Average Error: 0.4 → 0.3
Time: 22.0s
Precision: 64
\[\frac{1 - 5 \cdot \left(v \cdot v\right)}{\left(\left(\pi \cdot t\right) \cdot \sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}\right) \cdot \left(1 - v \cdot v\right)}\]
↓
\[\frac{\frac{1 - 5 \cdot \left(v \cdot v\right)}{t} \cdot \frac{\frac{1}{\pi}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - v \cdot v}\]
\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{\frac{1 - 5 \cdot \left(v \cdot v\right)}{t} \cdot \frac{\frac{1}{\pi}}{\sqrt{2 \cdot \left(1 - 3 \cdot \left(v \cdot v\right)\right)}}}{1 - v \cdot v}
double f(double v, double t) {
        double r226250 = 1.0;
        double r226251 = 5.0;
        double r226252 = v;
        double r226253 = r226252 * r226252;
        double r226254 = r226251 * r226253;
        double r226255 = r226250 - r226254;
        double r226256 = atan2(1.0, 0.0);
        double r226257 = t;
        double r226258 = r226256 * r226257;
        double r226259 = 2.0;
        double r226260 = 3.0;
        double r226261 = r226260 * r226253;
        double r226262 = r226250 - r226261;
        double r226263 = r226259 * r226262;
        double r226264 = sqrt(r226263);
        double r226265 = r226258 * r226264;
        double r226266 = r226250 - r226253;
        double r226267 = r226265 * r226266;
        double r226268 = r226255 / r226267;
        return r226268;
}
↓
double f(double v, double t) {
        double r226269 = 1.0;
        double r226270 = 5.0;
        double r226271 = v;
        double r226272 = r226271 * r226271;
        double r226273 = r226270 * r226272;
        double r226274 = r226269 - r226273;
        double r226275 = t;
        double r226276 = r226274 / r226275;
        double r226277 = 1.0;
        double r226278 = atan2(1.0, 0.0);
        double r226279 = r226277 / r226278;
        double r226280 = 2.0;
        double r226281 = 3.0;
        double r226282 = r226281 * r226272;
        double r226283 = r226269 - r226282;
        double r226284 = r226280 * r226283;
        double r226285 = sqrt(r226284);
        double r226286 = r226279 / r226285;
        double r226287 = r226276 * r226286;
        double r226288 = r226269 - r226272;
        double r226289 = r226287 / r226288;
        return r226289;
}

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-/r*0.4

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

  5. Applied associate-*l*0.4

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

  7. Applied associate-/r*0.3

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

  9. Applied div-inv0.3

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

  10. Applied times-frac0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019323 
(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)))))