Average Error: 0.4 → 0.4
Time: 17.6s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{1 - 5 \cdot \left(v \cdot v\right)}{1 - v \cdot v}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)} \cdot \left(t \cdot \pi\right)}\]
\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{\frac{1 - 5 \cdot \left(v \cdot v\right)}{1 - v \cdot v}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)} \cdot \left(t \cdot \pi\right)}
double f(double v, double t) {
        double r168453 = 1.0;
        double r168454 = 5.0;
        double r168455 = v;
        double r168456 = r168455 * r168455;
        double r168457 = r168454 * r168456;
        double r168458 = r168453 - r168457;
        double r168459 = atan2(1.0, 0.0);
        double r168460 = t;
        double r168461 = r168459 * r168460;
        double r168462 = 2.0;
        double r168463 = 3.0;
        double r168464 = r168463 * r168456;
        double r168465 = r168453 - r168464;
        double r168466 = r168462 * r168465;
        double r168467 = sqrt(r168466);
        double r168468 = r168461 * r168467;
        double r168469 = r168453 - r168456;
        double r168470 = r168468 * r168469;
        double r168471 = r168458 / r168470;
        return r168471;
}
↓
double f(double v, double t) {
        double r168472 = 1.0;
        double r168473 = 5.0;
        double r168474 = v;
        double r168475 = r168474 * r168474;
        double r168476 = r168473 * r168475;
        double r168477 = r168472 - r168476;
        double r168478 = r168472 - r168475;
        double r168479 = r168477 / r168478;
        double r168480 = 2.0;
        double r168481 = 3.0;
        double r168482 = r168481 * r168475;
        double r168483 = r168472 - r168482;
        double r168484 = r168480 * r168483;
        double r168485 = sqrt(r168484);
        double r168486 = t;
        double r168487 = atan2(1.0, 0.0);
        double r168488 = r168486 * r168487;
        double r168489 = r168485 * r168488;
        double r168490 = r168479 / r168489;
        return r168490;
}

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 *-un-lft-identity0.4

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

  4. Applied times-frac0.4

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

  6. Applied associate-/r*0.4

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

  8. Applied associate-/r*0.3

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019291 
(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)))))