Average Error: 1.0 → 0.0
Time: 16.0s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}} \cdot \sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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{\sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}} \cdot \sqrt{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r5338901 = 4.0;
        double r5338902 = 3.0;
        double r5338903 = atan2(1.0, 0.0);
        double r5338904 = r5338902 * r5338903;
        double r5338905 = 1.0;
        double r5338906 = v;
        double r5338907 = r5338906 * r5338906;
        double r5338908 = r5338905 - r5338907;
        double r5338909 = r5338904 * r5338908;
        double r5338910 = 2.0;
        double r5338911 = 6.0;
        double r5338912 = r5338911 * r5338907;
        double r5338913 = r5338910 - r5338912;
        double r5338914 = sqrt(r5338913);
        double r5338915 = r5338909 * r5338914;
        double r5338916 = r5338901 / r5338915;
        return r5338916;
}
↓
double f(double v) {
        double r5338917 = 1.3333333333333333;
        double r5338918 = atan2(1.0, 0.0);
        double r5338919 = v;
        double r5338920 = r5338919 * r5338919;
        double r5338921 = r5338920 * r5338918;
        double r5338922 = r5338918 - r5338921;
        double r5338923 = r5338917 / r5338922;
        double r5338924 = sqrt(r5338923);
        double r5338925 = r5338924 * r5338924;
        double r5338926 = 2.0;
        double r5338927 = 6.0;
        double r5338928 = r5338927 * r5338920;
        double r5338929 = r5338926 - r5338928;
        double r5338930 = sqrt(r5338929);
        double r5338931 = r5338925 / r5338930;
        return r5338931;
}

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

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

  4. Applied add-sqr-sqrt0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019135 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))