Average Error: 0.0 → 0.0
Time: 13.9s
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 r157646 = 2.0;
        double r157647 = sqrt(r157646);
        double r157648 = 4.0;
        double r157649 = r157647 / r157648;
        double r157650 = 1.0;
        double r157651 = 3.0;
        double r157652 = v;
        double r157653 = r157652 * r157652;
        double r157654 = r157651 * r157653;
        double r157655 = r157650 - r157654;
        double r157656 = sqrt(r157655);
        double r157657 = r157649 * r157656;
        double r157658 = r157650 - r157653;
        double r157659 = r157657 * r157658;
        return r157659;
}
↓
double f(double v) {
        double r157660 = 2.0;
        double r157661 = sqrt(r157660);
        double r157662 = 4.0;
        double r157663 = r157661 / r157662;
        double r157664 = 1.0;
        double r157665 = 3.0;
        double r157666 = v;
        double r157667 = r157666 * r157666;
        double r157668 = r157665 * r157667;
        double r157669 = r157664 - r157668;
        double r157670 = sqrt(r157669);
        double r157671 = r157663 * r157670;
        double r157672 = r157664 - r157667;
        double r157673 = r157671 * r157672;
        return r157673;
}

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 2019195 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))