Average Error: 0.1 → 0.1
Time: 12.5s
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 r19908 = e;
        double r19909 = v;
        double r19910 = sin(r19909);
        double r19911 = r19908 * r19910;
        double r19912 = 1.0;
        double r19913 = cos(r19909);
        double r19914 = r19908 * r19913;
        double r19915 = r19912 + r19914;
        double r19916 = r19911 / r19915;
        return r19916;
}
↓
double f(double e, double v) {
        double r19917 = e;
        double r19918 = v;
        double r19919 = sin(r19918);
        double r19920 = 1.0;
        double r19921 = cos(r19918);
        double r19922 = r19917 * r19921;
        double r19923 = r19920 + r19922;
        double r19924 = r19919 / r19923;
        double r19925 = r19917 * r19924;
        return r19925;
}

Error

Bits error versus e

Bits error versus v

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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 2019303 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))