Average Error: 14.9 → 0.3
Time: 23.7s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
\frac{r \cdot \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 r714887 = r;
        double r714888 = b;
        double r714889 = sin(r714888);
        double r714890 = r714887 * r714889;
        double r714891 = a;
        double r714892 = r714891 + r714888;
        double r714893 = cos(r714892);
        double r714894 = r714890 / r714893;
        return r714894;
}
↓
double f(double r, double a, double b) {
        double r714895 = r;
        double r714896 = b;
        double r714897 = sin(r714896);
        double r714898 = a;
        double r714899 = cos(r714898);
        double r714900 = cos(r714896);
        double r714901 = r714899 * r714900;
        double r714902 = sin(r714898);
        double r714903 = r714902 * r714897;
        double r714904 = r714901 - r714903;
        double r714905 = r714897 / r714904;
        double r714906 = r714895 * r714905;
        return r714906;
}

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 14.9

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  2. Using strategy rm

  3. Applied cos-sum0.3

    \[\leadsto \frac{r \cdot \sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity0.3

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

  6. Applied times-frac0.3

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019130 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))