Average Error: 14.7 → 0.3
Time: 48.9s
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 r2089676 = r;
        double r2089677 = b;
        double r2089678 = sin(r2089677);
        double r2089679 = r2089676 * r2089678;
        double r2089680 = a;
        double r2089681 = r2089680 + r2089677;
        double r2089682 = cos(r2089681);
        double r2089683 = r2089679 / r2089682;
        return r2089683;
}
↓
double f(double r, double a, double b) {
        double r2089684 = r;
        double r2089685 = b;
        double r2089686 = sin(r2089685);
        double r2089687 = a;
        double r2089688 = cos(r2089687);
        double r2089689 = cos(r2089685);
        double r2089690 = r2089688 * r2089689;
        double r2089691 = sin(r2089687);
        double r2089692 = r2089691 * r2089686;
        double r2089693 = r2089690 - r2089692;
        double r2089694 = r2089686 / r2089693;
        double r2089695 = r2089684 * r2089694;
        return r2089695;
}

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 14.7

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 2019125 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))