Average Error: 1.0 → 0.0
Time: 17.6s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{4}{\left(3 \cdot \pi\right) \cdot \left(1 \cdot 1 - {v}^{4}\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}} \cdot \left(1 + v \cdot v\right)\]
\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 \cdot 1 - {v}^{4}\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}} \cdot \left(1 + v \cdot v\right)
double f(double v) {
        double r135214 = 4.0;
        double r135215 = 3.0;
        double r135216 = atan2(1.0, 0.0);
        double r135217 = r135215 * r135216;
        double r135218 = 1.0;
        double r135219 = v;
        double r135220 = r135219 * r135219;
        double r135221 = r135218 - r135220;
        double r135222 = r135217 * r135221;
        double r135223 = 2.0;
        double r135224 = 6.0;
        double r135225 = r135224 * r135220;
        double r135226 = r135223 - r135225;
        double r135227 = sqrt(r135226);
        double r135228 = r135222 * r135227;
        double r135229 = r135214 / r135228;
        return r135229;
}
↓
double f(double v) {
        double r135230 = 4.0;
        double r135231 = 3.0;
        double r135232 = atan2(1.0, 0.0);
        double r135233 = r135231 * r135232;
        double r135234 = 1.0;
        double r135235 = r135234 * r135234;
        double r135236 = v;
        double r135237 = 4.0;
        double r135238 = pow(r135236, r135237);
        double r135239 = r135235 - r135238;
        double r135240 = r135233 * r135239;
        double r135241 = r135230 / r135240;
        double r135242 = 2.0;
        double r135243 = 6.0;
        double r135244 = r135236 * r135236;
        double r135245 = r135243 * r135244;
        double r135246 = r135242 - r135245;
        double r135247 = sqrt(r135246);
        double r135248 = r135241 / r135247;
        double r135249 = r135234 + r135244;
        double r135250 = r135248 * r135249;
        return r135250;
}

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 flip--1.0

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

  4. Applied associate-*r/1.0

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

  5. Applied associate-*l/1.0

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

  6. Applied associate-/r/1.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))