Average Error: 0.0 → 0.0
Time: 3.6s
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 r143221 = 2.0;
        double r143222 = sqrt(r143221);
        double r143223 = 4.0;
        double r143224 = r143222 / r143223;
        double r143225 = 1.0;
        double r143226 = 3.0;
        double r143227 = v;
        double r143228 = r143227 * r143227;
        double r143229 = r143226 * r143228;
        double r143230 = r143225 - r143229;
        double r143231 = sqrt(r143230);
        double r143232 = r143224 * r143231;
        double r143233 = r143225 - r143228;
        double r143234 = r143232 * r143233;
        return r143234;
}
↓
double f(double v) {
        double r143235 = 2.0;
        double r143236 = sqrt(r143235);
        double r143237 = 4.0;
        double r143238 = r143236 / r143237;
        double r143239 = 1.0;
        double r143240 = 3.0;
        double r143241 = v;
        double r143242 = r143241 * r143241;
        double r143243 = r143240 * r143242;
        double r143244 = r143239 - r143243;
        double r143245 = sqrt(r143244);
        double r143246 = r143238 * r143245;
        double r143247 = r143239 - r143242;
        double r143248 = r143246 * r143247;
        return r143248;
}

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 2020034 +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))))