Average Error: 0.1 → 0.1
Time: 52.4s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{\cos v \cdot e + 1}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{\cos v \cdot e + 1}
double f(double e, double v) {
        double r1763156 = e;
        double r1763157 = v;
        double r1763158 = sin(r1763157);
        double r1763159 = r1763156 * r1763158;
        double r1763160 = 1.0;
        double r1763161 = cos(r1763157);
        double r1763162 = r1763156 * r1763161;
        double r1763163 = r1763160 + r1763162;
        double r1763164 = r1763159 / r1763163;
        return r1763164;
}
↓
double f(double e, double v) {
        double r1763165 = e;
        double r1763166 = v;
        double r1763167 = sin(r1763166);
        double r1763168 = r1763165 * r1763167;
        double r1763169 = cos(r1763166);
        double r1763170 = r1763169 * r1763165;
        double r1763171 = 1.0;
        double r1763172 = r1763170 + r1763171;
        double r1763173 = r1763168 / r1763172;
        return r1763173;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019138 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))