Average Error: 15.3 → 0.4
Time: 21.6s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{1}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}} \cdot r\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{1}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}} \cdot r
double f(double r, double a, double b) {
        double r995129 = r;
        double r995130 = b;
        double r995131 = sin(r995130);
        double r995132 = r995129 * r995131;
        double r995133 = a;
        double r995134 = r995133 + r995130;
        double r995135 = cos(r995134);
        double r995136 = r995132 / r995135;
        return r995136;
}
↓
double f(double r, double a, double b) {
        double r995137 = 1.0;
        double r995138 = a;
        double r995139 = cos(r995138);
        double r995140 = b;
        double r995141 = cos(r995140);
        double r995142 = r995139 * r995141;
        double r995143 = sin(r995138);
        double r995144 = sin(r995140);
        double r995145 = r995143 * r995144;
        double r995146 = r995142 - r995145;
        double r995147 = r995146 / r995144;
        double r995148 = r995137 / r995147;
        double r995149 = r;
        double r995150 = r995148 * r995149;
        return r995150;
}

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 15.3

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  2. Using strategy rm

  3. Applied cos-sum0.3

    \[\leadsto \frac{r \cdot \sin b}{\color{blue}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity0.3

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

  6. Applied times-frac0.3

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

  7. Simplified0.3

    \[\leadsto \color{blue}{r} \cdot \frac{\sin b}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
  8. Using strategy rm

  9. Applied clear-num0.4

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

  10. Final simplification0.4

    \[\leadsto \frac{1}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}} \cdot r\]

Reproduce

herbie shell --seed 2019179 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))