Average Error: 1.0 → 0.0
Time: 19.4s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\frac{\frac{\frac{4}{3}}{\sqrt{\log \left(e^{v \cdot \left(v \cdot \pi\right)}\right)} + \sqrt{\pi}}}{\sqrt{\pi} - \sqrt{\log \left(e^{v \cdot \left(v \cdot \pi\right)}\right)}}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}\]
\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{\frac{\frac{4}{3}}{\sqrt{\log \left(e^{v \cdot \left(v \cdot \pi\right)}\right)} + \sqrt{\pi}}}{\sqrt{\pi} - \sqrt{\log \left(e^{v \cdot \left(v \cdot \pi\right)}\right)}}}{\sqrt{2 - \left(v \cdot v\right) \cdot 6}}
double f(double v) {
        double r8060538 = 4.0;
        double r8060539 = 3.0;
        double r8060540 = atan2(1.0, 0.0);
        double r8060541 = r8060539 * r8060540;
        double r8060542 = 1.0;
        double r8060543 = v;
        double r8060544 = r8060543 * r8060543;
        double r8060545 = r8060542 - r8060544;
        double r8060546 = r8060541 * r8060545;
        double r8060547 = 2.0;
        double r8060548 = 6.0;
        double r8060549 = r8060548 * r8060544;
        double r8060550 = r8060547 - r8060549;
        double r8060551 = sqrt(r8060550);
        double r8060552 = r8060546 * r8060551;
        double r8060553 = r8060538 / r8060552;
        return r8060553;
}
↓
double f(double v) {
        double r8060554 = 1.3333333333333333;
        double r8060555 = v;
        double r8060556 = atan2(1.0, 0.0);
        double r8060557 = r8060555 * r8060556;
        double r8060558 = r8060555 * r8060557;
        double r8060559 = exp(r8060558);
        double r8060560 = log(r8060559);
        double r8060561 = sqrt(r8060560);
        double r8060562 = sqrt(r8060556);
        double r8060563 = r8060561 + r8060562;
        double r8060564 = r8060554 / r8060563;
        double r8060565 = r8060562 - r8060561;
        double r8060566 = r8060564 / r8060565;
        double r8060567 = 2.0;
        double r8060568 = r8060555 * r8060555;
        double r8060569 = 6.0;
        double r8060570 = r8060568 * r8060569;
        double r8060571 = r8060567 - r8060570;
        double r8060572 = sqrt(r8060571);
        double r8060573 = r8060566 / r8060572;
        return r8060573;
}

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. Simplified0.0

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

  4. Applied add-log-exp0.0

    \[\leadsto \frac{\frac{\frac{4}{3}}{\pi - \color{blue}{\log \left(e^{v \cdot \left(\pi \cdot v\right)}\right)}}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
  5. Using strategy rm

  6. Applied add-sqr-sqrt0.0

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

  7. Applied add-sqr-sqrt0.0

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

  8. Applied difference-of-squares0.0

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

  9. Applied associate-/r*0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019149 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))