Average Error: 0.1 → 0.1
Time: 34.4s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\sin v \cdot \frac{e}{1 + \cos v \cdot e}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\sin v \cdot \frac{e}{1 + \cos v \cdot e}
double f(double e, double v) {
        double r1323845 = e;
        double r1323846 = v;
        double r1323847 = sin(r1323846);
        double r1323848 = r1323845 * r1323847;
        double r1323849 = 1.0;
        double r1323850 = cos(r1323846);
        double r1323851 = r1323845 * r1323850;
        double r1323852 = r1323849 + r1323851;
        double r1323853 = r1323848 / r1323852;
        return r1323853;
}
↓
double f(double e, double v) {
        double r1323854 = v;
        double r1323855 = sin(r1323854);
        double r1323856 = e;
        double r1323857 = 1.0;
        double r1323858 = cos(r1323854);
        double r1323859 = r1323858 * r1323856;
        double r1323860 = r1323857 + r1323859;
        double r1323861 = r1323856 / r1323860;
        double r1323862 = r1323855 * r1323861;
        return r1323862;
}

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

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

Reproduce

herbie shell --seed 2019112 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))