Average Error: 0.5 → 0.1
Time: 37.6s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{\frac{1 + \left(v \cdot v\right) \cdot -5}{\pi}}{\sqrt{\left(1 - 9 \cdot \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)\right) \cdot 2}}}{t}}{1 - \left(v \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot \left(v \cdot v\right)\right)} \cdot \left(\sqrt{\left(v \cdot v\right) \cdot 3 + 1} \cdot \left(\left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + v \cdot v\right) + 1\right)\right)\]
\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{\frac{\frac{\frac{1 + \left(v \cdot v\right) \cdot -5}{\pi}}{\sqrt{\left(1 - 9 \cdot \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)\right) \cdot 2}}}{t}}{1 - \left(v \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot \left(v \cdot v\right)\right)} \cdot \left(\sqrt{\left(v \cdot v\right) \cdot 3 + 1} \cdot \left(\left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + v \cdot v\right) + 1\right)\right)
double f(double v, double t) {
        double r4792324 = 1.0;
        double r4792325 = 5.0;
        double r4792326 = v;
        double r4792327 = r4792326 * r4792326;
        double r4792328 = r4792325 * r4792327;
        double r4792329 = r4792324 - r4792328;
        double r4792330 = atan2(1.0, 0.0);
        double r4792331 = t;
        double r4792332 = r4792330 * r4792331;
        double r4792333 = 2.0;
        double r4792334 = 3.0;
        double r4792335 = r4792334 * r4792327;
        double r4792336 = r4792324 - r4792335;
        double r4792337 = r4792333 * r4792336;
        double r4792338 = sqrt(r4792337);
        double r4792339 = r4792332 * r4792338;
        double r4792340 = r4792324 - r4792327;
        double r4792341 = r4792339 * r4792340;
        double r4792342 = r4792329 / r4792341;
        return r4792342;
}
↓
double f(double v, double t) {
        double r4792343 = 1.0;
        double r4792344 = v;
        double r4792345 = r4792344 * r4792344;
        double r4792346 = -5.0;
        double r4792347 = r4792345 * r4792346;
        double r4792348 = r4792343 + r4792347;
        double r4792349 = atan2(1.0, 0.0);
        double r4792350 = r4792348 / r4792349;
        double r4792351 = 9.0;
        double r4792352 = r4792345 * r4792345;
        double r4792353 = r4792351 * r4792352;
        double r4792354 = r4792343 - r4792353;
        double r4792355 = 2.0;
        double r4792356 = r4792354 * r4792355;
        double r4792357 = sqrt(r4792356);
        double r4792358 = r4792350 / r4792357;
        double r4792359 = t;
        double r4792360 = r4792358 / r4792359;
        double r4792361 = r4792344 * r4792345;
        double r4792362 = r4792361 * r4792361;
        double r4792363 = r4792343 - r4792362;
        double r4792364 = r4792360 / r4792363;
        double r4792365 = 3.0;
        double r4792366 = r4792345 * r4792365;
        double r4792367 = r4792366 + r4792343;
        double r4792368 = sqrt(r4792367);
        double r4792369 = r4792352 + r4792345;
        double r4792370 = r4792369 + r4792343;
        double r4792371 = r4792368 * r4792370;
        double r4792372 = r4792364 * r4792371;
        return r4792372;
}

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 0.5

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

  3. Applied flip3--0.5

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

  4. Applied flip--0.5

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

  5. Applied associate-*r/0.5

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

  6. Applied sqrt-div0.5

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

  7. Applied associate-*r/0.5

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

  8. Applied frac-times0.5

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

  9. Applied associate-/r/0.5

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

  10. Simplified0.4

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

  12. Applied associate-/r*0.1

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

  13. Simplified0.1

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

  14. Final simplification0.1

    \[\leadsto \frac{\frac{\frac{\frac{1 + \left(v \cdot v\right) \cdot -5}{\pi}}{\sqrt{\left(1 - 9 \cdot \left(\left(v \cdot v\right) \cdot \left(v \cdot v\right)\right)\right) \cdot 2}}}{t}}{1 - \left(v \cdot \left(v \cdot v\right)\right) \cdot \left(v \cdot \left(v \cdot v\right)\right)} \cdot \left(\sqrt{\left(v \cdot v\right) \cdot 3 + 1} \cdot \left(\left(\left(v \cdot v\right) \cdot \left(v \cdot v\right) + v \cdot v\right) + 1\right)\right)\]

Reproduce

herbie shell --seed 2019139 
(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)))))