Average Error: 1.0 → 0.0
Time: 15.3s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\sqrt[3]{{\left(\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\right)}^{3}}\]
\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]{{\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)}}\right)}^{3}}
double f(double v) {
        double r238323 = 4.0;
        double r238324 = 3.0;
        double r238325 = atan2(1.0, 0.0);
        double r238326 = r238324 * r238325;
        double r238327 = 1.0;
        double r238328 = v;
        double r238329 = r238328 * r238328;
        double r238330 = r238327 - r238329;
        double r238331 = r238326 * r238330;
        double r238332 = 2.0;
        double r238333 = 6.0;
        double r238334 = r238333 * r238329;
        double r238335 = r238332 - r238334;
        double r238336 = sqrt(r238335);
        double r238337 = r238331 * r238336;
        double r238338 = r238323 / r238337;
        return r238338;
}
↓
double f(double v) {
        double r238339 = 4.0;
        double r238340 = 3.0;
        double r238341 = atan2(1.0, 0.0);
        double r238342 = r238340 * r238341;
        double r238343 = 1.0;
        double r238344 = v;
        double r238345 = r238344 * r238344;
        double r238346 = r238343 - r238345;
        double r238347 = r238342 * r238346;
        double r238348 = 2.0;
        double r238349 = 6.0;
        double r238350 = r238349 * r238345;
        double r238351 = r238348 - r238350;
        double r238352 = sqrt(r238351);
        double r238353 = r238347 * r238352;
        double r238354 = r238339 / r238353;
        double r238355 = 3.0;
        double r238356 = pow(r238354, r238355);
        double r238357 = cbrt(r238356);
        return r238357;
}

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-cube1.0

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

  4. Applied add-cbrt-cube1.0

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

  5. Applied cbrt-undiv1.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019208 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))