Average Error: 0.5 → 0.5
Time: 6.4s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right) \cdot \left(1 - v \cdot v\right)}\]
\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 r234658 = 1.0;
        double r234659 = 5.0;
        double r234660 = v;
        double r234661 = r234660 * r234660;
        double r234662 = r234659 * r234661;
        double r234663 = r234658 - r234662;
        double r234664 = atan2(1.0, 0.0);
        double r234665 = t;
        double r234666 = r234664 * r234665;
        double r234667 = 2.0;
        double r234668 = 3.0;
        double r234669 = r234668 * r234661;
        double r234670 = r234658 - r234669;
        double r234671 = r234667 * r234670;
        double r234672 = sqrt(r234671);
        double r234673 = r234666 * r234672;
        double r234674 = r234658 - r234661;
        double r234675 = r234673 * r234674;
        double r234676 = r234663 / r234675;
        return r234676;
}
↓
double f(double v, double t) {
        double r234677 = 1.0;
        double r234678 = 5.0;
        double r234679 = v;
        double r234680 = r234679 * r234679;
        double r234681 = r234678 * r234680;
        double r234682 = r234677 - r234681;
        double r234683 = atan2(1.0, 0.0);
        double r234684 = t;
        double r234685 = 2.0;
        double r234686 = 3.0;
        double r234687 = r234686 * r234680;
        double r234688 = r234677 - r234687;
        double r234689 = r234685 * r234688;
        double r234690 = sqrt(r234689);
        double r234691 = r234684 * r234690;
        double r234692 = r234683 * r234691;
        double r234693 = r234677 - r234680;
        double r234694 = r234692 * r234693;
        double r234695 = r234682 / r234694;
        return r234695;
}

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 2020064 
(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)))))