Average Error: 15.1 → 0.4
Time: 6.7s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\frac{\left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right) - \left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)}{\cos a \cdot \cos b + \sin a \cdot \sin b}}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\frac{\left(\cos a \cdot \cos b\right) \cdot \left(\cos a \cdot \cos b\right) - \left(\sin a \cdot \sin b\right) \cdot \left(\sin a \cdot \sin b\right)}{\cos a \cdot \cos b + \sin a \cdot \sin b}}
double f(double r, double a, double b) {
        double r17054 = r;
        double r17055 = b;
        double r17056 = sin(r17055);
        double r17057 = a;
        double r17058 = r17057 + r17055;
        double r17059 = cos(r17058);
        double r17060 = r17056 / r17059;
        double r17061 = r17054 * r17060;
        return r17061;
}
↓
double f(double r, double a, double b) {
        double r17062 = r;
        double r17063 = b;
        double r17064 = sin(r17063);
        double r17065 = a;
        double r17066 = cos(r17065);
        double r17067 = cos(r17063);
        double r17068 = r17066 * r17067;
        double r17069 = r17068 * r17068;
        double r17070 = sin(r17065);
        double r17071 = r17070 * r17064;
        double r17072 = r17071 * r17071;
        double r17073 = r17069 - r17072;
        double r17074 = r17068 + r17071;
        double r17075 = r17073 / r17074;
        double r17076 = r17064 / r17075;
        double r17077 = r17062 * r17076;
        return r17077;
}

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 15.1

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

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019356 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))