Average Error: 0.1 → 0.1
Time: 23.0s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{\cos v \cdot e + 1}\]
\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 r1236068 = e;
        double r1236069 = v;
        double r1236070 = sin(r1236069);
        double r1236071 = r1236068 * r1236070;
        double r1236072 = 1.0;
        double r1236073 = cos(r1236069);
        double r1236074 = r1236068 * r1236073;
        double r1236075 = r1236072 + r1236074;
        double r1236076 = r1236071 / r1236075;
        return r1236076;
}
↓
double f(double e, double v) {
        double r1236077 = e;
        double r1236078 = v;
        double r1236079 = sin(r1236078);
        double r1236080 = r1236077 * r1236079;
        double r1236081 = cos(r1236078);
        double r1236082 = r1236081 * r1236077;
        double r1236083 = 1.0;
        double r1236084 = r1236082 + r1236083;
        double r1236085 = r1236080 / r1236084;
        return r1236085;
}

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 2019171 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))