Average Error: 15.3 → 0.4
Time: 7.0s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r \cdot \sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r \cdot \sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}
double f(double r, double a, double b) {
        double r17236 = r;
        double r17237 = b;
        double r17238 = sin(r17237);
        double r17239 = a;
        double r17240 = r17239 + r17237;
        double r17241 = cos(r17240);
        double r17242 = r17238 / r17241;
        double r17243 = r17236 * r17242;
        return r17243;
}
↓
double f(double r, double a, double b) {
        double r17244 = r;
        double r17245 = b;
        double r17246 = sin(r17245);
        double r17247 = r17244 * r17246;
        double r17248 = a;
        double r17249 = cos(r17248);
        double r17250 = cos(r17245);
        double r17251 = r17249 * r17250;
        double r17252 = sin(r17248);
        double r17253 = r17252 * r17246;
        double r17254 = exp(r17253);
        double r17255 = log(r17254);
        double r17256 = r17251 - r17255;
        double r17257 = r17247 / r17256;
        return r17257;
}

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

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 associate-*r/0.3

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

  7. Applied add-log-exp0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019352 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))