Average Error: 0.4 → 0.3
Time: 20.4s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{1 - 5 \cdot \left(v \cdot v\right)}{\pi}}{t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - v \cdot v}\]
\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{1 - 5 \cdot \left(v \cdot v\right)}{\pi}}{t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - v \cdot v}
double f(double v, double t) {
        double r222357 = 1.0;
        double r222358 = 5.0;
        double r222359 = v;
        double r222360 = r222359 * r222359;
        double r222361 = r222358 * r222360;
        double r222362 = r222357 - r222361;
        double r222363 = atan2(1.0, 0.0);
        double r222364 = t;
        double r222365 = r222363 * r222364;
        double r222366 = 2.0;
        double r222367 = 3.0;
        double r222368 = r222367 * r222360;
        double r222369 = r222357 - r222368;
        double r222370 = r222366 * r222369;
        double r222371 = sqrt(r222370);
        double r222372 = r222365 * r222371;
        double r222373 = r222357 - r222360;
        double r222374 = r222372 * r222373;
        double r222375 = r222362 / r222374;
        return r222375;
}
↓
double f(double v, double t) {
        double r222376 = 1.0;
        double r222377 = 5.0;
        double r222378 = v;
        double r222379 = r222378 * r222378;
        double r222380 = r222377 * r222379;
        double r222381 = r222376 - r222380;
        double r222382 = atan2(1.0, 0.0);
        double r222383 = r222381 / r222382;
        double r222384 = t;
        double r222385 = 2.0;
        double r222386 = 3.0;
        double r222387 = r222386 * r222379;
        double r222388 = r222376 - r222387;
        double r222389 = r222385 * r222388;
        double r222390 = sqrt(r222389);
        double r222391 = r222384 * r222390;
        double r222392 = r222383 / r222391;
        double r222393 = r222376 - r222379;
        double r222394 = r222392 / r222393;
        return r222394;
}

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 associate-/r*0.4

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

  5. Applied associate-*l*0.4

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

  7. Applied associate-/r*0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019325 
(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)))))