Average Error: 1.0 → 0.0
Time: 6.0s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{4}{\left(\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \left(\sqrt[3]{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}} \cdot \sqrt[3]{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\right)\right) \cdot \sqrt[3]{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}\]
\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
↓
\frac{4}{\left(\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \left(\sqrt[3]{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}} \cdot \sqrt[3]{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\right)\right) \cdot \sqrt[3]{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}
double f(double v) {
        double r245522 = 4.0;
        double r245523 = 3.0;
        double r245524 = atan2(1.0, 0.0);
        double r245525 = r245523 * r245524;
        double r245526 = 1.0;
        double r245527 = v;
        double r245528 = r245527 * r245527;
        double r245529 = r245526 - r245528;
        double r245530 = r245525 * r245529;
        double r245531 = 2.0;
        double r245532 = 6.0;
        double r245533 = r245532 * r245528;
        double r245534 = r245531 - r245533;
        double r245535 = sqrt(r245534);
        double r245536 = r245530 * r245535;
        double r245537 = r245522 / r245536;
        return r245537;
}
↓
double f(double v) {
        double r245538 = 4.0;
        double r245539 = 3.0;
        double r245540 = atan2(1.0, 0.0);
        double r245541 = r245539 * r245540;
        double r245542 = 1.0;
        double r245543 = v;
        double r245544 = r245543 * r245543;
        double r245545 = r245542 - r245544;
        double r245546 = r245541 * r245545;
        double r245547 = 2.0;
        double r245548 = 6.0;
        double r245549 = r245548 * r245544;
        double r245550 = r245547 - r245549;
        double r245551 = sqrt(r245550);
        double r245552 = cbrt(r245551);
        double r245553 = r245552 * r245552;
        double r245554 = r245546 * r245553;
        double r245555 = r245554 * r245552;
        double r245556 = r245538 / r245555;
        return r245556;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.0

    \[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt1.0

    \[\leadsto \frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}} \cdot \sqrt[3]{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\right) \cdot \sqrt[3]{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\right)}}\]

  4. Applied associate-*r*0.0

    \[\leadsto \frac{4}{\color{blue}{\left(\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \left(\sqrt[3]{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}} \cdot \sqrt[3]{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\right)\right) \cdot \sqrt[3]{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}}\]

  5. Final simplification0.0

    \[\leadsto \frac{4}{\left(\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \left(\sqrt[3]{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}} \cdot \sqrt[3]{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\right)\right) \cdot \sqrt[3]{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}\]

Reproduce

herbie shell --seed 2019354 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))