Average Error: 0.5 → 0.5
Time: 8.8s
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 r314844 = 1.0;
        double r314845 = 5.0;
        double r314846 = v;
        double r314847 = r314846 * r314846;
        double r314848 = r314845 * r314847;
        double r314849 = r314844 - r314848;
        double r314850 = atan2(1.0, 0.0);
        double r314851 = t;
        double r314852 = r314850 * r314851;
        double r314853 = 2.0;
        double r314854 = 3.0;
        double r314855 = r314854 * r314847;
        double r314856 = r314844 - r314855;
        double r314857 = r314853 * r314856;
        double r314858 = sqrt(r314857);
        double r314859 = r314852 * r314858;
        double r314860 = r314844 - r314847;
        double r314861 = r314859 * r314860;
        double r314862 = r314849 / r314861;
        return r314862;
}
↓
double f(double v, double t) {
        double r314863 = 1.0;
        double r314864 = 5.0;
        double r314865 = v;
        double r314866 = r314865 * r314865;
        double r314867 = r314864 * r314866;
        double r314868 = r314863 - r314867;
        double r314869 = atan2(1.0, 0.0);
        double r314870 = t;
        double r314871 = 2.0;
        double r314872 = 3.0;
        double r314873 = r314872 * r314866;
        double r314874 = r314863 - r314873;
        double r314875 = r314871 * r314874;
        double r314876 = sqrt(r314875);
        double r314877 = r314870 * r314876;
        double r314878 = r314869 * r314877;
        double r314879 = r314863 - r314866;
        double r314880 = r314878 * r314879;
        double r314881 = r314868 / r314880;
        return r314881;
}

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 2020057 
(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)))))