Average Error: 14.8 → 0.4
Time: 23.4s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\cos b \cdot \frac{\cos a}{\sin b} - \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\cos b \cdot \frac{\cos a}{\sin b} - \sin a}
double f(double r, double a, double b) {
        double r955183 = r;
        double r955184 = b;
        double r955185 = sin(r955184);
        double r955186 = a;
        double r955187 = r955186 + r955184;
        double r955188 = cos(r955187);
        double r955189 = r955185 / r955188;
        double r955190 = r955183 * r955189;
        return r955190;
}
↓
double f(double r, double a, double b) {
        double r955191 = r;
        double r955192 = b;
        double r955193 = cos(r955192);
        double r955194 = a;
        double r955195 = cos(r955194);
        double r955196 = sin(r955192);
        double r955197 = r955195 / r955196;
        double r955198 = r955193 * r955197;
        double r955199 = sin(r955194);
        double r955200 = r955198 - r955199;
        double r955201 = r955191 / r955200;
        return r955201;
}

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 14.8

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 *-un-lft-identity0.3

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

  6. Applied associate-*l*0.3

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

  7. Simplified0.4

    \[\leadsto 1 \cdot \color{blue}{\frac{r}{\frac{\cos b \cdot \cos a}{\sin b} - \sin a}}\]
  8. Using strategy rm

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

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

  10. Applied times-frac0.4

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

  11. Simplified0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2019171 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))