Average Error: 0.0 → 0.0
Time: 13.5s
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 r154406 = 2.0;
        double r154407 = sqrt(r154406);
        double r154408 = 4.0;
        double r154409 = r154407 / r154408;
        double r154410 = 1.0;
        double r154411 = 3.0;
        double r154412 = v;
        double r154413 = r154412 * r154412;
        double r154414 = r154411 * r154413;
        double r154415 = r154410 - r154414;
        double r154416 = sqrt(r154415);
        double r154417 = r154409 * r154416;
        double r154418 = r154410 - r154413;
        double r154419 = r154417 * r154418;
        return r154419;
}
↓
double f(double v) {
        double r154420 = 2.0;
        double r154421 = sqrt(r154420);
        double r154422 = 4.0;
        double r154423 = r154421 / r154422;
        double r154424 = 1.0;
        double r154425 = 3.0;
        double r154426 = v;
        double r154427 = r154426 * r154426;
        double r154428 = r154425 * r154427;
        double r154429 = r154424 - r154428;
        double r154430 = sqrt(r154429);
        double r154431 = r154423 * r154430;
        double r154432 = r154424 - r154427;
        double r154433 = r154431 * r154432;
        return r154433;
}

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 2019347 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))