Average Error: 0.1 → 0.4
Time: 5.1s
Precision: 64
\[0.0 \le e \le 1\]
\[\frac{e \cdot \sin v}{1 + e \cdot \cos v}\]
↓
\[\sqrt{e} \cdot \left(\sqrt{e} \cdot \frac{\sin v}{1 + e \cdot \cos v}\right)\]
\frac{e \cdot \sin v}{1 + e \cdot \cos v}
↓
\sqrt{e} \cdot \left(\sqrt{e} \cdot \frac{\sin v}{1 + e \cdot \cos v}\right)
double f(double e, double v) {
        double r13555 = e;
        double r13556 = v;
        double r13557 = sin(r13556);
        double r13558 = r13555 * r13557;
        double r13559 = 1.0;
        double r13560 = cos(r13556);
        double r13561 = r13555 * r13560;
        double r13562 = r13559 + r13561;
        double r13563 = r13558 / r13562;
        return r13563;
}
↓
double f(double e, double v) {
        double r13564 = e;
        double r13565 = sqrt(r13564);
        double r13566 = v;
        double r13567 = sin(r13566);
        double r13568 = 1.0;
        double r13569 = cos(r13566);
        double r13570 = r13564 * r13569;
        double r13571 = r13568 + r13570;
        double r13572 = r13567 / r13571;
        double r13573 = r13565 * r13572;
        double r13574 = r13565 * r13573;
        return r13574;
}

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 *-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. Using strategy rm

  7. Applied add-sqr-sqrt0.4

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

  8. Applied associate-*l*0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2020046 
(FPCore (e v)
  :name "Trigonometry A"
  :precision binary64
  :pre (<= 0.0 e 1)
  (/ (* e (sin v)) (+ 1 (* e (cos v)))))