Average Error: 0.0 → 0.0
Time: 3.5m
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(1 - v \cdot v\right)\]
double f(double v) {
        double r59214064 = 2.0;
        double r59214065 = sqrt(r59214064);
        double r59214066 = 4.0;
        double r59214067 = r59214065 / r59214066;
        double r59214068 = 1.0;
        double r59214069 = 3.0;
        double r59214070 = v;
        double r59214071 = r59214070 * r59214070;
        double r59214072 = r59214069 * r59214071;
        double r59214073 = r59214068 - r59214072;
        double r59214074 = sqrt(r59214073);
        double r59214075 = r59214067 * r59214074;
        double r59214076 = r59214068 - r59214071;
        double r59214077 = r59214075 * r59214076;
        return r59214077;
}
↓
double f(double v) {
        double r59214078 = 1.0;
        double r59214079 = v;
        double r59214080 = r59214079 * r59214079;
        double r59214081 = 3.0;
        double r59214082 = r59214080 * r59214081;
        double r59214083 = r59214078 - r59214082;
        double r59214084 = sqrt(r59214083);
        double r59214085 = 2.0;
        double r59214086 = sqrt(r59214085);
        double r59214087 = 4.0;
        double r59214088 = r59214086 / r59214087;
        double r59214089 = r59214084 * r59214088;
        double r59214090 = r59214078 - r59214080;
        double r59214091 = r59214089 * r59214090;
        return r59214091;
}


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

Error

Bits error versus v

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

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

Reproduce

herbie shell --seed 2019101 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))