Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
\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 r261930 = 2.0;
        double r261931 = sqrt(r261930);
        double r261932 = 4.0;
        double r261933 = r261931 / r261932;
        double r261934 = 1.0;
        double r261935 = 3.0;
        double r261936 = v;
        double r261937 = r261936 * r261936;
        double r261938 = r261935 * r261937;
        double r261939 = r261934 - r261938;
        double r261940 = sqrt(r261939);
        double r261941 = r261933 * r261940;
        double r261942 = r261934 - r261937;
        double r261943 = r261941 * r261942;
        return r261943;
}
↓
double f(double v) {
        double r261944 = 2.0;
        double r261945 = sqrt(r261944);
        double r261946 = 4.0;
        double r261947 = r261945 / r261946;
        double r261948 = 1.0;
        double r261949 = 3.0;
        double r261950 = v;
        double r261951 = r261950 * r261950;
        double r261952 = r261949 * r261951;
        double r261953 = r261948 - r261952;
        double r261954 = sqrt(r261953);
        double r261955 = r261947 * r261954;
        double r261956 = r261948 - r261951;
        double r261957 = r261955 * r261956;
        return r261957;
}

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