Average Error: 0.0 → 0.0
Time: 20.7s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(1 - v \cdot v\right)\]
\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(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r5071041 = 2.0;
        double r5071042 = sqrt(r5071041);
        double r5071043 = 4.0;
        double r5071044 = r5071042 / r5071043;
        double r5071045 = 1.0;
        double r5071046 = 3.0;
        double r5071047 = v;
        double r5071048 = r5071047 * r5071047;
        double r5071049 = r5071046 * r5071048;
        double r5071050 = r5071045 - r5071049;
        double r5071051 = sqrt(r5071050);
        double r5071052 = r5071044 * r5071051;
        double r5071053 = r5071045 - r5071048;
        double r5071054 = r5071052 * r5071053;
        return r5071054;
}
↓
double f(double v) {
        double r5071055 = 1.0;
        double r5071056 = v;
        double r5071057 = r5071056 * r5071056;
        double r5071058 = 3.0;
        double r5071059 = r5071057 * r5071058;
        double r5071060 = r5071055 - r5071059;
        double r5071061 = sqrt(r5071060);
        double r5071062 = 2.0;
        double r5071063 = sqrt(r5071062);
        double r5071064 = 4.0;
        double r5071065 = r5071063 / r5071064;
        double r5071066 = r5071061 * r5071065;
        double r5071067 = r5071055 - r5071057;
        double r5071068 = r5071066 * r5071067;
        return r5071068;
}

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

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

Reproduce

herbie shell --seed 2019153 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))