Average Error: 14.8 → 0.4
Time: 21.1s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\left(\cos a \cdot \cos b + \sin b \cdot \sin a\right) \cdot \left(\frac{\sin b}{\left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right) - \left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)} \cdot r\right)\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\left(\cos a \cdot \cos b + \sin b \cdot \sin a\right) \cdot \left(\frac{\sin b}{\left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right) - \left(\sin b \cdot \sin a\right) \cdot \left(\sin b \cdot \sin a\right)} \cdot r\right)
double f(double r, double a, double b) {
        double r983462 = r;
        double r983463 = b;
        double r983464 = sin(r983463);
        double r983465 = a;
        double r983466 = r983465 + r983463;
        double r983467 = cos(r983466);
        double r983468 = r983464 / r983467;
        double r983469 = r983462 * r983468;
        return r983469;
}
↓
double f(double r, double a, double b) {
        double r983470 = a;
        double r983471 = cos(r983470);
        double r983472 = b;
        double r983473 = cos(r983472);
        double r983474 = r983471 * r983473;
        double r983475 = sin(r983472);
        double r983476 = sin(r983470);
        double r983477 = r983475 * r983476;
        double r983478 = r983474 + r983477;
        double r983479 = r983474 * r983474;
        double r983480 = r983477 * r983477;
        double r983481 = r983479 - r983480;
        double r983482 = r983475 / r983481;
        double r983483 = r;
        double r983484 = r983482 * r983483;
        double r983485 = r983478 * r983484;
        return r983485;
}

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

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 flip--0.4

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

  6. Applied associate-/r/0.4

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

  7. Applied associate-*r*0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019171 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))