Average Error: 15.0 → 0.4
Time: 41.6s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{\sin b}{\cos a \cdot \cos b - \sqrt[3]{\left(\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)\right) \cdot \left(\sin a \cdot \sin b\right)}} \cdot r\]
r \cdot \frac{\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 r1395484 = r;
        double r1395485 = b;
        double r1395486 = sin(r1395485);
        double r1395487 = a;
        double r1395488 = r1395487 + r1395485;
        double r1395489 = cos(r1395488);
        double r1395490 = r1395486 / r1395489;
        double r1395491 = r1395484 * r1395490;
        return r1395491;
}
↓
double f(double r, double a, double b) {
        double r1395492 = b;
        double r1395493 = sin(r1395492);
        double r1395494 = a;
        double r1395495 = cos(r1395494);
        double r1395496 = cos(r1395492);
        double r1395497 = r1395495 * r1395496;
        double r1395498 = sin(r1395494);
        double r1395499 = r1395498 * r1395493;
        double r1395500 = r1395499 * r1395499;
        double r1395501 = r1395500 * r1395499;
        double r1395502 = cbrt(r1395501);
        double r1395503 = r1395497 - r1395502;
        double r1395504 = r1395493 / r1395503;
        double r1395505 = r;
        double r1395506 = r1395504 * r1395505;
        return r1395506;
}

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 add-cbrt-cube0.4

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

  6. 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), B"
  (* r (/ (sin b) (cos (+ a b)))))