Average Error: 15.0 → 0.4
Time: 13.9s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin b \cdot \sin a\right)}^{3}}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin b \cdot \sin a\right)}^{3}}}
double f(double r, double a, double b) {
        double r16775 = r;
        double r16776 = b;
        double r16777 = sin(r16776);
        double r16778 = a;
        double r16779 = r16778 + r16776;
        double r16780 = cos(r16779);
        double r16781 = r16777 / r16780;
        double r16782 = r16775 * r16781;
        return r16782;
}
↓
double f(double r, double a, double b) {
        double r16783 = r;
        double r16784 = b;
        double r16785 = sin(r16784);
        double r16786 = r16783 * r16785;
        double r16787 = a;
        double r16788 = cos(r16787);
        double r16789 = cos(r16784);
        double r16790 = r16788 * r16789;
        double r16791 = sin(r16787);
        double r16792 = r16785 * r16791;
        double r16793 = 3.0;
        double r16794 = pow(r16792, r16793);
        double r16795 = cbrt(r16794);
        double r16796 = r16790 - r16795;
        double r16797 = r16786 / r16796;
        return r16797;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.0

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 associate-*r/0.3

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

  7. Applied add-cbrt-cube0.4

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \color{blue}{\sqrt[3]{\left(\sin b \cdot \sin b\right) \cdot \sin b}}}\]

  8. Applied add-cbrt-cube0.4

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{\left(\sin a \cdot \sin a\right) \cdot \sin a}} \cdot \sqrt[3]{\left(\sin b \cdot \sin b\right) \cdot \sin b}}\]

  9. Applied cbrt-unprod0.4

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{\left(\left(\sin a \cdot \sin a\right) \cdot \sin a\right) \cdot \left(\left(\sin b \cdot \sin b\right) \cdot \sin b\right)}}}\]

  10. Simplified0.4

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{\color{blue}{{\left(\sin b \cdot \sin a\right)}^{3}}}}\]

  11. Final simplification0.4

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin b \cdot \sin a\right)}^{3}}}\]

Reproduce

herbie shell --seed 2019351 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))