Average Error: 15.8 → 0.3
Time: 33.5s
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 r961735 = r;
        double r961736 = b;
        double r961737 = sin(r961736);
        double r961738 = r961735 * r961737;
        double r961739 = a;
        double r961740 = r961739 + r961736;
        double r961741 = cos(r961740);
        double r961742 = r961738 / r961741;
        return r961742;
}
↓
double f(double r, double a, double b) {
        double r961743 = r;
        double r961744 = b;
        double r961745 = sin(r961744);
        double r961746 = a;
        double r961747 = cos(r961746);
        double r961748 = cos(r961744);
        double r961749 = r961747 * r961748;
        double r961750 = sin(r961746);
        double r961751 = r961750 * r961745;
        double r961752 = r961749 - r961751;
        double r961753 = r961745 / r961752;
        double r961754 = r961743 * r961753;
        return r961754;
}

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 15.8

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 2019143 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))