Average Error: 0.0 → 0.0
Time: 7.6s
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 r170055 = 2.0;
        double r170056 = sqrt(r170055);
        double r170057 = 4.0;
        double r170058 = r170056 / r170057;
        double r170059 = 1.0;
        double r170060 = 3.0;
        double r170061 = v;
        double r170062 = r170061 * r170061;
        double r170063 = r170060 * r170062;
        double r170064 = r170059 - r170063;
        double r170065 = sqrt(r170064);
        double r170066 = r170058 * r170065;
        double r170067 = r170059 - r170062;
        double r170068 = r170066 * r170067;
        return r170068;
}
↓
double f(double v) {
        double r170069 = 2.0;
        double r170070 = sqrt(r170069);
        double r170071 = 4.0;
        double r170072 = r170070 / r170071;
        double r170073 = 1.0;
        double r170074 = 3.0;
        double r170075 = v;
        double r170076 = r170075 * r170075;
        double r170077 = r170074 * r170076;
        double r170078 = r170073 - r170077;
        double r170079 = sqrt(r170078);
        double r170080 = r170072 * r170079;
        double r170081 = r170073 - r170076;
        double r170082 = r170080 * r170081;
        return r170082;
}

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 2019298 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))