Average Error: 14.8 → 0.4
Time: 20.3s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\left(\cos a \cdot \cos b + \sin b \cdot \sin a\right) \cdot \left(\frac{\sin b}{\left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right) - \sin a \cdot \left(\sin b \cdot \left(\sin b \cdot \sin a\right)\right)} \cdot r\right)\]
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) - \sin a \cdot \left(\sin b \cdot \left(\sin b \cdot \sin a\right)\right)} \cdot r\right)
double f(double r, double a, double b) {
        double r391704 = r;
        double r391705 = b;
        double r391706 = sin(r391705);
        double r391707 = a;
        double r391708 = r391707 + r391705;
        double r391709 = cos(r391708);
        double r391710 = r391706 / r391709;
        double r391711 = r391704 * r391710;
        return r391711;
}
↓
double f(double r, double a, double b) {
        double r391712 = a;
        double r391713 = cos(r391712);
        double r391714 = b;
        double r391715 = cos(r391714);
        double r391716 = r391713 * r391715;
        double r391717 = sin(r391714);
        double r391718 = sin(r391712);
        double r391719 = r391717 * r391718;
        double r391720 = r391716 + r391719;
        double r391721 = r391716 * r391716;
        double r391722 = r391717 * r391719;
        double r391723 = r391718 * r391722;
        double r391724 = r391721 - r391723;
        double r391725 = r391717 / r391724;
        double r391726 = r;
        double r391727 = r391725 * r391726;
        double r391728 = r391720 * r391727;
        return r391728;
}

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. Using strategy rm

  9. Applied associate-*l*0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019154 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))