Average Error: 0.4 → 0.4
Time: 7.9s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right) \cdot \left(1 - v \cdot v\right)}\]
\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 r281160 = 1.0;
        double r281161 = 5.0;
        double r281162 = v;
        double r281163 = r281162 * r281162;
        double r281164 = r281161 * r281163;
        double r281165 = r281160 - r281164;
        double r281166 = atan2(1.0, 0.0);
        double r281167 = t;
        double r281168 = r281166 * r281167;
        double r281169 = 2.0;
        double r281170 = 3.0;
        double r281171 = r281170 * r281163;
        double r281172 = r281160 - r281171;
        double r281173 = r281169 * r281172;
        double r281174 = sqrt(r281173);
        double r281175 = r281168 * r281174;
        double r281176 = r281160 - r281163;
        double r281177 = r281175 * r281176;
        double r281178 = r281165 / r281177;
        return r281178;
}
↓
double f(double v, double t) {
        double r281179 = 1.0;
        double r281180 = 5.0;
        double r281181 = v;
        double r281182 = r281181 * r281181;
        double r281183 = r281180 * r281182;
        double r281184 = r281179 - r281183;
        double r281185 = atan2(1.0, 0.0);
        double r281186 = t;
        double r281187 = 2.0;
        double r281188 = 3.0;
        double r281189 = r281188 * r281182;
        double r281190 = r281179 - r281189;
        double r281191 = r281187 * r281190;
        double r281192 = sqrt(r281191);
        double r281193 = r281186 * r281192;
        double r281194 = r281185 * r281193;
        double r281195 = r281179 - r281182;
        double r281196 = r281194 * r281195;
        double r281197 = r281184 / r281196;
        return r281197;
}

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 2020062 
(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)))))