Average Error: 0.1 → 0.1
Time: 4.8s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[e \cdot \frac{\sin v}{1 + e \cdot \cos v}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
e \cdot \frac{\sin v}{1 + e \cdot \cos v}
double f(double e, double v) {
        double r11809 = e;
        double r11810 = v;
        double r11811 = sin(r11810);
        double r11812 = r11809 * r11811;
        double r11813 = 1.0;
        double r11814 = cos(r11810);
        double r11815 = r11809 * r11814;
        double r11816 = r11813 + r11815;
        double r11817 = r11812 / r11816;
        return r11817;
}
↓
double f(double e, double v) {
        double r11818 = e;
        double r11819 = v;
        double r11820 = sin(r11819);
        double r11821 = 1.0;
        double r11822 = cos(r11819);
        double r11823 = r11818 * r11822;
        double r11824 = r11821 + r11823;
        double r11825 = r11820 / r11824;
        double r11826 = r11818 * r11825;
        return r11826;
}

Error

Bits error versus e

Bits error versus v

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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 *-un-lft-identity0.1

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

  4. Applied times-frac0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020024 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))