Average Error: 14.4 → 0.4
Time: 23.0s
Precision: 64
\[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
↓
\[\frac{r}{\cos a \cdot \frac{\cos b}{\sin b} - \sin a}\]
r \cdot \frac{\sin b}{\cos \left(a + b\right)}
↓
\frac{r}{\cos a \cdot \frac{\cos b}{\sin b} - \sin a}
double f(double r, double a, double b) {
        double r922619 = r;
        double r922620 = b;
        double r922621 = sin(r922620);
        double r922622 = a;
        double r922623 = r922622 + r922620;
        double r922624 = cos(r922623);
        double r922625 = r922621 / r922624;
        double r922626 = r922619 * r922625;
        return r922626;
}
↓
double f(double r, double a, double b) {
        double r922627 = r;
        double r922628 = a;
        double r922629 = cos(r922628);
        double r922630 = b;
        double r922631 = cos(r922630);
        double r922632 = sin(r922630);
        double r922633 = r922631 / r922632;
        double r922634 = r922629 * r922633;
        double r922635 = sin(r922628);
        double r922636 = r922634 - r922635;
        double r922637 = r922627 / r922636;
        return r922637;
}

Error

Bits error versus r

Bits error versus a

Bits error versus b

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.4

    \[r \cdot \frac{\sin b}{\cos \left(a + b\right)}\]
  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 *-un-lft-identity0.3

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

  6. Applied associate-*l*0.3

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

  7. Simplified0.4

    \[\leadsto 1 \cdot \color{blue}{\frac{r}{\frac{\cos b}{\frac{\sin b}{\cos a}} - \sin a}}\]
  8. Using strategy rm

  9. Applied associate-/r/0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2019164 
(FPCore (r a b)
  :name "r*sin(b)/cos(a+b), B"
  (* r (/ (sin b) (cos (+ a b)))))