Average Error: 0.0 → 0.0
Time: 6.3m
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\sqrt{1 - \left(3 \cdot v\right) \cdot v} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(1 - v \cdot v\right)\]
\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(3 \cdot v\right) \cdot v} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r62752081 = 2.0;
        double r62752082 = sqrt(r62752081);
        double r62752083 = 4.0;
        double r62752084 = r62752082 / r62752083;
        double r62752085 = 1.0;
        double r62752086 = 3.0;
        double r62752087 = v;
        double r62752088 = r62752087 * r62752087;
        double r62752089 = r62752086 * r62752088;
        double r62752090 = r62752085 - r62752089;
        double r62752091 = sqrt(r62752090);
        double r62752092 = r62752084 * r62752091;
        double r62752093 = r62752085 - r62752088;
        double r62752094 = r62752092 * r62752093;
        return r62752094;
}
↓
double f(double v) {
        double r62752095 = 1.0;
        double r62752096 = 3.0;
        double r62752097 = v;
        double r62752098 = r62752096 * r62752097;
        double r62752099 = r62752098 * r62752097;
        double r62752100 = r62752095 - r62752099;
        double r62752101 = sqrt(r62752100);
        double r62752102 = 2.0;
        double r62752103 = sqrt(r62752102);
        double r62752104 = 4.0;
        double r62752105 = r62752103 / r62752104;
        double r62752106 = r62752101 * r62752105;
        double r62752107 = r62752097 * r62752097;
        double r62752108 = r62752095 - r62752107;
        double r62752109 = r62752106 * r62752108;
        return r62752109;
}

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. Using strategy rm

  3. Applied associate-*r*0.0

    \[\leadsto \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - \color{blue}{\left(3 \cdot v\right) \cdot v}}\right) \cdot \left(1 - v \cdot v\right)\]

  4. Final simplification0.0

    \[\leadsto \left(\sqrt{1 - \left(3 \cdot v\right) \cdot v} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(1 - v \cdot v\right)\]

Reproduce

herbie shell --seed 2019120 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))