Average Error: 15.7 → 0.4
Time: 24.7s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{1}{\cos b \cdot \cos a - \sin b \cdot \sin a} \cdot \left(r \cdot \sin b\right)\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{1}{\cos b \cdot \cos a - \sin b \cdot \sin a} \cdot \left(r \cdot \sin b\right)
double f(double r, double a, double b) {
        double r948101 = r;
        double r948102 = b;
        double r948103 = sin(r948102);
        double r948104 = a;
        double r948105 = r948104 + r948102;
        double r948106 = cos(r948105);
        double r948107 = r948103 / r948106;
        double r948108 = r948101 * r948107;
        return r948108;
}
↓
double f(double r, double a, double b) {
        double r948109 = 1.0;
        double r948110 = b;
        double r948111 = cos(r948110);
        double r948112 = a;
        double r948113 = cos(r948112);
        double r948114 = r948111 * r948113;
        double r948115 = sin(r948110);
        double r948116 = sin(r948112);
        double r948117 = r948115 * r948116;
        double r948118 = r948114 - r948117;
        double r948119 = r948109 / r948118;
        double r948120 = r;
        double r948121 = r948120 * r948115;
        double r948122 = r948119 * r948121;
        return r948122;
}

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 15.7

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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. Final simplification0.4

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

Reproduce

herbie shell --seed 2019162 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))