Average Error: 0.1 → 0.1
Time: 35.3s
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 r739025 = e;
        double r739026 = v;
        double r739027 = sin(r739026);
        double r739028 = r739025 * r739027;
        double r739029 = 1.0;
        double r739030 = cos(r739026);
        double r739031 = r739025 * r739030;
        double r739032 = r739029 + r739031;
        double r739033 = r739028 / r739032;
        return r739033;
}
↓
double f(double e, double v) {
        double r739034 = e;
        double r739035 = v;
        double r739036 = sin(r739035);
        double r739037 = r739034 * r739036;
        double r739038 = cos(r739035);
        double r739039 = r739038 * r739034;
        double r739040 = 1.0;
        double r739041 = r739039 + r739040;
        double r739042 = r739037 / r739041;
        return r739042;
}

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 2019135 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))