Average Error: 0.0 → 0.0
Time: 2.9s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r277354 = 2.0;
        double r277355 = sqrt(r277354);
        double r277356 = 4.0;
        double r277357 = r277355 / r277356;
        double r277358 = 1.0;
        double r277359 = 3.0;
        double r277360 = v;
        double r277361 = r277360 * r277360;
        double r277362 = r277359 * r277361;
        double r277363 = r277358 - r277362;
        double r277364 = sqrt(r277363);
        double r277365 = r277357 * r277364;
        double r277366 = r277358 - r277361;
        double r277367 = r277365 * r277366;
        return r277367;
}
↓
double f(double v) {
        double r277368 = 2.0;
        double r277369 = sqrt(r277368);
        double r277370 = 4.0;
        double r277371 = r277369 / r277370;
        double r277372 = 1.0;
        double r277373 = 3.0;
        double r277374 = v;
        double r277375 = r277374 * r277374;
        double r277376 = r277373 * r277375;
        double r277377 = r277372 - r277376;
        double r277378 = sqrt(r277377);
        double r277379 = r277371 * r277378;
        double r277380 = r277372 - r277375;
        double r277381 = r277379 * r277380;
        return r277381;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]

  2. Final simplification0.0

    \[\leadsto \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]

Reproduce

herbie shell --seed 2020039 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))