Average Error: 14.9 → 0.3
Time: 37.5s
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 r1277935 = r;
        double r1277936 = b;
        double r1277937 = sin(r1277936);
        double r1277938 = a;
        double r1277939 = r1277938 + r1277936;
        double r1277940 = cos(r1277939);
        double r1277941 = r1277937 / r1277940;
        double r1277942 = r1277935 * r1277941;
        return r1277942;
}
↓
double f(double r, double a, double b) {
        double r1277943 = r;
        double r1277944 = b;
        double r1277945 = sin(r1277944);
        double r1277946 = a;
        double r1277947 = cos(r1277946);
        double r1277948 = cos(r1277944);
        double r1277949 = r1277947 * r1277948;
        double r1277950 = sin(r1277946);
        double r1277951 = r1277950 * r1277945;
        double r1277952 = r1277949 - r1277951;
        double r1277953 = r1277945 / r1277952;
        double r1277954 = r1277943 * r1277953;
        return r1277954;
}

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 14.9

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

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019121 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))