Average Error: 0.1 → 0.1
Time: 13.5s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e}{\cos v \cdot e + 1} \cdot \sin v\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e}{\cos v \cdot e + 1} \cdot \sin v
double f(double e, double v) {
        double r20749 = e;
        double r20750 = v;
        double r20751 = sin(r20750);
        double r20752 = r20749 * r20751;
        double r20753 = 1.0;
        double r20754 = cos(r20750);
        double r20755 = r20749 * r20754;
        double r20756 = r20753 + r20755;
        double r20757 = r20752 / r20756;
        return r20757;
}
↓
double f(double e, double v) {
        double r20758 = e;
        double r20759 = v;
        double r20760 = cos(r20759);
        double r20761 = r20760 * r20758;
        double r20762 = 1.0;
        double r20763 = r20761 + r20762;
        double r20764 = r20758 / r20763;
        double r20765 = sin(r20759);
        double r20766 = r20764 * r20765;
        return r20766;
}

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. Simplified0.3

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

  6. Applied associate-/r/0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019297 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))