Average Error: 0.0 → 0.0
Time: 3.5s
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 r254603 = 2.0;
        double r254604 = sqrt(r254603);
        double r254605 = 4.0;
        double r254606 = r254604 / r254605;
        double r254607 = 1.0;
        double r254608 = 3.0;
        double r254609 = v;
        double r254610 = r254609 * r254609;
        double r254611 = r254608 * r254610;
        double r254612 = r254607 - r254611;
        double r254613 = sqrt(r254612);
        double r254614 = r254606 * r254613;
        double r254615 = r254607 - r254610;
        double r254616 = r254614 * r254615;
        return r254616;
}
↓
double f(double v) {
        double r254617 = 2.0;
        double r254618 = sqrt(r254617);
        double r254619 = 4.0;
        double r254620 = r254618 / r254619;
        double r254621 = 1.0;
        double r254622 = 3.0;
        double r254623 = v;
        double r254624 = r254623 * r254623;
        double r254625 = r254622 * r254624;
        double r254626 = r254621 - r254625;
        double r254627 = sqrt(r254626);
        double r254628 = r254620 * r254627;
        double r254629 = r254621 - r254624;
        double r254630 = r254628 * r254629;
        return r254630;
}

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 2020089 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))