Average Error: 0.0 → 0.0
Time: 9.6s
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 r2409539 = 2.0;
        double r2409540 = sqrt(r2409539);
        double r2409541 = 4.0;
        double r2409542 = r2409540 / r2409541;
        double r2409543 = 1.0;
        double r2409544 = 3.0;
        double r2409545 = v;
        double r2409546 = r2409545 * r2409545;
        double r2409547 = r2409544 * r2409546;
        double r2409548 = r2409543 - r2409547;
        double r2409549 = sqrt(r2409548);
        double r2409550 = r2409542 * r2409549;
        double r2409551 = r2409543 - r2409546;
        double r2409552 = r2409550 * r2409551;
        return r2409552;
}
↓
double f(double v) {
        double r2409553 = 1.0;
        double r2409554 = v;
        double r2409555 = r2409554 * r2409554;
        double r2409556 = 3.0;
        double r2409557 = r2409555 * r2409556;
        double r2409558 = r2409553 - r2409557;
        double r2409559 = sqrt(r2409558);
        double r2409560 = 2.0;
        double r2409561 = sqrt(r2409560);
        double r2409562 = 4.0;
        double r2409563 = r2409561 / r2409562;
        double r2409564 = r2409559 * r2409563;
        double r2409565 = r2409553 - r2409555;
        double r2409566 = r2409564 * r2409565;
        return r2409566;
}

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 2019156 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))