Average Error: 1.0 → 0.0
Time: 23.0s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\left(\left(\left(\left(v \cdot v\right) \cdot \pi\right) \cdot \left(\left(v \cdot v\right) \cdot \pi\right) + \left(\left(v \cdot v\right) \cdot \pi\right) \cdot \pi\right) + \pi \cdot \pi\right) \cdot \frac{\frac{4}{3}}{\left(\pi \cdot \pi\right) \cdot \pi - \left(\left(\left(\left(v \cdot v\right) \cdot \pi\right) \cdot \left(\left(v \cdot v\right) \cdot \pi\right)\right) \cdot \left(v \cdot v\right)\right) \cdot \pi}}{\sqrt{2 - v \cdot \left(v \cdot 6\right)}}\]
\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{\left(\left(\left(\left(v \cdot v\right) \cdot \pi\right) \cdot \left(\left(v \cdot v\right) \cdot \pi\right) + \left(\left(v \cdot v\right) \cdot \pi\right) \cdot \pi\right) + \pi \cdot \pi\right) \cdot \frac{\frac{4}{3}}{\left(\pi \cdot \pi\right) \cdot \pi - \left(\left(\left(\left(v \cdot v\right) \cdot \pi\right) \cdot \left(\left(v \cdot v\right) \cdot \pi\right)\right) \cdot \left(v \cdot v\right)\right) \cdot \pi}}{\sqrt{2 - v \cdot \left(v \cdot 6\right)}}
double f(double v) {
        double r2613015 = 4.0;
        double r2613016 = 3.0;
        double r2613017 = atan2(1.0, 0.0);
        double r2613018 = r2613016 * r2613017;
        double r2613019 = 1.0;
        double r2613020 = v;
        double r2613021 = r2613020 * r2613020;
        double r2613022 = r2613019 - r2613021;
        double r2613023 = r2613018 * r2613022;
        double r2613024 = 2.0;
        double r2613025 = 6.0;
        double r2613026 = r2613025 * r2613021;
        double r2613027 = r2613024 - r2613026;
        double r2613028 = sqrt(r2613027);
        double r2613029 = r2613023 * r2613028;
        double r2613030 = r2613015 / r2613029;
        return r2613030;
}
↓
double f(double v) {
        double r2613031 = v;
        double r2613032 = r2613031 * r2613031;
        double r2613033 = atan2(1.0, 0.0);
        double r2613034 = r2613032 * r2613033;
        double r2613035 = r2613034 * r2613034;
        double r2613036 = r2613034 * r2613033;
        double r2613037 = r2613035 + r2613036;
        double r2613038 = r2613033 * r2613033;
        double r2613039 = r2613037 + r2613038;
        double r2613040 = 1.3333333333333333;
        double r2613041 = r2613038 * r2613033;
        double r2613042 = r2613035 * r2613032;
        double r2613043 = r2613042 * r2613033;
        double r2613044 = r2613041 - r2613043;
        double r2613045 = r2613040 / r2613044;
        double r2613046 = r2613039 * r2613045;
        double r2613047 = 2.0;
        double r2613048 = 6.0;
        double r2613049 = r2613031 * r2613048;
        double r2613050 = r2613031 * r2613049;
        double r2613051 = r2613047 - r2613050;
        double r2613052 = sqrt(r2613051);
        double r2613053 = r2613046 / r2613052;
        return r2613053;
}

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 flip3--0.0

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

  5. Applied associate-/r/0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019155 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))