Average Error: 15.4 → 0.4
Time: 33.3s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos b \cdot \cos a}{\sin b} - \sin a}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos b \cdot \cos a}{\sin b} - \sin a}
double f(double r, double a, double b) {
        double r1073924 = r;
        double r1073925 = b;
        double r1073926 = sin(r1073925);
        double r1073927 = r1073924 * r1073926;
        double r1073928 = a;
        double r1073929 = r1073928 + r1073925;
        double r1073930 = cos(r1073929);
        double r1073931 = r1073927 / r1073930;
        return r1073931;
}
↓
double f(double r, double a, double b) {
        double r1073932 = r;
        double r1073933 = b;
        double r1073934 = cos(r1073933);
        double r1073935 = a;
        double r1073936 = cos(r1073935);
        double r1073937 = r1073934 * r1073936;
        double r1073938 = sin(r1073933);
        double r1073939 = r1073937 / r1073938;
        double r1073940 = sin(r1073935);
        double r1073941 = r1073939 - r1073940;
        double r1073942 = r1073932 / r1073941;
        return r1073942;
}

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 15.4

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

  3. Applied cos-sum0.4

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

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

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

  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. Taylor expanded around inf 0.4

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

  9. Simplified0.4

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

  10. Taylor expanded around inf 0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2019124 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))