Average Error: 0.0 → 0.0
Time: 16.7s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
\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 r155256 = 2.0;
        double r155257 = sqrt(r155256);
        double r155258 = 4.0;
        double r155259 = r155257 / r155258;
        double r155260 = 1.0;
        double r155261 = 3.0;
        double r155262 = v;
        double r155263 = r155262 * r155262;
        double r155264 = r155261 * r155263;
        double r155265 = r155260 - r155264;
        double r155266 = sqrt(r155265);
        double r155267 = r155259 * r155266;
        double r155268 = r155260 - r155263;
        double r155269 = r155267 * r155268;
        return r155269;
}
↓
double f(double v) {
        double r155270 = 2.0;
        double r155271 = sqrt(r155270);
        double r155272 = 4.0;
        double r155273 = r155271 / r155272;
        double r155274 = 1.0;
        double r155275 = 3.0;
        double r155276 = v;
        double r155277 = r155276 * r155276;
        double r155278 = r155275 * r155277;
        double r155279 = r155274 - r155278;
        double r155280 = sqrt(r155279);
        double r155281 = r155273 * r155280;
        double r155282 = r155274 - r155277;
        double r155283 = r155281 * r155282;
        return r155283;
}

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 2019347 +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))))