Average Error: 14.8 → 0.4
Time: 23.3s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\left(r \cdot \frac{\sin b}{\left(\cos a \cdot \cos b\right) \cdot \left(\left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right)\right) - \left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\sin a \cdot \sin b\right)}\right) \cdot \left(\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right) + \left(\sin a \cdot \sin b\right) \cdot \left(\cos a \cdot \cos b\right)\right) + \left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right)\right)\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\left(r \cdot \frac{\sin b}{\left(\cos a \cdot \cos b\right) \cdot \left(\left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right)\right) - \left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\sin a \cdot \sin b\right)}\right) \cdot \left(\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right) + \left(\sin a \cdot \sin b\right) \cdot \left(\cos a \cdot \cos b\right)\right) + \left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right)\right)
double f(double r, double a, double b) {
        double r717215 = r;
        double r717216 = b;
        double r717217 = sin(r717216);
        double r717218 = r717215 * r717217;
        double r717219 = a;
        double r717220 = r717219 + r717216;
        double r717221 = cos(r717220);
        double r717222 = r717218 / r717221;
        return r717222;
}
↓
double f(double r, double a, double b) {
        double r717223 = r;
        double r717224 = b;
        double r717225 = sin(r717224);
        double r717226 = a;
        double r717227 = cos(r717226);
        double r717228 = cos(r717224);
        double r717229 = r717227 * r717228;
        double r717230 = r717229 * r717229;
        double r717231 = r717229 * r717230;
        double r717232 = sin(r717226);
        double r717233 = r717232 * r717225;
        double r717234 = r717233 * r717233;
        double r717235 = r717234 * r717233;
        double r717236 = r717231 - r717235;
        double r717237 = r717225 / r717236;
        double r717238 = r717223 * r717237;
        double r717239 = r717233 * r717229;
        double r717240 = r717234 + r717239;
        double r717241 = r717240 + r717230;
        double r717242 = r717238 * r717241;
        return r717242;
}

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

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  2. Using strategy rm

  3. Applied cos-sum0.3

    \[\leadsto \frac{r \cdot \sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
  4. Using strategy rm

  5. Applied flip3--0.4

    \[\leadsto \frac{r \cdot \sin b}{\color{blue}{\frac{{\left(\cos a \cdot \cos b\right)}^{3} - {\left(\sin a \cdot \sin b\right)}^{3}}{\left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right) + \left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right) + \left(\cos a \cdot \cos b\right) \cdot \left(\sin a \cdot \sin b\right)\right)}}}\]

  6. Applied associate-/r/0.5

    \[\leadsto \color{blue}{\frac{r \cdot \sin b}{{\left(\cos a \cdot \cos b\right)}^{3} - {\left(\sin a \cdot \sin b\right)}^{3}} \cdot \left(\left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right) + \left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right) + \left(\cos a \cdot \cos b\right) \cdot \left(\sin a \cdot \sin b\right)\right)\right)}\]

  7. Simplified0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019135 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))