Average Error: 15.2 → 0.4
Time: 8.6s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin a \cdot \sin b\right)}^{3}}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin a \cdot \sin b\right)}^{3}}}
double f(double r, double a, double b) {
        double r24275 = r;
        double r24276 = b;
        double r24277 = sin(r24276);
        double r24278 = a;
        double r24279 = r24278 + r24276;
        double r24280 = cos(r24279);
        double r24281 = r24277 / r24280;
        double r24282 = r24275 * r24281;
        return r24282;
}
↓
double f(double r, double a, double b) {
        double r24283 = r;
        double r24284 = b;
        double r24285 = sin(r24284);
        double r24286 = a;
        double r24287 = cos(r24286);
        double r24288 = cos(r24284);
        double r24289 = r24287 * r24288;
        double r24290 = sin(r24286);
        double r24291 = r24290 * r24285;
        double r24292 = 3.0;
        double r24293 = pow(r24291, r24292);
        double r24294 = cbrt(r24293);
        double r24295 = r24289 - r24294;
        double r24296 = r24285 / r24295;
        double r24297 = r24283 * r24296;
        return r24297;
}

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 15.2

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

  7. Applied add-cbrt-cube0.4

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

  8. Simplified0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019318 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))