Average Error: 0.0 → 0.0
Time: 8.3s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt[3]{{\left(\sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)}^{3}}\right) \cdot \left(1 - v \cdot v\right)\]
\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[3]{{\left(\sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)}^{3}}\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r330521 = 2.0;
        double r330522 = sqrt(r330521);
        double r330523 = 4.0;
        double r330524 = r330522 / r330523;
        double r330525 = 1.0;
        double r330526 = 3.0;
        double r330527 = v;
        double r330528 = r330527 * r330527;
        double r330529 = r330526 * r330528;
        double r330530 = r330525 - r330529;
        double r330531 = sqrt(r330530);
        double r330532 = r330524 * r330531;
        double r330533 = r330525 - r330528;
        double r330534 = r330532 * r330533;
        return r330534;
}
↓
double f(double v) {
        double r330535 = 2.0;
        double r330536 = sqrt(r330535);
        double r330537 = 4.0;
        double r330538 = r330536 / r330537;
        double r330539 = 1.0;
        double r330540 = 3.0;
        double r330541 = v;
        double r330542 = r330541 * r330541;
        double r330543 = r330540 * r330542;
        double r330544 = r330539 - r330543;
        double r330545 = sqrt(r330544);
        double r330546 = 3.0;
        double r330547 = pow(r330545, r330546);
        double r330548 = cbrt(r330547);
        double r330549 = r330538 * r330548;
        double r330550 = r330539 - r330542;
        double r330551 = r330549 * r330550;
        return r330551;
}

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. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto \left(\frac{\sqrt{2}}{4} \cdot \color{blue}{\sqrt[3]{\left(\sqrt{1 - 3 \cdot \left(v \cdot v\right)} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}}}\right) \cdot \left(1 - v \cdot v\right)\]

  4. Simplified0.0

    \[\leadsto \left(\frac{\sqrt{2}}{4} \cdot \sqrt[3]{\color{blue}{{\left(\sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)}^{3}}}\right) \cdot \left(1 - v \cdot v\right)\]

  5. Final simplification0.0

    \[\leadsto \left(\frac{\sqrt{2}}{4} \cdot \sqrt[3]{{\left(\sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)}^{3}}\right) \cdot \left(1 - v \cdot v\right)\]

Reproduce

herbie shell --seed 2020045 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))