Average Error: 0.0 → 0.0
Time: 28.3s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\left(1 - v \cdot v\right) \cdot \sqrt{1 - \left(v \cdot v\right) \cdot 3}\right) \cdot \frac{\sqrt{2}}{4}\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(\left(1 - v \cdot v\right) \cdot \sqrt{1 - \left(v \cdot v\right) \cdot 3}\right) \cdot \frac{\sqrt{2}}{4}
double f(double v) {
        double r7235039 = 2.0;
        double r7235040 = sqrt(r7235039);
        double r7235041 = 4.0;
        double r7235042 = r7235040 / r7235041;
        double r7235043 = 1.0;
        double r7235044 = 3.0;
        double r7235045 = v;
        double r7235046 = r7235045 * r7235045;
        double r7235047 = r7235044 * r7235046;
        double r7235048 = r7235043 - r7235047;
        double r7235049 = sqrt(r7235048);
        double r7235050 = r7235042 * r7235049;
        double r7235051 = r7235043 - r7235046;
        double r7235052 = r7235050 * r7235051;
        return r7235052;
}
↓
double f(double v) {
        double r7235053 = 1.0;
        double r7235054 = v;
        double r7235055 = r7235054 * r7235054;
        double r7235056 = r7235053 - r7235055;
        double r7235057 = 3.0;
        double r7235058 = r7235055 * r7235057;
        double r7235059 = r7235053 - r7235058;
        double r7235060 = sqrt(r7235059);
        double r7235061 = r7235056 * r7235060;
        double r7235062 = 2.0;
        double r7235063 = sqrt(r7235062);
        double r7235064 = 4.0;
        double r7235065 = r7235063 / r7235064;
        double r7235066 = r7235061 * r7235065;
        return r7235066;
}

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-*l*0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))