Average Error: 14.5 → 0.4
Time: 39.7s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{1}{\cos b \cdot \cos a - \sin b \cdot \sin a} \cdot \left(r \cdot \sin b\right)\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{1}{\cos b \cdot \cos a - \sin b \cdot \sin a} \cdot \left(r \cdot \sin b\right)
double f(double r, double a, double b) {
        double r822052 = r;
        double r822053 = b;
        double r822054 = sin(r822053);
        double r822055 = a;
        double r822056 = r822055 + r822053;
        double r822057 = cos(r822056);
        double r822058 = r822054 / r822057;
        double r822059 = r822052 * r822058;
        return r822059;
}
↓
double f(double r, double a, double b) {
        double r822060 = 1.0;
        double r822061 = b;
        double r822062 = cos(r822061);
        double r822063 = a;
        double r822064 = cos(r822063);
        double r822065 = r822062 * r822064;
        double r822066 = sin(r822061);
        double r822067 = sin(r822063);
        double r822068 = r822066 * r822067;
        double r822069 = r822065 - r822068;
        double r822070 = r822060 / r822069;
        double r822071 = r;
        double r822072 = r822071 * r822066;
        double r822073 = r822070 * r822072;
        return r822073;
}

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 14.5

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 div-inv0.4

    \[\leadsto r \cdot \color{blue}{\left(\sin b \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}\right)}\]

  6. Applied associate-*r*0.4

    \[\leadsto \color{blue}{\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]

  7. Final simplification0.4

    \[\leadsto \frac{1}{\cos b \cdot \cos a - \sin b \cdot \sin a} \cdot \left(r \cdot \sin b\right)\]

Reproduce

herbie shell --seed 2019149 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))