Average Error: 15.1 → 0.4
Time: 6.0s
Precision: 64
\[\frac{r \cdot \sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot \sin b\]
\frac{r \cdot \sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\cos a \cdot \cos b - \sin a \cdot \sin b} \cdot \sin b
double f(double r, double a, double b) {
        double r15640 = r;
        double r15641 = b;
        double r15642 = sin(r15641);
        double r15643 = r15640 * r15642;
        double r15644 = a;
        double r15645 = r15644 + r15641;
        double r15646 = cos(r15645);
        double r15647 = r15643 / r15646;
        return r15647;
}
↓
double f(double r, double a, double b) {
        double r15648 = r;
        double r15649 = a;
        double r15650 = cos(r15649);
        double r15651 = b;
        double r15652 = cos(r15651);
        double r15653 = r15650 * r15652;
        double r15654 = sin(r15649);
        double r15655 = sin(r15651);
        double r15656 = r15654 * r15655;
        double r15657 = r15653 - r15656;
        double r15658 = r15648 / r15657;
        double r15659 = r15658 * r15655;
        return r15659;
}

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. 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

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

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))))