Average Error: 0.1 → 0.1
Time: 39.5s
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 r1005206 = e;
        double r1005207 = v;
        double r1005208 = sin(r1005207);
        double r1005209 = r1005206 * r1005208;
        double r1005210 = 1.0;
        double r1005211 = cos(r1005207);
        double r1005212 = r1005206 * r1005211;
        double r1005213 = r1005210 + r1005212;
        double r1005214 = r1005209 / r1005213;
        return r1005214;
}
↓
double f(double e, double v) {
        double r1005215 = e;
        double r1005216 = v;
        double r1005217 = sin(r1005216);
        double r1005218 = r1005215 * r1005217;
        double r1005219 = cos(r1005216);
        double r1005220 = r1005219 * r1005215;
        double r1005221 = 1.0;
        double r1005222 = r1005220 + r1005221;
        double r1005223 = r1005218 / r1005222;
        return r1005223;
}

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 2019151 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))