Average Error: 1.0 → 0.0
Time: 21.7s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{1}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)} \cdot \frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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{1}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)} \cdot \frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r12214479 = 4.0;
        double r12214480 = 3.0;
        double r12214481 = atan2(1.0, 0.0);
        double r12214482 = r12214480 * r12214481;
        double r12214483 = 1.0;
        double r12214484 = v;
        double r12214485 = r12214484 * r12214484;
        double r12214486 = r12214483 - r12214485;
        double r12214487 = r12214482 * r12214486;
        double r12214488 = 2.0;
        double r12214489 = 6.0;
        double r12214490 = r12214489 * r12214485;
        double r12214491 = r12214488 - r12214490;
        double r12214492 = sqrt(r12214491);
        double r12214493 = r12214487 * r12214492;
        double r12214494 = r12214479 / r12214493;
        return r12214494;
}
↓
double f(double v) {
        double r12214495 = 1.0;
        double r12214496 = 3.0;
        double r12214497 = atan2(1.0, 0.0);
        double r12214498 = r12214496 * r12214497;
        double r12214499 = 1.0;
        double r12214500 = v;
        double r12214501 = r12214500 * r12214500;
        double r12214502 = r12214499 - r12214501;
        double r12214503 = r12214498 * r12214502;
        double r12214504 = r12214495 / r12214503;
        double r12214505 = 4.0;
        double r12214506 = 2.0;
        double r12214507 = 6.0;
        double r12214508 = r12214507 * r12214501;
        double r12214509 = r12214506 - r12214508;
        double r12214510 = sqrt(r12214509);
        double r12214511 = r12214505 / r12214510;
        double r12214512 = r12214504 * r12214511;
        return r12214512;
}

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 *-un-lft-identity1.0

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

  4. Applied times-frac0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019173 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))