shell --seed 2019124 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))