Average Error: 1.0 → 0.0
Time: 10.2s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{2 - v \cdot \left(v \cdot 6\right)}}\]
\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{\frac{\frac{4}{3}}{\pi - \left(v \cdot v\right) \cdot \pi}}{\sqrt{2 - v \cdot \left(v \cdot 6\right)}}
double f(double v) {
        double r2904228 = 4.0;
        double r2904229 = 3.0;
        double r2904230 = atan2(1.0, 0.0);
        double r2904231 = r2904229 * r2904230;
        double r2904232 = 1.0;
        double r2904233 = v;
        double r2904234 = r2904233 * r2904233;
        double r2904235 = r2904232 - r2904234;
        double r2904236 = r2904231 * r2904235;
        double r2904237 = 2.0;
        double r2904238 = 6.0;
        double r2904239 = r2904238 * r2904234;
        double r2904240 = r2904237 - r2904239;
        double r2904241 = sqrt(r2904240);
        double r2904242 = r2904236 * r2904241;
        double r2904243 = r2904228 / r2904242;
        return r2904243;
}
↓
double f(double v) {
        double r2904244 = 1.3333333333333333;
        double r2904245 = atan2(1.0, 0.0);
        double r2904246 = v;
        double r2904247 = r2904246 * r2904246;
        double r2904248 = r2904247 * r2904245;
        double r2904249 = r2904245 - r2904248;
        double r2904250 = r2904244 / r2904249;
        double r2904251 = 2.0;
        double r2904252 = 6.0;
        double r2904253 = r2904246 * r2904252;
        double r2904254 = r2904246 * r2904253;
        double r2904255 = r2904251 - r2904254;
        double r2904256 = sqrt(r2904255);
        double r2904257 = r2904250 / r2904256;
        return r2904257;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019153 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))