Average Error: 0.4 → 0.4
Time: 19.3s
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 r182915 = 1.0;
        double r182916 = 5.0;
        double r182917 = v;
        double r182918 = r182917 * r182917;
        double r182919 = r182916 * r182918;
        double r182920 = r182915 - r182919;
        double r182921 = atan2(1.0, 0.0);
        double r182922 = t;
        double r182923 = r182921 * r182922;
        double r182924 = 2.0;
        double r182925 = 3.0;
        double r182926 = r182925 * r182918;
        double r182927 = r182915 - r182926;
        double r182928 = r182924 * r182927;
        double r182929 = sqrt(r182928);
        double r182930 = r182923 * r182929;
        double r182931 = r182915 - r182918;
        double r182932 = r182930 * r182931;
        double r182933 = r182920 / r182932;
        return r182933;
}
↓
double f(double v, double t) {
        double r182934 = 1.0;
        double r182935 = 5.0;
        double r182936 = v;
        double r182937 = r182936 * r182936;
        double r182938 = r182935 * r182937;
        double r182939 = r182934 - r182938;
        double r182940 = atan2(1.0, 0.0);
        double r182941 = t;
        double r182942 = 2.0;
        double r182943 = 3.0;
        double r182944 = r182943 * r182937;
        double r182945 = r182934 - r182944;
        double r182946 = r182942 * r182945;
        double r182947 = sqrt(r182946);
        double r182948 = r182941 * r182947;
        double r182949 = r182940 * r182948;
        double r182950 = r182934 - r182937;
        double r182951 = r182949 * r182950;
        double r182952 = r182939 / r182951;
        return r182952;
}

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-*l*0.4

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

  4. Final simplification0.4

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

Reproduce

herbie shell --seed 2019209 
(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)))))