Average Error: 15.0 → 0.4
Time: 39.2s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\sin a \cdot \sin b\right)}} \cdot r\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{\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)}} \cdot r
double f(double r, double a, double b) {
        double r1371516 = r;
        double r1371517 = b;
        double r1371518 = sin(r1371517);
        double r1371519 = r1371516 * r1371518;
        double r1371520 = a;
        double r1371521 = r1371520 + r1371517;
        double r1371522 = cos(r1371521);
        double r1371523 = r1371519 / r1371522;
        return r1371523;
}
↓
double f(double r, double a, double b) {
        double r1371524 = b;
        double r1371525 = sin(r1371524);
        double r1371526 = a;
        double r1371527 = cos(r1371526);
        double r1371528 = cos(r1371524);
        double r1371529 = r1371527 * r1371528;
        double r1371530 = sin(r1371526);
        double r1371531 = r1371530 * r1371525;
        double r1371532 = r1371531 * r1371531;
        double r1371533 = r1371532 * r1371531;
        double r1371534 = cbrt(r1371533);
        double r1371535 = r1371529 - r1371534;
        double r1371536 = r1371525 / r1371535;
        double r1371537 = r;
        double r1371538 = r1371536 * r1371537;
        return r1371538;
}

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

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 *-un-lft-identity0.3

    \[\leadsto \frac{r \cdot \sin b}{\color{blue}{1 \cdot \left(\cos a \cdot \cos b - \sin a \cdot \sin b\right)}}\]

  6. Applied times-frac0.3

    \[\leadsto \color{blue}{\frac{r}{1} \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]

  7. Simplified0.3

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

  9. Applied add-cbrt-cube0.4

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

  10. Applied add-cbrt-cube0.4

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

  11. Applied cbrt-unprod0.4

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

  12. Simplified0.4

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

  13. Final simplification0.4

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

Reproduce

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