Average Error: 1.0 → 0.0
Time: 8.8s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{3}}{\pi - v \cdot \left(v \cdot \pi\right)}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}\]
\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{\frac{4}{3}}{\pi - v \cdot \left(v \cdot \pi\right)}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}
double f(double v) {
        double r3509100 = 4.0;
        double r3509101 = 3.0;
        double r3509102 = atan2(1.0, 0.0);
        double r3509103 = r3509101 * r3509102;
        double r3509104 = 1.0;
        double r3509105 = v;
        double r3509106 = r3509105 * r3509105;
        double r3509107 = r3509104 - r3509106;
        double r3509108 = r3509103 * r3509107;
        double r3509109 = 2.0;
        double r3509110 = 6.0;
        double r3509111 = r3509110 * r3509106;
        double r3509112 = r3509109 - r3509111;
        double r3509113 = sqrt(r3509112);
        double r3509114 = r3509108 * r3509113;
        double r3509115 = r3509100 / r3509114;
        return r3509115;
}
↓
double f(double v) {
        double r3509116 = 1.3333333333333333;
        double r3509117 = atan2(1.0, 0.0);
        double r3509118 = v;
        double r3509119 = r3509118 * r3509117;
        double r3509120 = r3509118 * r3509119;
        double r3509121 = r3509117 - r3509120;
        double r3509122 = r3509116 / r3509121;
        double r3509123 = 2.0;
        double r3509124 = r3509118 * r3509118;
        double r3509125 = 6.0;
        double r3509126 = r3509124 * r3509125;
        double r3509127 = r3509123 - r3509126;
        double r3509128 = sqrt(r3509127);
        double r3509129 = r3509122 / r3509128;
        return r3509129;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019146 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))