Average Error: 0.0 → 0.0
Time: 2.8s
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 r138584 = 2.0;
        double r138585 = sqrt(r138584);
        double r138586 = 4.0;
        double r138587 = r138585 / r138586;
        double r138588 = 1.0;
        double r138589 = 3.0;
        double r138590 = v;
        double r138591 = r138590 * r138590;
        double r138592 = r138589 * r138591;
        double r138593 = r138588 - r138592;
        double r138594 = sqrt(r138593);
        double r138595 = r138587 * r138594;
        double r138596 = r138588 - r138591;
        double r138597 = r138595 * r138596;
        return r138597;
}
↓
double f(double v) {
        double r138598 = 2.0;
        double r138599 = sqrt(r138598);
        double r138600 = 4.0;
        double r138601 = r138599 / r138600;
        double r138602 = 1.0;
        double r138603 = 3.0;
        double r138604 = v;
        double r138605 = r138604 * r138604;
        double r138606 = r138603 * r138605;
        double r138607 = r138602 - r138606;
        double r138608 = sqrt(r138607);
        double r138609 = r138601 * r138608;
        double r138610 = r138602 - r138605;
        double r138611 = r138609 * r138610;
        return r138611;
}

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 2020064 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))