Average Error: 0.0 → 0.0
Time: 3.0s
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 r234086 = 2.0;
        double r234087 = sqrt(r234086);
        double r234088 = 4.0;
        double r234089 = r234087 / r234088;
        double r234090 = 1.0;
        double r234091 = 3.0;
        double r234092 = v;
        double r234093 = r234092 * r234092;
        double r234094 = r234091 * r234093;
        double r234095 = r234090 - r234094;
        double r234096 = sqrt(r234095);
        double r234097 = r234089 * r234096;
        double r234098 = r234090 - r234093;
        double r234099 = r234097 * r234098;
        return r234099;
}
↓
double f(double v) {
        double r234100 = 2.0;
        double r234101 = sqrt(r234100);
        double r234102 = 4.0;
        double r234103 = r234101 / r234102;
        double r234104 = 1.0;
        double r234105 = 3.0;
        double r234106 = v;
        double r234107 = r234106 * r234106;
        double r234108 = r234105 * r234107;
        double r234109 = r234104 - r234108;
        double r234110 = sqrt(r234109);
        double r234111 = r234103 * r234110;
        double r234112 = r234104 - r234107;
        double r234113 = r234111 * r234112;
        return r234113;
}

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 2020060 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))