Average Error: 0.4 → 0.4
Time: 8.0s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{1}{\frac{\left(\pi \cdot \left(t \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right)\right) \cdot \left(1 - v \cdot v\right)}{1 - 5 \cdot \left(v \cdot v\right)}}\]
\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}{\frac{\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)}{1 - 5 \cdot \left(v \cdot v\right)}}
double f(double v, double t) {
        double r331275 = 1.0;
        double r331276 = 5.0;
        double r331277 = v;
        double r331278 = r331277 * r331277;
        double r331279 = r331276 * r331278;
        double r331280 = r331275 - r331279;
        double r331281 = atan2(1.0, 0.0);
        double r331282 = t;
        double r331283 = r331281 * r331282;
        double r331284 = 2.0;
        double r331285 = 3.0;
        double r331286 = r331285 * r331278;
        double r331287 = r331275 - r331286;
        double r331288 = r331284 * r331287;
        double r331289 = sqrt(r331288);
        double r331290 = r331283 * r331289;
        double r331291 = r331275 - r331278;
        double r331292 = r331290 * r331291;
        double r331293 = r331280 / r331292;
        return r331293;
}
↓
double f(double v, double t) {
        double r331294 = 1.0;
        double r331295 = atan2(1.0, 0.0);
        double r331296 = t;
        double r331297 = 2.0;
        double r331298 = 1.0;
        double r331299 = 3.0;
        double r331300 = v;
        double r331301 = r331300 * r331300;
        double r331302 = r331299 * r331301;
        double r331303 = r331298 - r331302;
        double r331304 = r331297 * r331303;
        double r331305 = sqrt(r331304);
        double r331306 = r331296 * r331305;
        double r331307 = r331295 * r331306;
        double r331308 = r331298 - r331301;
        double r331309 = r331307 * r331308;
        double r331310 = 5.0;
        double r331311 = r331310 * r331301;
        double r331312 = r331298 - r331311;
        double r331313 = r331309 / r331312;
        double r331314 = r331294 / r331313;
        return r331314;
}

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 clear-num0.4

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

  5. Applied associate-*l*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2020056 
(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)))))