Average Error: 0.5 → 0.5
Time: 10.9s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right) \cdot \left(1 - v \cdot v\right)}\]
\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(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right) \cdot \left(1 - v \cdot v\right)}
double f(double v, double t) {
        double r314351 = 1.0;
        double r314352 = 5.0;
        double r314353 = v;
        double r314354 = r314353 * r314353;
        double r314355 = r314352 * r314354;
        double r314356 = r314351 - r314355;
        double r314357 = atan2(1.0, 0.0);
        double r314358 = t;
        double r314359 = r314357 * r314358;
        double r314360 = 2.0;
        double r314361 = 3.0;
        double r314362 = r314361 * r314354;
        double r314363 = r314351 - r314362;
        double r314364 = r314360 * r314363;
        double r314365 = sqrt(r314364);
        double r314366 = r314359 * r314365;
        double r314367 = r314351 - r314354;
        double r314368 = r314366 * r314367;
        double r314369 = r314356 / r314368;
        return r314369;
}
↓
double f(double v, double t) {
        double r314370 = 1.0;
        double r314371 = 5.0;
        double r314372 = v;
        double r314373 = r314372 * r314372;
        double r314374 = r314371 * r314373;
        double r314375 = r314370 - r314374;
        double r314376 = atan2(1.0, 0.0);
        double r314377 = t;
        double r314378 = 2.0;
        double r314379 = 3.0;
        double r314380 = r314379 * r314373;
        double r314381 = r314370 - r314380;
        double r314382 = r314378 * r314381;
        double r314383 = sqrt(r314382);
        double r314384 = r314377 * r314383;
        double r314385 = r314376 * r314384;
        double r314386 = r314370 - r314373;
        double r314387 = r314385 * r314386;
        double r314388 = r314375 / r314387;
        return r314388;
}

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 associate-*l*0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2020039 
(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)))))