Average Error: 15.1 → 0.4
Time: 6.2s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\frac{\cos a \cdot \cos b - \sin a \cdot \sin b}{\sin b}}
double f(double r, double a, double b) {
        double r15703 = r;
        double r15704 = b;
        double r15705 = sin(r15704);
        double r15706 = r15703 * r15705;
        double r15707 = a;
        double r15708 = r15707 + r15704;
        double r15709 = cos(r15708);
        double r15710 = r15706 / r15709;
        return r15710;
}
↓
double f(double r, double a, double b) {
        double r15711 = r;
        double r15712 = a;
        double r15713 = cos(r15712);
        double r15714 = b;
        double r15715 = cos(r15714);
        double r15716 = r15713 * r15715;
        double r15717 = sin(r15712);
        double r15718 = sin(r15714);
        double r15719 = r15717 * r15718;
        double r15720 = r15716 - r15719;
        double r15721 = r15720 / r15718;
        double r15722 = r15711 / r15721;
        return r15722;
}

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 15.1

    \[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
  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. Final simplification0.4

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), A"
  :precision binary64
  (/ (* r (sin b)) (cos (+ a b))))