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 r882167 = e;
        double r882168 = v;
        double r882169 = sin(r882168);
        double r882170 = r882167 * r882169;
        double r882171 = 1.0;
        double r882172 = cos(r882168);
        double r882173 = r882167 * r882172;
        double r882174 = r882171 + r882173;
        double r882175 = r882170 / r882174;
        return r882175;
}
↓
double f(double e, double v) {
        double r882176 = v;
        double r882177 = sin(r882176);
        double r882178 = 1.0;
        double r882179 = cos(r882176);
        double r882180 = e;
        double r882181 = r882179 * r882180;
        double r882182 = r882178 + r882181;
        double r882183 = r882177 / r882182;
        double r882184 = r882183 * r882180;
        return r882184;
}

Error

Bits error versus e

Bits error versus v

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Your Program's Arguments

Results

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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)))))