Average Error: 15.0 → 0.3
Time: 18.2s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r26131 = r;
        double r26132 = b;
        double r26133 = sin(r26132);
        double r26134 = a;
        double r26135 = r26134 + r26132;
        double r26136 = cos(r26135);
        double r26137 = r26133 / r26136;
        double r26138 = r26131 * r26137;
        return r26138;
}
↓
double f(double r, double a, double b) {
        double r26139 = r;
        double r26140 = b;
        double r26141 = sin(r26140);
        double r26142 = r26139 * r26141;
        double r26143 = a;
        double r26144 = cos(r26143);
        double r26145 = cos(r26140);
        double r26146 = r26144 * r26145;
        double r26147 = sin(r26143);
        double r26148 = r26147 * r26141;
        double r26149 = r26146 - r26148;
        double r26150 = r26142 / r26149;
        return r26150;
}

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 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 simplification0.3

    \[\leadsto \frac{r \cdot \sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]

Reproduce

herbie shell --seed 2019294 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))