Average Error: 15.0 → 0.4
Time: 15.1s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}
double f(double r, double a, double b) {
        double r16586 = r;
        double r16587 = b;
        double r16588 = sin(r16587);
        double r16589 = a;
        double r16590 = r16589 + r16587;
        double r16591 = cos(r16590);
        double r16592 = r16588 / r16591;
        double r16593 = r16586 * r16592;
        return r16593;
}
↓
double f(double r, double a, double b) {
        double r16594 = r;
        double r16595 = b;
        double r16596 = sin(r16595);
        double r16597 = r16594 * r16596;
        double r16598 = 1.0;
        double r16599 = a;
        double r16600 = cos(r16599);
        double r16601 = cos(r16595);
        double r16602 = r16600 * r16601;
        double r16603 = sin(r16599);
        double r16604 = r16603 * r16596;
        double r16605 = r16602 - r16604;
        double r16606 = r16598 / r16605;
        double r16607 = r16597 * r16606;
        return r16607;
}

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 15.0

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 div-inv0.4

    \[\leadsto r \cdot \color{blue}{\left(\sin b \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}\right)}\]

  6. Applied associate-*r*0.4

    \[\leadsto \color{blue}{\left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}}\]

  7. Final simplification0.4

    \[\leadsto \left(r \cdot \sin b\right) \cdot \frac{1}{\cos a \cdot \cos b - \sin a \cdot \sin b}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  :precision binary64
  (* r (/ (sin b) (cos (+ a b)))))