Average Error: 14.9 → 0.4
Time: 6.3s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin a \cdot \sin b\right)}^{3}}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin a \cdot \sin b\right)}^{3}}}
double code(double r, double a, double b) {
	return ((double) (r * ((double) (((double) sin(b)) / ((double) cos(((double) (a + b))))))));
}
↓
double code(double r, double a, double b) {
	return ((double) (((double) (r * ((double) sin(b)))) * ((double) (1.0 / ((double) (((double) (((double) cos(a)) * ((double) cos(b)))) - ((double) cbrt(((double) pow(((double) (((double) sin(a)) * ((double) sin(b)))), 3.0))))))))));
}

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 14.9

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 div-inv0.4

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

  6. Applied associate-*r*0.4

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

  8. Applied add-cbrt-cube0.4

    \[\leadsto \left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \color{blue}{\sqrt[3]{\left(\sin b \cdot \sin b\right) \cdot \sin b}}}\]

  9. Applied add-cbrt-cube0.4

    \[\leadsto \left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{\left(\sin a \cdot \sin a\right) \cdot \sin a}} \cdot \sqrt[3]{\left(\sin b \cdot \sin b\right) \cdot \sin b}}\]

  10. Applied cbrt-unprod0.4

    \[\leadsto \left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \color{blue}{\sqrt[3]{\left(\left(\sin a \cdot \sin a\right) \cdot \sin a\right) \cdot \left(\left(\sin b \cdot \sin b\right) \cdot \sin b\right)}}}\]

  11. Simplified0.4

    \[\leadsto \left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sqrt[3]{\color{blue}{{\left(\sin a \cdot \sin b\right)}^{3}}}}\]

  12. Final simplification0.4

    \[\leadsto \left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sqrt[3]{{\left(\sin a \cdot \sin b\right)}^{3}}}\]

Reproduce

herbie shell --seed 2020120 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))