Average Error: 0.5 → 0.5
Time: 8.9s
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 r304896 = 1.0;
        double r304897 = 5.0;
        double r304898 = v;
        double r304899 = r304898 * r304898;
        double r304900 = r304897 * r304899;
        double r304901 = r304896 - r304900;
        double r304902 = atan2(1.0, 0.0);
        double r304903 = t;
        double r304904 = r304902 * r304903;
        double r304905 = 2.0;
        double r304906 = 3.0;
        double r304907 = r304906 * r304899;
        double r304908 = r304896 - r304907;
        double r304909 = r304905 * r304908;
        double r304910 = sqrt(r304909);
        double r304911 = r304904 * r304910;
        double r304912 = r304896 - r304899;
        double r304913 = r304911 * r304912;
        double r304914 = r304901 / r304913;
        return r304914;
}
↓
double f(double v, double t) {
        double r304915 = 1.0;
        double r304916 = 5.0;
        double r304917 = v;
        double r304918 = r304917 * r304917;
        double r304919 = r304916 * r304918;
        double r304920 = r304915 - r304919;
        double r304921 = atan2(1.0, 0.0);
        double r304922 = t;
        double r304923 = r304921 * r304922;
        double r304924 = 2.0;
        double r304925 = 3.0;
        double r304926 = r304925 * r304918;
        double r304927 = r304915 - r304926;
        double r304928 = r304924 * r304927;
        double r304929 = sqrt(r304928);
        double r304930 = r304923 * r304929;
        double r304931 = r304915 - r304918;
        double r304932 = r304930 * r304931;
        double r304933 = r304920 / r304932;
        return r304933;
}

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 2020020 +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)))))