Average Error: 0.0 → 0.0
Time: 5.3s
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 r54885513 = 2.0;
        double r54885514 = sqrt(r54885513);
        double r54885515 = 4.0;
        double r54885516 = r54885514 / r54885515;
        double r54885517 = 1.0;
        double r54885518 = 3.0;
        double r54885519 = v;
        double r54885520 = r54885519 * r54885519;
        double r54885521 = r54885518 * r54885520;
        double r54885522 = r54885517 - r54885521;
        double r54885523 = sqrt(r54885522);
        double r54885524 = r54885516 * r54885523;
        double r54885525 = r54885517 - r54885520;
        double r54885526 = r54885524 * r54885525;
        return r54885526;
}
↓
double f(double v) {
        double r54885527 = 1.0;
        double r54885528 = v;
        double r54885529 = r54885528 * r54885528;
        double r54885530 = 3.0;
        double r54885531 = r54885529 * r54885530;
        double r54885532 = r54885527 - r54885531;
        double r54885533 = sqrt(r54885532);
        double r54885534 = 2.0;
        double r54885535 = sqrt(r54885534);
        double r54885536 = 4.0;
        double r54885537 = r54885535 / r54885536;
        double r54885538 = r54885533 * r54885537;
        double r54885539 = r54885527 - r54885529;
        double r54885540 = r54885538 * r54885539;
        return r54885540;
}

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 2019125 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))