Average Error: 15.3 → 0.3
Time: 35.8s
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 r1180995 = r;
        double r1180996 = b;
        double r1180997 = sin(r1180996);
        double r1180998 = a;
        double r1180999 = r1180998 + r1180996;
        double r1181000 = cos(r1180999);
        double r1181001 = r1180997 / r1181000;
        double r1181002 = r1180995 * r1181001;
        return r1181002;
}
↓
double f(double r, double a, double b) {
        double r1181003 = r;
        double r1181004 = b;
        double r1181005 = sin(r1181004);
        double r1181006 = a;
        double r1181007 = cos(r1181006);
        double r1181008 = cos(r1181004);
        double r1181009 = r1181007 * r1181008;
        double r1181010 = sin(r1181006);
        double r1181011 = r1181010 * r1181005;
        double r1181012 = r1181009 - r1181011;
        double r1181013 = r1181005 / r1181012;
        double r1181014 = r1181003 * r1181013;
        return r1181014;
}

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 15.3

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

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019124 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))