Average Error: 15.0 → 0.3
Time: 28.1s
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 r719828 = r;
        double r719829 = b;
        double r719830 = sin(r719829);
        double r719831 = r719828 * r719830;
        double r719832 = a;
        double r719833 = r719832 + r719829;
        double r719834 = cos(r719833);
        double r719835 = r719831 / r719834;
        return r719835;
}
↓
double f(double r, double a, double b) {
        double r719836 = r;
        double r719837 = b;
        double r719838 = sin(r719837);
        double r719839 = a;
        double r719840 = cos(r719839);
        double r719841 = cos(r719837);
        double r719842 = r719840 * r719841;
        double r719843 = sin(r719839);
        double r719844 = r719843 * r719838;
        double r719845 = r719842 - r719844;
        double r719846 = r719838 / r719845;
        double r719847 = r719836 * r719846;
        return r719847;
}

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 15.0

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 2019142 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))