Average Error: 0.1 → 0.1
Time: 19.4s
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 r899948 = e;
        double r899949 = v;
        double r899950 = sin(r899949);
        double r899951 = r899948 * r899950;
        double r899952 = 1.0;
        double r899953 = cos(r899949);
        double r899954 = r899948 * r899953;
        double r899955 = r899952 + r899954;
        double r899956 = r899951 / r899955;
        return r899956;
}
↓
double f(double e, double v) {
        double r899957 = e;
        double r899958 = v;
        double r899959 = sin(r899958);
        double r899960 = r899957 * r899959;
        double r899961 = cos(r899958);
        double r899962 = r899961 * r899957;
        double r899963 = 1.0;
        double r899964 = r899962 + r899963;
        double r899965 = r899960 / r899964;
        return r899965;
}

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 2019162 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))