Average Error: 0.0 → 0.0
Time: 23.4s
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 r6960500 = 2.0;
        double r6960501 = sqrt(r6960500);
        double r6960502 = 4.0;
        double r6960503 = r6960501 / r6960502;
        double r6960504 = 1.0;
        double r6960505 = 3.0;
        double r6960506 = v;
        double r6960507 = r6960506 * r6960506;
        double r6960508 = r6960505 * r6960507;
        double r6960509 = r6960504 - r6960508;
        double r6960510 = sqrt(r6960509);
        double r6960511 = r6960503 * r6960510;
        double r6960512 = r6960504 - r6960507;
        double r6960513 = r6960511 * r6960512;
        return r6960513;
}
↓
double f(double v) {
        double r6960514 = 1.0;
        double r6960515 = v;
        double r6960516 = r6960515 * r6960515;
        double r6960517 = 3.0;
        double r6960518 = r6960516 * r6960517;
        double r6960519 = r6960514 - r6960518;
        double r6960520 = sqrt(r6960519);
        double r6960521 = 2.0;
        double r6960522 = sqrt(r6960521);
        double r6960523 = 4.0;
        double r6960524 = r6960522 / r6960523;
        double r6960525 = r6960520 * r6960524;
        double r6960526 = r6960514 - r6960516;
        double r6960527 = r6960525 * r6960526;
        return r6960527;
}

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 2019151 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))