Average Error: 0.0 → 0.0
Time: 15.1s
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 r8379335 = 2.0;
        double r8379336 = sqrt(r8379335);
        double r8379337 = 4.0;
        double r8379338 = r8379336 / r8379337;
        double r8379339 = 1.0;
        double r8379340 = 3.0;
        double r8379341 = v;
        double r8379342 = r8379341 * r8379341;
        double r8379343 = r8379340 * r8379342;
        double r8379344 = r8379339 - r8379343;
        double r8379345 = sqrt(r8379344);
        double r8379346 = r8379338 * r8379345;
        double r8379347 = r8379339 - r8379342;
        double r8379348 = r8379346 * r8379347;
        return r8379348;
}
↓
double f(double v) {
        double r8379349 = 1.0;
        double r8379350 = v;
        double r8379351 = r8379350 * r8379350;
        double r8379352 = 3.0;
        double r8379353 = r8379351 * r8379352;
        double r8379354 = r8379349 - r8379353;
        double r8379355 = sqrt(r8379354);
        double r8379356 = 2.0;
        double r8379357 = sqrt(r8379356);
        double r8379358 = 4.0;
        double r8379359 = r8379357 / r8379358;
        double r8379360 = r8379355 * r8379359;
        double r8379361 = r8379349 - r8379351;
        double r8379362 = r8379360 * r8379361;
        return r8379362;
}

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 2019149 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))