Average Error: 0.0 → 0.0
Time: 5.3m
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 r77809388 = 2.0;
        double r77809389 = sqrt(r77809388);
        double r77809390 = 4.0;
        double r77809391 = r77809389 / r77809390;
        double r77809392 = 1.0;
        double r77809393 = 3.0;
        double r77809394 = v;
        double r77809395 = r77809394 * r77809394;
        double r77809396 = r77809393 * r77809395;
        double r77809397 = r77809392 - r77809396;
        double r77809398 = sqrt(r77809397);
        double r77809399 = r77809391 * r77809398;
        double r77809400 = r77809392 - r77809395;
        double r77809401 = r77809399 * r77809400;
        return r77809401;
}
↓
double f(double v) {
        double r77809402 = 1.0;
        double r77809403 = v;
        double r77809404 = r77809403 * r77809403;
        double r77809405 = 3.0;
        double r77809406 = r77809404 * r77809405;
        double r77809407 = r77809402 - r77809406;
        double r77809408 = sqrt(r77809407);
        double r77809409 = 2.0;
        double r77809410 = sqrt(r77809409);
        double r77809411 = 4.0;
        double r77809412 = r77809410 / r77809411;
        double r77809413 = r77809408 * r77809412;
        double r77809414 = r77809402 - r77809404;
        double r77809415 = r77809413 * r77809414;
        return r77809415;
}

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 2019124 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))