Average Error: 0.5 → 0.5
Time: 8.6s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot \left(t \cdot \sqrt{2}\right)\right) \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
\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(\left(\pi \cdot \left(t \cdot \sqrt{2}\right)\right) \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)}
double f(double v, double t) {
        double r257525 = 1.0;
        double r257526 = 5.0;
        double r257527 = v;
        double r257528 = r257527 * r257527;
        double r257529 = r257526 * r257528;
        double r257530 = r257525 - r257529;
        double r257531 = atan2(1.0, 0.0);
        double r257532 = t;
        double r257533 = r257531 * r257532;
        double r257534 = 2.0;
        double r257535 = 3.0;
        double r257536 = r257535 * r257528;
        double r257537 = r257525 - r257536;
        double r257538 = r257534 * r257537;
        double r257539 = sqrt(r257538);
        double r257540 = r257533 * r257539;
        double r257541 = r257525 - r257528;
        double r257542 = r257540 * r257541;
        double r257543 = r257530 / r257542;
        return r257543;
}
↓
double f(double v, double t) {
        double r257544 = 1.0;
        double r257545 = 5.0;
        double r257546 = v;
        double r257547 = r257546 * r257546;
        double r257548 = r257545 * r257547;
        double r257549 = r257544 - r257548;
        double r257550 = atan2(1.0, 0.0);
        double r257551 = t;
        double r257552 = 2.0;
        double r257553 = sqrt(r257552);
        double r257554 = r257551 * r257553;
        double r257555 = r257550 * r257554;
        double r257556 = 3.0;
        double r257557 = r257556 * r257547;
        double r257558 = r257544 - r257557;
        double r257559 = sqrt(r257558);
        double r257560 = r257555 * r257559;
        double r257561 = r257544 - r257547;
        double r257562 = r257560 * r257561;
        double r257563 = r257549 / r257562;
        return r257563;
}

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 sqrt-prod0.5

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

  4. Applied associate-*r*0.5

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

  6. Applied associate-*l*0.5

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

  7. Final simplification0.5

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

Reproduce

herbie shell --seed 2020089 
(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)))))