Average Error: 0.1 → 0.1
Time: 4.7s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\frac{1}{1 + e \cdot \cos v} \cdot \left(e \cdot \sin v\right)\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\frac{1}{1 + e \cdot \cos v} \cdot \left(e \cdot \sin v\right)
double f(double e, double v) {
        double r12099 = e;
        double r12100 = v;
        double r12101 = sin(r12100);
        double r12102 = r12099 * r12101;
        double r12103 = 1.0;
        double r12104 = cos(r12100);
        double r12105 = r12099 * r12104;
        double r12106 = r12103 + r12105;
        double r12107 = r12102 / r12106;
        return r12107;
}
↓
double f(double e, double v) {
        double r12108 = 1.0;
        double r12109 = 1.0;
        double r12110 = e;
        double r12111 = v;
        double r12112 = cos(r12111);
        double r12113 = r12110 * r12112;
        double r12114 = r12109 + r12113;
        double r12115 = r12108 / r12114;
        double r12116 = sin(r12111);
        double r12117 = r12110 * r12116;
        double r12118 = r12115 * r12117;
        return r12118;
}

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 associate-/l*0.3

    \[\leadsto \color{blue}{\frac{e}{\frac{1 + e \cdot \cos v}{\sin v}}}\]
  4. Using strategy rm

  5. Applied div-inv0.3

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

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

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

  7. Applied times-frac0.3

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020020 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))