Average Error: 0.1 → 0.1
Time: 15.0s
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 r23006 = e;
        double r23007 = v;
        double r23008 = sin(r23007);
        double r23009 = r23006 * r23008;
        double r23010 = 1.0;
        double r23011 = cos(r23007);
        double r23012 = r23006 * r23011;
        double r23013 = r23010 + r23012;
        double r23014 = r23009 / r23013;
        return r23014;
}
↓
double f(double e, double v) {
        double r23015 = e;
        double r23016 = v;
        double r23017 = sin(r23016);
        double r23018 = r23015 * r23017;
        double r23019 = 1.0;
        double r23020 = cos(r23016);
        double r23021 = r23015 * r23020;
        double r23022 = r23019 + r23021;
        double r23023 = r23018 / r23022;
        return r23023;
}

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 2019305 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))