Average Error: 0.5 → 0.5
Time: 8.4s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
\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 r231851 = 1.0;
        double r231852 = 5.0;
        double r231853 = v;
        double r231854 = r231853 * r231853;
        double r231855 = r231852 * r231854;
        double r231856 = r231851 - r231855;
        double r231857 = atan2(1.0, 0.0);
        double r231858 = t;
        double r231859 = r231857 * r231858;
        double r231860 = 2.0;
        double r231861 = 3.0;
        double r231862 = r231861 * r231854;
        double r231863 = r231851 - r231862;
        double r231864 = r231860 * r231863;
        double r231865 = sqrt(r231864);
        double r231866 = r231859 * r231865;
        double r231867 = r231851 - r231854;
        double r231868 = r231866 * r231867;
        double r231869 = r231856 / r231868;
        return r231869;
}
↓
double f(double v, double t) {
        double r231870 = 1.0;
        double r231871 = 5.0;
        double r231872 = v;
        double r231873 = r231872 * r231872;
        double r231874 = r231871 * r231873;
        double r231875 = r231870 - r231874;
        double r231876 = atan2(1.0, 0.0);
        double r231877 = t;
        double r231878 = r231876 * r231877;
        double r231879 = 2.0;
        double r231880 = 3.0;
        double r231881 = r231880 * r231873;
        double r231882 = r231870 - r231881;
        double r231883 = r231879 * r231882;
        double r231884 = sqrt(r231883);
        double r231885 = r231878 * r231884;
        double r231886 = r231870 - r231873;
        double r231887 = r231885 * r231886;
        double r231888 = r231875 / r231887;
        return r231888;
}

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 
(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)))))