Average Error: 0.4 → 0.4
Time: 8.1s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{\frac{1 - 5 \cdot \left(v \cdot v\right)}{\pi \cdot t}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - v \cdot v}\]
\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 \cdot t}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - v \cdot v}
double f(double v, double t) {
        double r255611 = 1.0;
        double r255612 = 5.0;
        double r255613 = v;
        double r255614 = r255613 * r255613;
        double r255615 = r255612 * r255614;
        double r255616 = r255611 - r255615;
        double r255617 = atan2(1.0, 0.0);
        double r255618 = t;
        double r255619 = r255617 * r255618;
        double r255620 = 2.0;
        double r255621 = 3.0;
        double r255622 = r255621 * r255614;
        double r255623 = r255611 - r255622;
        double r255624 = r255620 * r255623;
        double r255625 = sqrt(r255624);
        double r255626 = r255619 * r255625;
        double r255627 = r255611 - r255614;
        double r255628 = r255626 * r255627;
        double r255629 = r255616 / r255628;
        return r255629;
}
↓
double f(double v, double t) {
        double r255630 = 1.0;
        double r255631 = 5.0;
        double r255632 = v;
        double r255633 = r255632 * r255632;
        double r255634 = r255631 * r255633;
        double r255635 = r255630 - r255634;
        double r255636 = atan2(1.0, 0.0);
        double r255637 = t;
        double r255638 = r255636 * r255637;
        double r255639 = r255635 / r255638;
        double r255640 = 2.0;
        double r255641 = 3.0;
        double r255642 = r255641 * r255633;
        double r255643 = r255630 - r255642;
        double r255644 = r255640 * r255643;
        double r255645 = sqrt(r255644);
        double r255646 = r255639 / r255645;
        double r255647 = r255630 - r255633;
        double r255648 = r255646 / r255647;
        return r255648;
}

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-/r*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2020081 
(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)))))