Average Error: 0.4 → 0.3
Time: 20.4s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{1 - 5 \cdot \left(v \cdot v\right)}{t} \cdot \frac{\frac{1}{\pi}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - v \cdot v}\]
\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{1 - 5 \cdot \left(v \cdot v\right)}{t} \cdot \frac{\frac{1}{\pi}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - v \cdot v}
double f(double v, double t) {
        double r228652 = 1.0;
        double r228653 = 5.0;
        double r228654 = v;
        double r228655 = r228654 * r228654;
        double r228656 = r228653 * r228655;
        double r228657 = r228652 - r228656;
        double r228658 = atan2(1.0, 0.0);
        double r228659 = t;
        double r228660 = r228658 * r228659;
        double r228661 = 2.0;
        double r228662 = 3.0;
        double r228663 = r228662 * r228655;
        double r228664 = r228652 - r228663;
        double r228665 = r228661 * r228664;
        double r228666 = sqrt(r228665);
        double r228667 = r228660 * r228666;
        double r228668 = r228652 - r228655;
        double r228669 = r228667 * r228668;
        double r228670 = r228657 / r228669;
        return r228670;
}
↓
double f(double v, double t) {
        double r228671 = 1.0;
        double r228672 = 5.0;
        double r228673 = v;
        double r228674 = r228673 * r228673;
        double r228675 = r228672 * r228674;
        double r228676 = r228671 - r228675;
        double r228677 = t;
        double r228678 = r228676 / r228677;
        double r228679 = 1.0;
        double r228680 = atan2(1.0, 0.0);
        double r228681 = r228679 / r228680;
        double r228682 = 2.0;
        double r228683 = 3.0;
        double r228684 = r228683 * r228674;
        double r228685 = r228671 - r228684;
        double r228686 = r228682 * r228685;
        double r228687 = sqrt(r228686);
        double r228688 = r228681 / r228687;
        double r228689 = r228678 * r228688;
        double r228690 = r228671 - r228674;
        double r228691 = r228689 / r228690;
        return r228691;
}

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. Using strategy rm

  9. Applied div-inv0.3

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

  10. Applied times-frac0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019323 
(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)))))