Average Error: 1.0 → 0.0
Time: 17.7s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\sqrt[3]{\frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)} \cdot \left(\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)\right)} \cdot \left(\frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)} \cdot \left(\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)\right)} \cdot \frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)} \cdot \left(\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)\right)}\right)}\]
\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)}}
↓
\sqrt[3]{\frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)} \cdot \left(\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)\right)} \cdot \left(\frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)} \cdot \left(\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)\right)} \cdot \frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)} \cdot \left(\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)\right)}\right)}
double f(double v) {
        double r6653352 = 4.0;
        double r6653353 = 3.0;
        double r6653354 = atan2(1.0, 0.0);
        double r6653355 = r6653353 * r6653354;
        double r6653356 = 1.0;
        double r6653357 = v;
        double r6653358 = r6653357 * r6653357;
        double r6653359 = r6653356 - r6653358;
        double r6653360 = r6653355 * r6653359;
        double r6653361 = 2.0;
        double r6653362 = 6.0;
        double r6653363 = r6653362 * r6653358;
        double r6653364 = r6653361 - r6653363;
        double r6653365 = sqrt(r6653364);
        double r6653366 = r6653360 * r6653365;
        double r6653367 = r6653352 / r6653366;
        return r6653367;
}
↓
double f(double v) {
        double r6653368 = 4.0;
        double r6653369 = 2.0;
        double r6653370 = 6.0;
        double r6653371 = v;
        double r6653372 = r6653371 * r6653371;
        double r6653373 = r6653370 * r6653372;
        double r6653374 = r6653369 - r6653373;
        double r6653375 = sqrt(r6653374);
        double r6653376 = atan2(1.0, 0.0);
        double r6653377 = 3.0;
        double r6653378 = r6653376 * r6653377;
        double r6653379 = 1.0;
        double r6653380 = r6653379 - r6653372;
        double r6653381 = r6653378 * r6653380;
        double r6653382 = r6653375 * r6653381;
        double r6653383 = r6653368 / r6653382;
        double r6653384 = r6653383 * r6653383;
        double r6653385 = r6653383 * r6653384;
        double r6653386 = cbrt(r6653385);
        return r6653386;
}

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-cbrt-cube0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019169 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))