Average Error: 0.1 → 0.1
Time: 27.4s
Precision: 64
\[0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{\sin v}{1 + \cos v \cdot e} \cdot e\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{\sin v}{1 + \cos v \cdot e} \cdot e
double f(double e, double v) {
        double r830255 = e;
        double r830256 = v;
        double r830257 = sin(r830256);
        double r830258 = r830255 * r830257;
        double r830259 = 1.0;
        double r830260 = cos(r830256);
        double r830261 = r830255 * r830260;
        double r830262 = r830259 + r830261;
        double r830263 = r830258 / r830262;
        return r830263;
}
↓
double f(double e, double v) {
        double r830264 = v;
        double r830265 = sin(r830264);
        double r830266 = 1.0;
        double r830267 = cos(r830264);
        double r830268 = e;
        double r830269 = r830267 * r830268;
        double r830270 = r830266 + r830269;
        double r830271 = r830265 / r830270;
        double r830272 = r830271 * r830268;
        return r830272;
}

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

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

Reproduce

herbie shell --seed 2019152 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))