Average Error: 0.1 → 0.1
Time: 9.5s
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 r11179 = e;
        double r11180 = v;
        double r11181 = sin(r11180);
        double r11182 = r11179 * r11181;
        double r11183 = 1.0;
        double r11184 = cos(r11180);
        double r11185 = r11179 * r11184;
        double r11186 = r11183 + r11185;
        double r11187 = r11182 / r11186;
        return r11187;
}
↓
double f(double e, double v) {
        double r11188 = e;
        double r11189 = 1.0;
        double r11190 = v;
        double r11191 = cos(r11190);
        double r11192 = r11188 * r11191;
        double r11193 = r11189 + r11192;
        double r11194 = r11188 / r11193;
        double r11195 = sin(r11190);
        double r11196 = r11194 * r11195;
        return r11196;
}

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 2020042 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))