Average Error: 0.1 → 0.1
Time: 27.6s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{\sin v}{1 + \cos v \cdot e} \cdot e\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{\sin v}{1 + \cos v \cdot e} \cdot e
double f(double e, double v) {
        double r547884 = e;
        double r547885 = v;
        double r547886 = sin(r547885);
        double r547887 = r547884 * r547886;
        double r547888 = 1.0;
        double r547889 = cos(r547885);
        double r547890 = r547884 * r547889;
        double r547891 = r547888 + r547890;
        double r547892 = r547887 / r547891;
        return r547892;
}
↓
double f(double e, double v) {
        double r547893 = v;
        double r547894 = sin(r547893);
        double r547895 = 1.0;
        double r547896 = cos(r547893);
        double r547897 = e;
        double r547898 = r547896 * r547897;
        double r547899 = r547895 + r547898;
        double r547900 = r547894 / r547899;
        double r547901 = r547900 * r547897;
        return r547901;
}

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 associate-/l*0.3

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

  5. Applied div-inv0.2

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019142 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))