Average Error: 0.4 → 0.4
Time: 8.2s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\left(\pi \cdot t\right) \cdot \sqrt{2}\right) \cdot \sqrt{{1}^{3} - {\left(3 \cdot \left(v \cdot v\right)\right)}^{3}}\right) \cdot \left(1 - v \cdot v\right)} \cdot \sqrt{1 \cdot 1 + \left(\left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right) + 1 \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right)}\]
\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)}
↓
\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\left(\pi \cdot t\right) \cdot \sqrt{2}\right) \cdot \sqrt{{1}^{3} - {\left(3 \cdot \left(v \cdot v\right)\right)}^{3}}\right) \cdot \left(1 - v \cdot v\right)} \cdot \sqrt{1 \cdot 1 + \left(\left(3 \cdot \left(v \cdot v\right)\right) \cdot \left(3 \cdot \left(v \cdot v\right)\right) + 1 \cdot \left(3 \cdot \left(v \cdot v\right)\right)\right)}
double f(double v, double t) {
        double r301430 = 1.0;
        double r301431 = 5.0;
        double r301432 = v;
        double r301433 = r301432 * r301432;
        double r301434 = r301431 * r301433;
        double r301435 = r301430 - r301434;
        double r301436 = atan2(1.0, 0.0);
        double r301437 = t;
        double r301438 = r301436 * r301437;
        double r301439 = 2.0;
        double r301440 = 3.0;
        double r301441 = r301440 * r301433;
        double r301442 = r301430 - r301441;
        double r301443 = r301439 * r301442;
        double r301444 = sqrt(r301443);
        double r301445 = r301438 * r301444;
        double r301446 = r301430 - r301433;
        double r301447 = r301445 * r301446;
        double r301448 = r301435 / r301447;
        return r301448;
}
↓
double f(double v, double t) {
        double r301449 = 1.0;
        double r301450 = 5.0;
        double r301451 = v;
        double r301452 = r301451 * r301451;
        double r301453 = r301450 * r301452;
        double r301454 = r301449 - r301453;
        double r301455 = atan2(1.0, 0.0);
        double r301456 = t;
        double r301457 = r301455 * r301456;
        double r301458 = 2.0;
        double r301459 = sqrt(r301458);
        double r301460 = r301457 * r301459;
        double r301461 = 3.0;
        double r301462 = pow(r301449, r301461);
        double r301463 = 3.0;
        double r301464 = r301463 * r301452;
        double r301465 = pow(r301464, r301461);
        double r301466 = r301462 - r301465;
        double r301467 = sqrt(r301466);
        double r301468 = r301460 * r301467;
        double r301469 = r301449 - r301452;
        double r301470 = r301468 * r301469;
        double r301471 = r301454 / r301470;
        double r301472 = r301449 * r301449;
        double r301473 = r301464 * r301464;
        double r301474 = r301449 * r301464;
        double r301475 = r301473 + r301474;
        double r301476 = r301472 + r301475;
        double r301477 = sqrt(r301476);
        double r301478 = r301471 * r301477;
        return r301478;
}

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

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

  4. Applied associate-*r/0.4

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

  5. Applied sqrt-div0.4

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

  6. Applied associate-*r/0.4

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

  7. Applied associate-*l/0.4

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

  8. Applied associate-/r/0.4

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

  10. Applied sqrt-prod0.4

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

  11. Applied associate-*r*0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2020047 
(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)))))