Average Error: 1.0 → 0.0
Time: 9.5s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\sqrt[3]{\frac{4}{3}} \cdot \sqrt[3]{\frac{4}{3}}}{\frac{\pi - \pi \cdot \left(v \cdot v\right)}{\sqrt[3]{\frac{4}{3}}}}}{\sqrt{2 - v \cdot \left(6 \cdot v\right)}}\]
\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{\frac{\sqrt[3]{\frac{4}{3}} \cdot \sqrt[3]{\frac{4}{3}}}{\frac{\pi - \pi \cdot \left(v \cdot v\right)}{\sqrt[3]{\frac{4}{3}}}}}{\sqrt{2 - v \cdot \left(6 \cdot v\right)}}
double f(double v) {
        double r2069559 = 4.0;
        double r2069560 = 3.0;
        double r2069561 = atan2(1.0, 0.0);
        double r2069562 = r2069560 * r2069561;
        double r2069563 = 1.0;
        double r2069564 = v;
        double r2069565 = r2069564 * r2069564;
        double r2069566 = r2069563 - r2069565;
        double r2069567 = r2069562 * r2069566;
        double r2069568 = 2.0;
        double r2069569 = 6.0;
        double r2069570 = r2069569 * r2069565;
        double r2069571 = r2069568 - r2069570;
        double r2069572 = sqrt(r2069571);
        double r2069573 = r2069567 * r2069572;
        double r2069574 = r2069559 / r2069573;
        return r2069574;
}
↓
double f(double v) {
        double r2069575 = 1.3333333333333333;
        double r2069576 = cbrt(r2069575);
        double r2069577 = r2069576 * r2069576;
        double r2069578 = atan2(1.0, 0.0);
        double r2069579 = v;
        double r2069580 = r2069579 * r2069579;
        double r2069581 = r2069578 * r2069580;
        double r2069582 = r2069578 - r2069581;
        double r2069583 = r2069582 / r2069576;
        double r2069584 = r2069577 / r2069583;
        double r2069585 = 2.0;
        double r2069586 = 6.0;
        double r2069587 = r2069586 * r2069579;
        double r2069588 = r2069579 * r2069587;
        double r2069589 = r2069585 - r2069588;
        double r2069590 = sqrt(r2069589);
        double r2069591 = r2069584 / r2069590;
        return r2069591;
}

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. Simplified0.0

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

  4. Applied add-cube-cbrt0.0

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

  5. Applied associate-/l*0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019156 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))