Average Error: 0.0 → 0.0
Time: 2.7s
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 r179965 = 2.0;
        double r179966 = sqrt(r179965);
        double r179967 = 4.0;
        double r179968 = r179966 / r179967;
        double r179969 = 1.0;
        double r179970 = 3.0;
        double r179971 = v;
        double r179972 = r179971 * r179971;
        double r179973 = r179970 * r179972;
        double r179974 = r179969 - r179973;
        double r179975 = sqrt(r179974);
        double r179976 = r179968 * r179975;
        double r179977 = r179969 - r179972;
        double r179978 = r179976 * r179977;
        return r179978;
}
↓
double f(double v) {
        double r179979 = 2.0;
        double r179980 = sqrt(r179979);
        double r179981 = 4.0;
        double r179982 = r179980 / r179981;
        double r179983 = 1.0;
        double r179984 = 3.0;
        double r179985 = v;
        double r179986 = r179985 * r179985;
        double r179987 = r179984 * r179986;
        double r179988 = r179983 - r179987;
        double r179989 = sqrt(r179988);
        double r179990 = r179982 * r179989;
        double r179991 = r179983 - r179986;
        double r179992 = r179990 * r179991;
        return r179992;
}

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 2020027 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))