Average Error: 15.0 → 0.4
Time: 44.5s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\mathsf{log1p}\left(\left(\mathsf{expm1}\left(\left(\cos a \cdot \cos b\right)\right)\right)\right) - \sin b \cdot \sin a} \cdot r\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b}{\mathsf{log1p}\left(\left(\mathsf{expm1}\left(\left(\cos a \cdot \cos b\right)\right)\right)\right) - \sin b \cdot \sin a} \cdot r
double f(double r, double a, double b) {
        double r1419300 = r;
        double r1419301 = b;
        double r1419302 = sin(r1419301);
        double r1419303 = a;
        double r1419304 = r1419303 + r1419301;
        double r1419305 = cos(r1419304);
        double r1419306 = r1419302 / r1419305;
        double r1419307 = r1419300 * r1419306;
        return r1419307;
}
↓
double f(double r, double a, double b) {
        double r1419308 = b;
        double r1419309 = sin(r1419308);
        double r1419310 = a;
        double r1419311 = cos(r1419310);
        double r1419312 = cos(r1419308);
        double r1419313 = r1419311 * r1419312;
        double r1419314 = expm1(r1419313);
        double r1419315 = log1p(r1419314);
        double r1419316 = sin(r1419310);
        double r1419317 = r1419309 * r1419316;
        double r1419318 = r1419315 - r1419317;
        double r1419319 = r1419309 / r1419318;
        double r1419320 = r;
        double r1419321 = r1419319 * r1419320;
        return r1419321;
}

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 log1p-expm1-u0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019120 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))