Average Error: 1.0 → 0.0
Time: 13.7s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{4}{\left(\pi - \left(v \cdot v\right) \cdot \pi\right) \cdot 3}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}\]
\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{4}{\left(\pi - \left(v \cdot v\right) \cdot \pi\right) \cdot 3}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}
double f(double v) {
        double r5961884 = 4.0;
        double r5961885 = 3.0;
        double r5961886 = atan2(1.0, 0.0);
        double r5961887 = r5961885 * r5961886;
        double r5961888 = 1.0;
        double r5961889 = v;
        double r5961890 = r5961889 * r5961889;
        double r5961891 = r5961888 - r5961890;
        double r5961892 = r5961887 * r5961891;
        double r5961893 = 2.0;
        double r5961894 = 6.0;
        double r5961895 = r5961894 * r5961890;
        double r5961896 = r5961893 - r5961895;
        double r5961897 = sqrt(r5961896);
        double r5961898 = r5961892 * r5961897;
        double r5961899 = r5961884 / r5961898;
        return r5961899;
}
↓
double f(double v) {
        double r5961900 = 4.0;
        double r5961901 = atan2(1.0, 0.0);
        double r5961902 = v;
        double r5961903 = r5961902 * r5961902;
        double r5961904 = r5961903 * r5961901;
        double r5961905 = r5961901 - r5961904;
        double r5961906 = 3.0;
        double r5961907 = r5961905 * r5961906;
        double r5961908 = r5961900 / r5961907;
        double r5961909 = 2.0;
        double r5961910 = 6.0;
        double r5961911 = r5961903 * r5961910;
        double r5961912 = r5961909 - r5961911;
        double r5961913 = sqrt(r5961912);
        double r5961914 = r5961908 / r5961913;
        return r5961914;
}

Error

Bits error versus v

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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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019134 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))