Average Error: 0.1 → 0.1
Time: 16.5s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\sin v \cdot \frac{e}{e \cdot \cos v + 1}\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\sin v \cdot \frac{e}{e \cdot \cos v + 1}
double f(double e, double v) {
        double r929431 = e;
        double r929432 = v;
        double r929433 = sin(r929432);
        double r929434 = r929431 * r929433;
        double r929435 = 1.0;
        double r929436 = cos(r929432);
        double r929437 = r929431 * r929436;
        double r929438 = r929435 + r929437;
        double r929439 = r929434 / r929438;
        return r929439;
}
↓
double f(double e, double v) {
        double r929440 = v;
        double r929441 = sin(r929440);
        double r929442 = e;
        double r929443 = cos(r929440);
        double r929444 = r929442 * r929443;
        double r929445 = 1.0;
        double r929446 = r929444 + r929445;
        double r929447 = r929442 / r929446;
        double r929448 = r929441 * r929447;
        return r929448;
}

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 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 add-sqr-sqrt0.5

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

  7. Applied times-frac0.5

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

  8. Simplified0.4

    \[\leadsto \frac{\sqrt{e}}{1 + e \cdot \cos v} \cdot \color{blue}{\left(\sqrt{e} \cdot \sin v\right)}\]
  9. Using strategy rm

  10. Applied associate-*r*0.4

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 
(FPCore (e v)
  :name "Trigonometry A"
  :pre (<= 0.0 e 1.0)
  (/ (* e (sin v)) (+ 1.0 (* e (cos v)))))