Average Error: 1.0 → 0.0
Time: 50.6s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{4}{3}}{\left(\pi - \left(v \cdot v\right) \cdot \pi\right) \cdot \sqrt{2 + \left(v \cdot -6\right) \cdot v}}\]
\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}{3}}{\left(\pi - \left(v \cdot v\right) \cdot \pi\right) \cdot \sqrt{2 + \left(v \cdot -6\right) \cdot v}}
double f(double v) {
        double r23841051 = 4.0;
        double r23841052 = 3.0;
        double r23841053 = atan2(1.0, 0.0);
        double r23841054 = r23841052 * r23841053;
        double r23841055 = 1.0;
        double r23841056 = v;
        double r23841057 = r23841056 * r23841056;
        double r23841058 = r23841055 - r23841057;
        double r23841059 = r23841054 * r23841058;
        double r23841060 = 2.0;
        double r23841061 = 6.0;
        double r23841062 = r23841061 * r23841057;
        double r23841063 = r23841060 - r23841062;
        double r23841064 = sqrt(r23841063);
        double r23841065 = r23841059 * r23841064;
        double r23841066 = r23841051 / r23841065;
        return r23841066;
}
↓
double f(double v) {
        double r23841067 = 1.3333333333333333;
        double r23841068 = atan2(1.0, 0.0);
        double r23841069 = v;
        double r23841070 = r23841069 * r23841069;
        double r23841071 = r23841070 * r23841068;
        double r23841072 = r23841068 - r23841071;
        double r23841073 = 2.0;
        double r23841074 = -6.0;
        double r23841075 = r23841069 * r23841074;
        double r23841076 = r23841075 * r23841069;
        double r23841077 = r23841073 + r23841076;
        double r23841078 = sqrt(r23841077);
        double r23841079 = r23841072 * r23841078;
        double r23841080 = r23841067 / r23841079;
        return r23841080;
}

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

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

  4. Applied associate-/l/0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019112 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))