Average Error: 1.0 → 0.0
Time: 14.2s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{4}{\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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{\frac{4}{\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r5853096 = 4.0;
        double r5853097 = 3.0;
        double r5853098 = atan2(1.0, 0.0);
        double r5853099 = r5853097 * r5853098;
        double r5853100 = 1.0;
        double r5853101 = v;
        double r5853102 = r5853101 * r5853101;
        double r5853103 = r5853100 - r5853102;
        double r5853104 = r5853099 * r5853103;
        double r5853105 = 2.0;
        double r5853106 = 6.0;
        double r5853107 = r5853106 * r5853102;
        double r5853108 = r5853105 - r5853107;
        double r5853109 = sqrt(r5853108);
        double r5853110 = r5853104 * r5853109;
        double r5853111 = r5853096 / r5853110;
        return r5853111;
}
↓
double f(double v) {
        double r5853112 = 4.0;
        double r5853113 = atan2(1.0, 0.0);
        double r5853114 = 3.0;
        double r5853115 = r5853113 * r5853114;
        double r5853116 = 1.0;
        double r5853117 = v;
        double r5853118 = r5853117 * r5853117;
        double r5853119 = r5853116 - r5853118;
        double r5853120 = r5853115 * r5853119;
        double r5853121 = r5853112 / r5853120;
        double r5853122 = 2.0;
        double r5853123 = 6.0;
        double r5853124 = r5853123 * r5853118;
        double r5853125 = r5853122 - r5853124;
        double r5853126 = sqrt(r5853125);
        double r5853127 = r5853121 / r5853126;
        return r5853127;
}

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 associate-/r*0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))