Trigonometry A

Average Error: 0.1 → 0.1

Time: 20.7s

Precision: 64

\[0 \le e \le 1\]

Math

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

↓

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

C

double f(double e, double v) {
        double r945898 = e;
        double r945899 = v;
        double r945900 = sin(r945899);
        double r945901 = r945898 * r945900;
        double r945902 = 1.0;
        double r945903 = cos(r945899);
        double r945904 = r945898 * r945903;
        double r945905 = r945902 + r945904;
        double r945906 = r945901 / r945905;
        return r945906;
}

↓

double f(double e, double v) {
        double r945907 = e;
        double r945908 = v;
        double r945909 = sin(r945908);
        double r945910 = r945907 * r945909;
        double r945911 = cos(r945908);
        double r945912 = r945911 * r945907;
        double r945913 = 1.0;
        double r945914 = r945912 + r945913;
        double r945915 = r945910 / r945914;
        return r945915;
}

Error

Bits error versus e

Bits error versus v

Derivation

1. Initial program 0.1

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

2. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))