Average Error: 1.0 → 0.0
Time: 15.3s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{4}{1 \cdot \left(3 \cdot \pi\right) + \left(-3 \cdot \left({v}^{2} \cdot \pi\right)\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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}{1 \cdot \left(3 \cdot \pi\right) + \left(-3 \cdot \left({v}^{2} \cdot \pi\right)\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r231192 = 4.0;
        double r231193 = 3.0;
        double r231194 = atan2(1.0, 0.0);
        double r231195 = r231193 * r231194;
        double r231196 = 1.0;
        double r231197 = v;
        double r231198 = r231197 * r231197;
        double r231199 = r231196 - r231198;
        double r231200 = r231195 * r231199;
        double r231201 = 2.0;
        double r231202 = 6.0;
        double r231203 = r231202 * r231198;
        double r231204 = r231201 - r231203;
        double r231205 = sqrt(r231204);
        double r231206 = r231200 * r231205;
        double r231207 = r231192 / r231206;
        return r231207;
}
↓
double f(double v) {
        double r231208 = 4.0;
        double r231209 = 1.0;
        double r231210 = 3.0;
        double r231211 = atan2(1.0, 0.0);
        double r231212 = r231210 * r231211;
        double r231213 = r231209 * r231212;
        double r231214 = v;
        double r231215 = 2.0;
        double r231216 = pow(r231214, r231215);
        double r231217 = r231216 * r231211;
        double r231218 = r231210 * r231217;
        double r231219 = -r231218;
        double r231220 = r231213 + r231219;
        double r231221 = r231208 / r231220;
        double r231222 = 2.0;
        double r231223 = 6.0;
        double r231224 = r231214 * r231214;
        double r231225 = r231223 * r231224;
        double r231226 = r231222 - r231225;
        double r231227 = sqrt(r231226);
        double r231228 = r231221 / r231227;
        return r231228;
}

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. Using strategy rm

  5. Applied sub-neg0.0

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

  6. Applied distribute-lft-in0.0

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

  7. Simplified0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))