Average Error: 0.1 → 0.1
Time: 19.9s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[e \cdot \frac{\sin v}{1 + e \cdot \cos v}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
e \cdot \frac{\sin v}{1 + e \cdot \cos v}
double f(double e, double v) {
        double r19990 = e;
        double r19991 = v;
        double r19992 = sin(r19991);
        double r19993 = r19990 * r19992;
        double r19994 = 1.0;
        double r19995 = cos(r19991);
        double r19996 = r19990 * r19995;
        double r19997 = r19994 + r19996;
        double r19998 = r19993 / r19997;
        return r19998;
}
↓
double f(double e, double v) {
        double r19999 = e;
        double r20000 = v;
        double r20001 = sin(r20000);
        double r20002 = 1.0;
        double r20003 = cos(r20000);
        double r20004 = r19999 * r20003;
        double r20005 = r20002 + r20004;
        double r20006 = r20001 / r20005;
        double r20007 = r19999 * r20006;
        return r20007;
}

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. Using strategy rm

  3. Applied *-un-lft-identity0.1

    \[\leadsto \frac{e \cdot \sin v}{\color{blue}{1 \cdot \left(1 + e \cdot \cos v\right)}}\]

  4. Applied times-frac0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))