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 r15668 = r;
        double r15669 = b;
        double r15670 = sin(r15669);
        double r15671 = r15668 * r15670;
        double r15672 = a;
        double r15673 = r15672 + r15669;
        double r15674 = cos(r15673);
        double r15675 = r15671 / r15674;
        return r15675;
}
↓
double f(double r, double a, double b) {
        double r15676 = r;
        double r15677 = a;
        double r15678 = cos(r15677);
        double r15679 = b;
        double r15680 = cos(r15679);
        double r15681 = r15678 * r15680;
        double r15682 = sin(r15677);
        double r15683 = sin(r15679);
        double r15684 = r15682 * r15683;
        double r15685 = r15681 - r15684;
        double r15686 = r15685 / r15683;
        double r15687 = r15676 / r15686;
        return r15687;
}

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))))