Average Error: 15.2 → 0.4
Time: 6.6s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{1 \cdot \left(\cos a \cdot \cos b - \sin a \cdot \sin b\right)}{\sin b}}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{1 \cdot \left(\cos a \cdot \cos b - \sin a \cdot \sin b\right)}{\sin b}}
double f(double r, double a, double b) {
        double r18302 = r;
        double r18303 = b;
        double r18304 = sin(r18303);
        double r18305 = r18302 * r18304;
        double r18306 = a;
        double r18307 = r18306 + r18303;
        double r18308 = cos(r18307);
        double r18309 = r18305 / r18308;
        return r18309;
}
↓
double f(double r, double a, double b) {
        double r18310 = r;
        double r18311 = 1.0;
        double r18312 = a;
        double r18313 = cos(r18312);
        double r18314 = b;
        double r18315 = cos(r18314);
        double r18316 = r18313 * r18315;
        double r18317 = sin(r18312);
        double r18318 = sin(r18314);
        double r18319 = r18317 * r18318;
        double r18320 = r18316 - r18319;
        double r18321 = r18311 * r18320;
        double r18322 = r18321 / r18318;
        double r18323 = r18310 / r18322;
        return r18323;
}

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 15.2

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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 associate-/l*0.4

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

  7. Applied *-un-lft-identity0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019344 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))