Average Error: 0.1 → 0.1
Time: 1.3m
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 r19737 = e;
        double r19738 = v;
        double r19739 = sin(r19738);
        double r19740 = r19737 * r19739;
        double r19741 = 1.0;
        double r19742 = cos(r19738);
        double r19743 = r19737 * r19742;
        double r19744 = r19741 + r19743;
        double r19745 = r19740 / r19744;
        return r19745;
}
↓
double f(double e, double v) {
        double r19746 = e;
        double r19747 = v;
        double r19748 = sin(r19747);
        double r19749 = 1.0;
        double r19750 = cos(r19747);
        double r19751 = r19746 * r19750;
        double r19752 = r19749 + r19751;
        double r19753 = r19748 / r19752;
        double r19754 = r19746 * r19753;
        return r19754;
}

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 2019202 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))