Average Error: 0.4 → 0.1
Time: 26.0s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\left(1 \cdot 1 + \left(\left(v \cdot v\right) \cdot 1 + \left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)\right) \cdot \frac{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{\sqrt{\left(1 - 3 \cdot \left(v \cdot v\right)\right) \cdot 2}}}{t}}{1 \cdot \left(1 \cdot 1\right) - \left(v \cdot v\right) \cdot \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)}\]
\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)}
↓
\left(1 \cdot 1 + \left(\left(v \cdot v\right) \cdot 1 + \left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)\right) \cdot \frac{\frac{\frac{\frac{1 - \left(v \cdot v\right) \cdot 5}{\pi}}{\sqrt{\left(1 - 3 \cdot \left(v \cdot v\right)\right) \cdot 2}}}{t}}{1 \cdot \left(1 \cdot 1\right) - \left(v \cdot v\right) \cdot \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)}
double f(double v, double t) {
        double r9576742 = 1.0;
        double r9576743 = 5.0;
        double r9576744 = v;
        double r9576745 = r9576744 * r9576744;
        double r9576746 = r9576743 * r9576745;
        double r9576747 = r9576742 - r9576746;
        double r9576748 = atan2(1.0, 0.0);
        double r9576749 = t;
        double r9576750 = r9576748 * r9576749;
        double r9576751 = 2.0;
        double r9576752 = 3.0;
        double r9576753 = r9576752 * r9576745;
        double r9576754 = r9576742 - r9576753;
        double r9576755 = r9576751 * r9576754;
        double r9576756 = sqrt(r9576755);
        double r9576757 = r9576750 * r9576756;
        double r9576758 = r9576742 - r9576745;
        double r9576759 = r9576757 * r9576758;
        double r9576760 = r9576747 / r9576759;
        return r9576760;
}
↓
double f(double v, double t) {
        double r9576761 = 1.0;
        double r9576762 = r9576761 * r9576761;
        double r9576763 = v;
        double r9576764 = r9576763 * r9576763;
        double r9576765 = r9576764 * r9576761;
        double r9576766 = r9576764 * r9576764;
        double r9576767 = r9576765 + r9576766;
        double r9576768 = r9576762 + r9576767;
        double r9576769 = 5.0;
        double r9576770 = r9576764 * r9576769;
        double r9576771 = r9576761 - r9576770;
        double r9576772 = atan2(1.0, 0.0);
        double r9576773 = r9576771 / r9576772;
        double r9576774 = 3.0;
        double r9576775 = r9576774 * r9576764;
        double r9576776 = r9576761 - r9576775;
        double r9576777 = 2.0;
        double r9576778 = r9576776 * r9576777;
        double r9576779 = sqrt(r9576778);
        double r9576780 = r9576773 / r9576779;
        double r9576781 = t;
        double r9576782 = r9576780 / r9576781;
        double r9576783 = r9576761 * r9576762;
        double r9576784 = r9576764 * r9576766;
        double r9576785 = r9576783 - r9576784;
        double r9576786 = r9576782 / r9576785;
        double r9576787 = r9576768 * r9576786;
        return r9576787;
}

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 flip3--0.4

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

  4. Applied associate-*r/0.4

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

  5. Applied associate-/r/0.4

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

  6. Simplified0.3

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

  8. Applied associate-/r*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  (/ (- 1.0 (* 5.0 (* v v))) (* (* (* PI t) (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v)))))) (- 1.0 (* v v)))))