Average Error: 0.0 → 0.0
Time: 15.5s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(1 - v \cdot v\right)\]
\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 r6054563 = 2.0;
        double r6054564 = sqrt(r6054563);
        double r6054565 = 4.0;
        double r6054566 = r6054564 / r6054565;
        double r6054567 = 1.0;
        double r6054568 = 3.0;
        double r6054569 = v;
        double r6054570 = r6054569 * r6054569;
        double r6054571 = r6054568 * r6054570;
        double r6054572 = r6054567 - r6054571;
        double r6054573 = sqrt(r6054572);
        double r6054574 = r6054566 * r6054573;
        double r6054575 = r6054567 - r6054570;
        double r6054576 = r6054574 * r6054575;
        return r6054576;
}
↓
double f(double v) {
        double r6054577 = 1.0;
        double r6054578 = v;
        double r6054579 = r6054578 * r6054578;
        double r6054580 = 3.0;
        double r6054581 = r6054579 * r6054580;
        double r6054582 = r6054577 - r6054581;
        double r6054583 = sqrt(r6054582);
        double r6054584 = 2.0;
        double r6054585 = sqrt(r6054584);
        double r6054586 = 4.0;
        double r6054587 = r6054585 / r6054586;
        double r6054588 = r6054583 * r6054587;
        double r6054589 = r6054577 - r6054579;
        double r6054590 = r6054588 * r6054589;
        return r6054590;
}

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 2019142 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))