Average Error: 0.4 → 0.3
Time: 29.4s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\left(\left(v \cdot v + \left(v \cdot v\right) \cdot \left(v \cdot v\right)\right) + 1\right) \cdot \frac{\frac{\frac{\sqrt{1 - v \cdot \left(v \cdot 5\right)}}{t}}{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}} \cdot \frac{\frac{\sqrt{1 - v \cdot \left(v \cdot 5\right)}}{\pi}}{\sqrt{2}}}{1 - \left(v \cdot v\right) \cdot \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)}\]
\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(\left(v \cdot v + \left(v \cdot v\right) \cdot \left(v \cdot v\right)\right) + 1\right) \cdot \frac{\frac{\frac{\sqrt{1 - v \cdot \left(v \cdot 5\right)}}{t}}{\sqrt{1 - 3 \cdot \left(v \cdot v\right)}} \cdot \frac{\frac{\sqrt{1 - v \cdot \left(v \cdot 5\right)}}{\pi}}{\sqrt{2}}}{1 - \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 r7345974 = 1.0;
        double r7345975 = 5.0;
        double r7345976 = v;
        double r7345977 = r7345976 * r7345976;
        double r7345978 = r7345975 * r7345977;
        double r7345979 = r7345974 - r7345978;
        double r7345980 = atan2(1.0, 0.0);
        double r7345981 = t;
        double r7345982 = r7345980 * r7345981;
        double r7345983 = 2.0;
        double r7345984 = 3.0;
        double r7345985 = r7345984 * r7345977;
        double r7345986 = r7345974 - r7345985;
        double r7345987 = r7345983 * r7345986;
        double r7345988 = sqrt(r7345987);
        double r7345989 = r7345982 * r7345988;
        double r7345990 = r7345974 - r7345977;
        double r7345991 = r7345989 * r7345990;
        double r7345992 = r7345979 / r7345991;
        return r7345992;
}
↓
double f(double v, double t) {
        double r7345993 = v;
        double r7345994 = r7345993 * r7345993;
        double r7345995 = r7345994 * r7345994;
        double r7345996 = r7345994 + r7345995;
        double r7345997 = 1.0;
        double r7345998 = r7345996 + r7345997;
        double r7345999 = 5.0;
        double r7346000 = r7345993 * r7345999;
        double r7346001 = r7345993 * r7346000;
        double r7346002 = r7345997 - r7346001;
        double r7346003 = sqrt(r7346002);
        double r7346004 = t;
        double r7346005 = r7346003 / r7346004;
        double r7346006 = 3.0;
        double r7346007 = r7346006 * r7345994;
        double r7346008 = r7345997 - r7346007;
        double r7346009 = sqrt(r7346008);
        double r7346010 = r7346005 / r7346009;
        double r7346011 = atan2(1.0, 0.0);
        double r7346012 = r7346003 / r7346011;
        double r7346013 = 2.0;
        double r7346014 = sqrt(r7346013);
        double r7346015 = r7346012 / r7346014;
        double r7346016 = r7346010 * r7346015;
        double r7346017 = r7345994 * r7345995;
        double r7346018 = r7345997 - r7346017;
        double r7346019 = r7346016 / r7346018;
        double r7346020 = r7345998 * r7346019;
        return r7346020;
}

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. Simplified0.4

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

  8. Applied sqrt-prod0.4

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

  9. Applied add-sqr-sqrt0.5

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

  10. Applied times-frac0.4

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

  11. Applied times-frac0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019164 
(FPCore (v t)
  :name "Falkner and Boettcher, Equation (20:1,3)"
  (/ (- 1 (* 5 (* v v))) (* (* (* PI t) (sqrt (* 2 (- 1 (* 3 (* v v)))))) (- 1 (* v v)))))