Average Error: 0.1 → 0.1
Time: 15.1s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
double f(double e, double v) {
        double r21184 = e;
        double r21185 = v;
        double r21186 = sin(r21185);
        double r21187 = r21184 * r21186;
        double r21188 = 1.0;
        double r21189 = cos(r21185);
        double r21190 = r21184 * r21189;
        double r21191 = r21188 + r21190;
        double r21192 = r21187 / r21191;
        return r21192;
}
↓
double f(double e, double v) {
        double r21193 = e;
        double r21194 = v;
        double r21195 = sin(r21194);
        double r21196 = r21193 * r21195;
        double r21197 = 1.0;
        double r21198 = cos(r21194);
        double r21199 = r21193 * r21198;
        double r21200 = r21197 + r21199;
        double r21201 = r21196 / r21200;
        return r21201;
}

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

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

Reproduce

herbie shell --seed 2019212 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))