Average Error: 0.1 → 0.1
Time: 6.3s
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 r18711 = e;
        double r18712 = v;
        double r18713 = sin(r18712);
        double r18714 = r18711 * r18713;
        double r18715 = 1.0;
        double r18716 = cos(r18712);
        double r18717 = r18711 * r18716;
        double r18718 = r18715 + r18717;
        double r18719 = r18714 / r18718;
        return r18719;
}
↓
double f(double e, double v) {
        double r18720 = e;
        double r18721 = 1.0;
        double r18722 = v;
        double r18723 = cos(r18722);
        double r18724 = r18720 * r18723;
        double r18725 = r18721 + r18724;
        double r18726 = r18720 / r18725;
        double r18727 = sin(r18722);
        double r18728 = r18726 * r18727;
        return r18728;
}

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 2019322 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))