Average Error: 15.8 → 0.3
Time: 56.8s
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 r684025 = r;
        double r684026 = b;
        double r684027 = sin(r684026);
        double r684028 = a;
        double r684029 = r684028 + r684026;
        double r684030 = cos(r684029);
        double r684031 = r684027 / r684030;
        double r684032 = r684025 * r684031;
        return r684032;
}
↓
double f(double r, double a, double b) {
        double r684033 = r;
        double r684034 = b;
        double r684035 = sin(r684034);
        double r684036 = a;
        double r684037 = cos(r684036);
        double r684038 = cos(r684034);
        double r684039 = r684037 * r684038;
        double r684040 = sin(r684036);
        double r684041 = r684040 * r684035;
        double r684042 = r684039 - r684041;
        double r684043 = r684035 / r684042;
        double r684044 = r684033 * r684043;
        return r684044;
}

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 15.8

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Taylor expanded around inf 0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019143 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))