Average Error: 14.7 → 0.4
Time: 26.1s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[r \cdot \frac{\sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
r \cdot \frac{\sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}
double f(double r, double a, double b) {
        double r25625 = r;
        double r25626 = b;
        double r25627 = sin(r25626);
        double r25628 = a;
        double r25629 = r25628 + r25626;
        double r25630 = cos(r25629);
        double r25631 = r25627 / r25630;
        double r25632 = r25625 * r25631;
        return r25632;
}
↓
double f(double r, double a, double b) {
        double r25633 = r;
        double r25634 = b;
        double r25635 = sin(r25634);
        double r25636 = a;
        double r25637 = cos(r25636);
        double r25638 = cos(r25634);
        double r25639 = r25637 * r25638;
        double r25640 = sin(r25636);
        double r25641 = r25640 * r25635;
        double r25642 = exp(r25641);
        double r25643 = log(r25642);
        double r25644 = r25639 - r25643;
        double r25645 = r25635 / r25644;
        double r25646 = r25633 * r25645;
        return r25646;
}

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 14.7

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 add-log-exp0.4

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

  6. Final simplification0.4

    \[\leadsto r \cdot \frac{\sin b}{\cos a \cdot \cos b - \log \left(e^{\sin a \cdot \sin b}\right)}\]

Reproduce

herbie shell --seed 2019304 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))