Average Error: 1.0 → 0.0
Time: 7.0s
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 r189291 = 4.0;
        double r189292 = 3.0;
        double r189293 = atan2(1.0, 0.0);
        double r189294 = r189292 * r189293;
        double r189295 = 1.0;
        double r189296 = v;
        double r189297 = r189296 * r189296;
        double r189298 = r189295 - r189297;
        double r189299 = r189294 * r189298;
        double r189300 = 2.0;
        double r189301 = 6.0;
        double r189302 = r189301 * r189297;
        double r189303 = r189300 - r189302;
        double r189304 = sqrt(r189303);
        double r189305 = r189299 * r189304;
        double r189306 = r189291 / r189305;
        return r189306;
}
↓
double f(double v) {
        double r189307 = 4.0;
        double r189308 = 3.0;
        double r189309 = atan2(1.0, 0.0);
        double r189310 = r189308 * r189309;
        double r189311 = 1.0;
        double r189312 = v;
        double r189313 = r189312 * r189312;
        double r189314 = r189311 - r189313;
        double r189315 = r189310 * r189314;
        double r189316 = r189307 / r189315;
        double r189317 = 2.0;
        double r189318 = 6.0;
        double r189319 = r189318 * r189313;
        double r189320 = r189317 - r189319;
        double r189321 = sqrt(r189320);
        double r189322 = r189316 / r189321;
        return r189322;
}

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 2019308 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))