Average Error: 0.4 → 0.5
Time: 9.6s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right) \cdot \left(1 - v \cdot v\right)}\]
\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}
↓
\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right) \cdot \left(1 - v \cdot v\right)}
double f(double v, double t) {
        double r258682 = 1.0;
        double r258683 = 5.0;
        double r258684 = v;
        double r258685 = r258684 * r258684;
        double r258686 = r258683 * r258685;
        double r258687 = r258682 - r258686;
        double r258688 = atan2(1.0, 0.0);
        double r258689 = t;
        double r258690 = r258688 * r258689;
        double r258691 = 2.0;
        double r258692 = 3.0;
        double r258693 = r258692 * r258685;
        double r258694 = r258682 - r258693;
        double r258695 = r258691 * r258694;
        double r258696 = sqrt(r258695);
        double r258697 = r258690 * r258696;
        double r258698 = r258682 - r258685;
        double r258699 = r258697 * r258698;
        double r258700 = r258687 / r258699;
        return r258700;
}
↓
double f(double v, double t) {
        double r258701 = 1.0;
        double r258702 = 5.0;
        double r258703 = v;
        double r258704 = r258703 * r258703;
        double r258705 = r258702 * r258704;
        double r258706 = r258701 - r258705;
        double r258707 = atan2(1.0, 0.0);
        double r258708 = t;
        double r258709 = 2.0;
        double r258710 = 3.0;
        double r258711 = r258710 * r258704;
        double r258712 = r258701 - r258711;
        double r258713 = r258709 * r258712;
        double r258714 = sqrt(r258713);
        double r258715 = r258708 * r258714;
        double r258716 = r258707 * r258715;
        double r258717 = r258701 - r258704;
        double r258718 = r258716 * r258717;
        double r258719 = r258706 / r258718;
        return r258719;
}

Error

Bits error versus v

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
  2. Using strategy rm

  3. Applied associate-*l*0.5

    \[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\color{blue}{\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right)} \cdot \left(1 - v \cdot v\right)}\]

  4. Final simplification0.5

    \[\leadsto \frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right) \cdot \left(1 - v \cdot v\right)}\]

Reproduce

herbie shell --seed 2020021 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  :precision binary64
  (/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v)))))