Average Error: 15.3 → 0.4
Time: 1.2m
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\left(\frac{1}{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot \sin b\right) \cdot r\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\left(\frac{1}{\cos a \cdot \cos b - \sin b \cdot \sin a} \cdot \sin b\right) \cdot r
double f(double r, double a, double b) {
        double r4465979 = r;
        double r4465980 = b;
        double r4465981 = sin(r4465980);
        double r4465982 = a;
        double r4465983 = r4465982 + r4465980;
        double r4465984 = cos(r4465983);
        double r4465985 = r4465981 / r4465984;
        double r4465986 = r4465979 * r4465985;
        return r4465986;
}
↓
double f(double r, double a, double b) {
        double r4465987 = 1.0;
        double r4465988 = a;
        double r4465989 = cos(r4465988);
        double r4465990 = b;
        double r4465991 = cos(r4465990);
        double r4465992 = r4465989 * r4465991;
        double r4465993 = sin(r4465990);
        double r4465994 = sin(r4465988);
        double r4465995 = r4465993 * r4465994;
        double r4465996 = r4465992 - r4465995;
        double r4465997 = r4465987 / r4465996;
        double r4465998 = r4465997 * r4465993;
        double r4465999 = r;
        double r4466000 = r4465998 * r4465999;
        return r4466000;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

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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. Using strategy rm

  5. Applied add-log-exp0.4

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \color{blue}{\log \left(e^{\sin a \cdot \sin b}\right)}}\]
  6. Using strategy rm

  7. Applied div-inv0.5

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

  8. Simplified0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019128 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))