Average Error: 1.0 → 0.0
Time: 14.7s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{4}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r8189979 = 4.0;
        double r8189980 = 3.0;
        double r8189981 = atan2(1.0, 0.0);
        double r8189982 = r8189980 * r8189981;
        double r8189983 = 1.0;
        double r8189984 = v;
        double r8189985 = r8189984 * r8189984;
        double r8189986 = r8189983 - r8189985;
        double r8189987 = r8189982 * r8189986;
        double r8189988 = 2.0;
        double r8189989 = 6.0;
        double r8189990 = r8189989 * r8189985;
        double r8189991 = r8189988 - r8189990;
        double r8189992 = sqrt(r8189991);
        double r8189993 = r8189987 * r8189992;
        double r8189994 = r8189979 / r8189993;
        return r8189994;
}
↓
double f(double v) {
        double r8189995 = 4.0;
        double r8189996 = 3.0;
        double r8189997 = atan2(1.0, 0.0);
        double r8189998 = r8189996 * r8189997;
        double r8189999 = 1.0;
        double r8190000 = v;
        double r8190001 = r8190000 * r8190000;
        double r8190002 = r8189999 - r8190001;
        double r8190003 = r8189998 * r8190002;
        double r8190004 = r8189995 / r8190003;
        double r8190005 = 2.0;
        double r8190006 = 6.0;
        double r8190007 = r8190006 * r8190001;
        double r8190008 = r8190005 - r8190007;
        double r8190009 = sqrt(r8190008);
        double r8190010 = r8190004 / r8190009;
        return r8190010;
}

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

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

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)))))))