Average Error: 15.2 → 0.4
Time: 7.3s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\frac{{\left(\cos a \cdot \cos b\right)}^{3} - {\left(\sin a \cdot \sin b\right)}^{3}}{\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b + \cos a \cdot \cos b\right) + \left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right)}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\frac{{\left(\cos a \cdot \cos b\right)}^{3} - {\left(\sin a \cdot \sin b\right)}^{3}}{\left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b + \cos a \cdot \cos b\right) + \left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right)}}
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) (r * ((double) (((double) sin(b)) / ((double) (((double) (((double) pow(((double) (((double) cos(a)) * ((double) cos(b)))), 3.0)) - ((double) pow(((double) (((double) sin(a)) * ((double) sin(b)))), 3.0)))) / ((double) (((double) (((double) (((double) sin(a)) * ((double) sin(b)))) * ((double) (((double) (((double) sin(a)) * ((double) sin(b)))) + ((double) (((double) cos(a)) * ((double) cos(b)))))))) + ((double) (((double) (((double) cos(a)) * ((double) cos(b)))) * ((double) (((double) cos(a)) * ((double) cos(b))))))))))))));
}

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 15.2

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 flip3--0.4

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

  6. Simplified0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2020130 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))