Average Error: 14.8 → 0.3
Time: 40.5s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r1050738 = r;
        double r1050739 = b;
        double r1050740 = sin(r1050739);
        double r1050741 = a;
        double r1050742 = r1050741 + r1050739;
        double r1050743 = cos(r1050742);
        double r1050744 = r1050740 / r1050743;
        double r1050745 = r1050738 * r1050744;
        return r1050745;
}
↓
double f(double r, double a, double b) {
        double r1050746 = r;
        double r1050747 = b;
        double r1050748 = sin(r1050747);
        double r1050749 = a;
        double r1050750 = cos(r1050749);
        double r1050751 = cos(r1050747);
        double r1050752 = r1050750 * r1050751;
        double r1050753 = sin(r1050749);
        double r1050754 = r1050753 * r1050748;
        double r1050755 = r1050752 - r1050754;
        double r1050756 = r1050748 / r1050755;
        double r1050757 = r1050746 * r1050756;
        return r1050757;
}

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 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. Taylor expanded around inf 0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019168 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))