Average Error: 0.0 → 0.0
Time: 12.3s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\frac{\sqrt{2}}{4} \cdot \left(\sqrt{1 - 3 \cdot \left(v \cdot v\right)} \cdot \left(1 - v \cdot v\right)\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\frac{\sqrt{2}}{4} \cdot \left(\sqrt{1 - 3 \cdot \left(v \cdot v\right)} \cdot \left(1 - v \cdot v\right)\right)
double f(double v) {
        double r140507 = 2.0;
        double r140508 = sqrt(r140507);
        double r140509 = 4.0;
        double r140510 = r140508 / r140509;
        double r140511 = 1.0;
        double r140512 = 3.0;
        double r140513 = v;
        double r140514 = r140513 * r140513;
        double r140515 = r140512 * r140514;
        double r140516 = r140511 - r140515;
        double r140517 = sqrt(r140516);
        double r140518 = r140510 * r140517;
        double r140519 = r140511 - r140514;
        double r140520 = r140518 * r140519;
        return r140520;
}
↓
double f(double v) {
        double r140521 = 2.0;
        double r140522 = sqrt(r140521);
        double r140523 = 4.0;
        double r140524 = r140522 / r140523;
        double r140525 = 1.0;
        double r140526 = 3.0;
        double r140527 = v;
        double r140528 = r140527 * r140527;
        double r140529 = r140526 * r140528;
        double r140530 = r140525 - r140529;
        double r140531 = sqrt(r140530);
        double r140532 = r140525 - r140528;
        double r140533 = r140531 * r140532;
        double r140534 = r140524 * r140533;
        return r140534;
}

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. Using strategy rm

  3. Applied associate-*l*0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019235 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))