Average Error: 1.0 → 0.0
Time: 17.4s
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 r139226 = 4.0;
        double r139227 = 3.0;
        double r139228 = atan2(1.0, 0.0);
        double r139229 = r139227 * r139228;
        double r139230 = 1.0;
        double r139231 = v;
        double r139232 = r139231 * r139231;
        double r139233 = r139230 - r139232;
        double r139234 = r139229 * r139233;
        double r139235 = 2.0;
        double r139236 = 6.0;
        double r139237 = r139236 * r139232;
        double r139238 = r139235 - r139237;
        double r139239 = sqrt(r139238);
        double r139240 = r139234 * r139239;
        double r139241 = r139226 / r139240;
        return r139241;
}
↓
double f(double v) {
        double r139242 = 4.0;
        double r139243 = 3.0;
        double r139244 = atan2(1.0, 0.0);
        double r139245 = r139243 * r139244;
        double r139246 = 1.0;
        double r139247 = v;
        double r139248 = r139247 * r139247;
        double r139249 = r139246 - r139248;
        double r139250 = r139245 * r139249;
        double r139251 = r139242 / r139250;
        double r139252 = 2.0;
        double r139253 = 6.0;
        double r139254 = r139253 * r139248;
        double r139255 = r139252 - r139254;
        double r139256 = sqrt(r139255);
        double r139257 = r139251 / r139256;
        return r139257;
}

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 2019212 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))