Average Error: 0.5 → 0.5
Time: 9.9s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot 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 t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}
double f(double v, double t) {
        double r223991 = 1.0;
        double r223992 = 5.0;
        double r223993 = v;
        double r223994 = r223993 * r223993;
        double r223995 = r223992 * r223994;
        double r223996 = r223991 - r223995;
        double r223997 = atan2(1.0, 0.0);
        double r223998 = t;
        double r223999 = r223997 * r223998;
        double r224000 = 2.0;
        double r224001 = 3.0;
        double r224002 = r224001 * r223994;
        double r224003 = r223991 - r224002;
        double r224004 = r224000 * r224003;
        double r224005 = sqrt(r224004);
        double r224006 = r223999 * r224005;
        double r224007 = r223991 - r223994;
        double r224008 = r224006 * r224007;
        double r224009 = r223996 / r224008;
        return r224009;
}
↓
double f(double v, double t) {
        double r224010 = 1.0;
        double r224011 = 5.0;
        double r224012 = v;
        double r224013 = r224012 * r224012;
        double r224014 = r224011 * r224013;
        double r224015 = r224010 - r224014;
        double r224016 = atan2(1.0, 0.0);
        double r224017 = t;
        double r224018 = r224016 * r224017;
        double r224019 = 2.0;
        double r224020 = 3.0;
        double r224021 = r224020 * r224013;
        double r224022 = r224010 - r224021;
        double r224023 = r224019 * r224022;
        double r224024 = sqrt(r224023);
        double r224025 = r224018 * r224024;
        double r224026 = r224010 - r224013;
        double r224027 = r224025 * r224026;
        double r224028 = r224015 / r224027;
        return r224028;
}

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. Final simplification0.5

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

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(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)))))