Average Error: 15.8 → 0.4
Time: 31.0s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\sin b \cdot \frac{r}{\cos b \cdot \cos a - \sin b \cdot \sin a}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\sin b \cdot \frac{r}{\cos b \cdot \cos a - \sin b \cdot \sin a}
double f(double r, double a, double b) {
        double r678759 = r;
        double r678760 = b;
        double r678761 = sin(r678760);
        double r678762 = r678759 * r678761;
        double r678763 = a;
        double r678764 = r678763 + r678760;
        double r678765 = cos(r678764);
        double r678766 = r678762 / r678765;
        return r678766;
}
↓
double f(double r, double a, double b) {
        double r678767 = b;
        double r678768 = sin(r678767);
        double r678769 = r;
        double r678770 = cos(r678767);
        double r678771 = a;
        double r678772 = cos(r678771);
        double r678773 = r678770 * r678772;
        double r678774 = sin(r678771);
        double r678775 = r678768 * r678774;
        double r678776 = r678773 - r678775;
        double r678777 = r678769 / r678776;
        double r678778 = r678768 * r678777;
        return r678778;
}

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 15.8

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

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019143 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  (/ (* r (sin b)) (cos (+ a b))))