Average Error: 0.1 → 0.1
Time: 15.4s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e}{1 + e \cdot \cos v} \cdot \sin v\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e}{1 + e \cdot \cos v} \cdot \sin v
double f(double e, double v) {
        double r21607 = e;
        double r21608 = v;
        double r21609 = sin(r21608);
        double r21610 = r21607 * r21609;
        double r21611 = 1.0;
        double r21612 = cos(r21608);
        double r21613 = r21607 * r21612;
        double r21614 = r21611 + r21613;
        double r21615 = r21610 / r21614;
        return r21615;
}
↓
double f(double e, double v) {
        double r21616 = e;
        double r21617 = 1.0;
        double r21618 = v;
        double r21619 = cos(r21618);
        double r21620 = r21616 * r21619;
        double r21621 = r21617 + r21620;
        double r21622 = r21616 / r21621;
        double r21623 = sin(r21618);
        double r21624 = r21622 * r21623;
        return r21624;
}

Error

Bits error versus e

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
  2. Using strategy rm

  3. Applied associate-/l*0.3

    \[\leadsto \color{blue}{\frac{e}{\frac{1 + e \cdot \cos v}{\sin v}}}\]
  4. Using strategy rm

  5. Applied associate-/r/0.1

    \[\leadsto \color{blue}{\frac{e}{1 + e \cdot \cos v} \cdot \sin v}\]

  6. Final simplification0.1

    \[\leadsto \frac{e}{1 + e \cdot \cos v} \cdot \sin v\]

Reproduce

herbie shell --seed 2019195 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))