Average Error: 0.1 → 0.1
Time: 18.7s
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 r20092 = e;
        double r20093 = v;
        double r20094 = sin(r20093);
        double r20095 = r20092 * r20094;
        double r20096 = 1.0;
        double r20097 = cos(r20093);
        double r20098 = r20092 * r20097;
        double r20099 = r20096 + r20098;
        double r20100 = r20095 / r20099;
        return r20100;
}
↓
double f(double e, double v) {
        double r20101 = e;
        double r20102 = v;
        double r20103 = sin(r20102);
        double r20104 = 1.0;
        double r20105 = cos(r20102);
        double r20106 = r20101 * r20105;
        double r20107 = r20104 + r20106;
        double r20108 = r20103 / r20107;
        double r20109 = r20101 * r20108;
        return r20109;
}

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)))))