Average Error: 0.0 → 0.0
Time: 13.6s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r5057573 = 2.0;
        double r5057574 = sqrt(r5057573);
        double r5057575 = 4.0;
        double r5057576 = r5057574 / r5057575;
        double r5057577 = 1.0;
        double r5057578 = 3.0;
        double r5057579 = v;
        double r5057580 = r5057579 * r5057579;
        double r5057581 = r5057578 * r5057580;
        double r5057582 = r5057577 - r5057581;
        double r5057583 = sqrt(r5057582);
        double r5057584 = r5057576 * r5057583;
        double r5057585 = r5057577 - r5057580;
        double r5057586 = r5057584 * r5057585;
        return r5057586;
}
↓
double f(double v) {
        double r5057587 = 1.0;
        double r5057588 = v;
        double r5057589 = r5057588 * r5057588;
        double r5057590 = 3.0;
        double r5057591 = r5057589 * r5057590;
        double r5057592 = r5057587 - r5057591;
        double r5057593 = sqrt(r5057592);
        double r5057594 = 2.0;
        double r5057595 = sqrt(r5057594);
        double r5057596 = 4.0;
        double r5057597 = r5057595 / r5057596;
        double r5057598 = r5057593 * r5057597;
        double r5057599 = r5057587 - r5057589;
        double r5057600 = r5057598 * r5057599;
        return r5057600;
}

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

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

Reproduce

herbie shell --seed 2019153 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))