Average Error: 6.5 → 1.3
Time: 33.9s
Precision: 64
\[\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}\]
\[\frac{\left(\sqrt[3]{\frac{48}{\frac{1.205 \cdot 10^{-29}}{\pi} \cdot \frac{1.205 \cdot 10^{-29}}{\pi}}} \cdot 10^{-06}\right) \cdot \frac{\sqrt[3]{i + 1}}{\sqrt[3]{e^{\frac{1.1}{8.625 \cdot 10^{-05} \cdot 823}} \cdot \left(e^{\frac{1.1}{8.625 \cdot 10^{-05} \cdot 823}} \cdot e^{\frac{1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)}}}{\left(\sqrt[3]{e^{\frac{1.77 - \frac{2}{\frac{\sqrt[3]{\left(\left(i + 1\right) \cdot \frac{1.205 \cdot 10^{-29}}{\pi}\right) \cdot \frac{3}{4}}}{1.205 \cdot 10^{-29}}} \cdot 6.25 \cdot 10^{+18}}{8.625 \cdot 10^{-05} \cdot 823}}} \cdot \sqrt[3]{e^{\frac{1.77 - \frac{2}{\frac{\sqrt[3]{\left(\left(i + 1\right) \cdot \frac{1.205 \cdot 10^{-29}}{\pi}\right) \cdot \frac{3}{4}}}{1.205 \cdot 10^{-29}}} \cdot 6.25 \cdot 10^{+18}}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \sqrt[3]{e^{\frac{1.77 - \frac{2}{\frac{\sqrt[3]{\left(\left(i + 1\right) \cdot \frac{1.205 \cdot 10^{-29}}{\pi}\right) \cdot \frac{3}{4}}}{1.205 \cdot 10^{-29}}} \cdot 6.25 \cdot 10^{+18}}{8.625 \cdot 10^{-05} \cdot 823}}}}\]
\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}
\frac{\left(\sqrt[3]{\frac{48}{\frac{1.205 \cdot 10^{-29}}{\pi} \cdot \frac{1.205 \cdot 10^{-29}}{\pi}}} \cdot 10^{-06}\right) \cdot \frac{\sqrt[3]{i + 1}}{\sqrt[3]{e^{\frac{1.1}{8.625 \cdot 10^{-05} \cdot 823}} \cdot \left(e^{\frac{1.1}{8.625 \cdot 10^{-05} \cdot 823}} \cdot e^{\frac{1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)}}}{\left(\sqrt[3]{e^{\frac{1.77 - \frac{2}{\frac{\sqrt[3]{\left(\left(i + 1\right) \cdot \frac{1.205 \cdot 10^{-29}}{\pi}\right) \cdot \frac{3}{4}}}{1.205 \cdot 10^{-29}}} \cdot 6.25 \cdot 10^{+18}}{8.625 \cdot 10^{-05} \cdot 823}}} \cdot \sqrt[3]{e^{\frac{1.77 - \frac{2}{\frac{\sqrt[3]{\left(\left(i + 1\right) \cdot \frac{1.205 \cdot 10^{-29}}{\pi}\right) \cdot \frac{3}{4}}}{1.205 \cdot 10^{-29}}} \cdot 6.25 \cdot 10^{+18}}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \sqrt[3]{e^{\frac{1.77 - \frac{2}{\frac{\sqrt[3]{\left(\left(i + 1\right) \cdot \frac{1.205 \cdot 10^{-29}}{\pi}\right) \cdot \frac{3}{4}}}{1.205 \cdot 10^{-29}}} \cdot 6.25 \cdot 10^{+18}}{8.625 \cdot 10^{-05} \cdot 823}}}}
double f(double i) {
        double r33520647 = 48.0;
        double r33520648 = atan2(1.0, 0.0);
        double r33520649 = r33520647 * r33520648;
        double r33520650 = r33520649 * r33520648;
        double r33520651 = 1.205e-29;
        double r33520652 = r33520650 / r33520651;
        double r33520653 = r33520652 / r33520651;
        double r33520654 = 1.0;
        double r33520655 = 3.0;
        double r33520656 = r33520654 / r33520655;
        double r33520657 = pow(r33520653, r33520656);
        double r33520658 = 1e-06;
        double r33520659 = 1.1;
        double r33520660 = -r33520659;
        double r33520661 = 8.625e-05;
        double r33520662 = 823.0;
        double r33520663 = r33520661 * r33520662;
        double r33520664 = r33520660 / r33520663;
        double r33520665 = exp(r33520664);
        double r33520666 = r33520658 * r33520665;
        double r33520667 = r33520657 * r33520666;
        double r33520668 = i;
        double r33520669 = r33520668 + r33520654;
        double r33520670 = pow(r33520669, r33520656);
        double r33520671 = r33520667 * r33520670;
        double r33520672 = 1.77;
        double r33520673 = 2.0;
        double r33520674 = 6.25e+18;
        double r33520675 = r33520673 * r33520674;
        double r33520676 = r33520675 * r33520651;
        double r33520677 = r33520655 * r33520669;
        double r33520678 = r33520677 * r33520651;
        double r33520679 = 4.0;
        double r33520680 = r33520679 * r33520648;
        double r33520681 = r33520678 / r33520680;
        double r33520682 = pow(r33520681, r33520656);
        double r33520683 = r33520676 / r33520682;
        double r33520684 = r33520672 - r33520683;
        double r33520685 = -r33520684;
        double r33520686 = r33520685 / r33520663;
        double r33520687 = exp(r33520686);
        double r33520688 = r33520671 * r33520687;
        return r33520688;
}

double f(double i) {
        double r33520689 = 48.0;
        double r33520690 = 1.205e-29;
        double r33520691 = atan2(1.0, 0.0);
        double r33520692 = r33520690 / r33520691;
        double r33520693 = r33520692 * r33520692;
        double r33520694 = r33520689 / r33520693;
        double r33520695 = cbrt(r33520694);
        double r33520696 = 1e-06;
        double r33520697 = r33520695 * r33520696;
        double r33520698 = i;
        double r33520699 = 1.0;
        double r33520700 = r33520698 + r33520699;
        double r33520701 = cbrt(r33520700);
        double r33520702 = 1.1;
        double r33520703 = 8.625e-05;
        double r33520704 = 823.0;
        double r33520705 = r33520703 * r33520704;
        double r33520706 = r33520702 / r33520705;
        double r33520707 = exp(r33520706);
        double r33520708 = r33520707 * r33520707;
        double r33520709 = r33520707 * r33520708;
        double r33520710 = cbrt(r33520709);
        double r33520711 = r33520701 / r33520710;
        double r33520712 = r33520697 * r33520711;
        double r33520713 = 1.77;
        double r33520714 = 2.0;
        double r33520715 = r33520700 * r33520692;
        double r33520716 = 0.75;
        double r33520717 = r33520715 * r33520716;
        double r33520718 = cbrt(r33520717);
        double r33520719 = r33520718 / r33520690;
        double r33520720 = r33520714 / r33520719;
        double r33520721 = 6.25e+18;
        double r33520722 = r33520720 * r33520721;
        double r33520723 = r33520713 - r33520722;
        double r33520724 = r33520723 / r33520705;
        double r33520725 = exp(r33520724);
        double r33520726 = cbrt(r33520725);
        double r33520727 = r33520726 * r33520726;
        double r33520728 = r33520727 * r33520726;
        double r33520729 = r33520712 / r33520728;
        return r33520729;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 6.5

    \[\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}\]
  2. Simplified2.3

    \[\leadsto \color{blue}{\frac{\left(\sqrt[3]{\frac{48}{\frac{1.205 \cdot 10^{-29}}{\pi} \cdot \frac{1.205 \cdot 10^{-29}}{\pi}}} \cdot 10^{-06}\right) \cdot \frac{\sqrt[3]{1 + i}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}}}{e^{\frac{1.77 - \frac{2}{\frac{\sqrt[3]{\frac{3}{4} \cdot \left(\left(1 + i\right) \cdot \frac{1.205 \cdot 10^{-29}}{\pi}\right)}}{1.205 \cdot 10^{-29}}} \cdot 6.25 \cdot 10^{+18}}{823 \cdot 8.625 \cdot 10^{-05}}}}}\]
  3. Using strategy rm
  4. Applied add-cube-cbrt1.5

    \[\leadsto \frac{\left(\sqrt[3]{\frac{48}{\frac{1.205 \cdot 10^{-29}}{\pi} \cdot \frac{1.205 \cdot 10^{-29}}{\pi}}} \cdot 10^{-06}\right) \cdot \frac{\sqrt[3]{1 + i}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}}}{\color{blue}{\left(\sqrt[3]{e^{\frac{1.77 - \frac{2}{\frac{\sqrt[3]{\frac{3}{4} \cdot \left(\left(1 + i\right) \cdot \frac{1.205 \cdot 10^{-29}}{\pi}\right)}}{1.205 \cdot 10^{-29}}} \cdot 6.25 \cdot 10^{+18}}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \sqrt[3]{e^{\frac{1.77 - \frac{2}{\frac{\sqrt[3]{\frac{3}{4} \cdot \left(\left(1 + i\right) \cdot \frac{1.205 \cdot 10^{-29}}{\pi}\right)}}{1.205 \cdot 10^{-29}}} \cdot 6.25 \cdot 10^{+18}}{823 \cdot 8.625 \cdot 10^{-05}}}}\right) \cdot \sqrt[3]{e^{\frac{1.77 - \frac{2}{\frac{\sqrt[3]{\frac{3}{4} \cdot \left(\left(1 + i\right) \cdot \frac{1.205 \cdot 10^{-29}}{\pi}\right)}}{1.205 \cdot 10^{-29}}} \cdot 6.25 \cdot 10^{+18}}{823 \cdot 8.625 \cdot 10^{-05}}}}}}\]
  5. Using strategy rm
  6. Applied add-cbrt-cube1.3

    \[\leadsto \frac{\left(\sqrt[3]{\frac{48}{\frac{1.205 \cdot 10^{-29}}{\pi} \cdot \frac{1.205 \cdot 10^{-29}}{\pi}}} \cdot 10^{-06}\right) \cdot \frac{\sqrt[3]{1 + i}}{\color{blue}{\sqrt[3]{\left(e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}} \cdot e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}\right) \cdot e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}}}}}{\left(\sqrt[3]{e^{\frac{1.77 - \frac{2}{\frac{\sqrt[3]{\frac{3}{4} \cdot \left(\left(1 + i\right) \cdot \frac{1.205 \cdot 10^{-29}}{\pi}\right)}}{1.205 \cdot 10^{-29}}} \cdot 6.25 \cdot 10^{+18}}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \sqrt[3]{e^{\frac{1.77 - \frac{2}{\frac{\sqrt[3]{\frac{3}{4} \cdot \left(\left(1 + i\right) \cdot \frac{1.205 \cdot 10^{-29}}{\pi}\right)}}{1.205 \cdot 10^{-29}}} \cdot 6.25 \cdot 10^{+18}}{823 \cdot 8.625 \cdot 10^{-05}}}}\right) \cdot \sqrt[3]{e^{\frac{1.77 - \frac{2}{\frac{\sqrt[3]{\frac{3}{4} \cdot \left(\left(1 + i\right) \cdot \frac{1.205 \cdot 10^{-29}}{\pi}\right)}}{1.205 \cdot 10^{-29}}} \cdot 6.25 \cdot 10^{+18}}{823 \cdot 8.625 \cdot 10^{-05}}}}}\]
  7. Final simplification1.3

    \[\leadsto \frac{\left(\sqrt[3]{\frac{48}{\frac{1.205 \cdot 10^{-29}}{\pi} \cdot \frac{1.205 \cdot 10^{-29}}{\pi}}} \cdot 10^{-06}\right) \cdot \frac{\sqrt[3]{i + 1}}{\sqrt[3]{e^{\frac{1.1}{8.625 \cdot 10^{-05} \cdot 823}} \cdot \left(e^{\frac{1.1}{8.625 \cdot 10^{-05} \cdot 823}} \cdot e^{\frac{1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)}}}{\left(\sqrt[3]{e^{\frac{1.77 - \frac{2}{\frac{\sqrt[3]{\left(\left(i + 1\right) \cdot \frac{1.205 \cdot 10^{-29}}{\pi}\right) \cdot \frac{3}{4}}}{1.205 \cdot 10^{-29}}} \cdot 6.25 \cdot 10^{+18}}{8.625 \cdot 10^{-05} \cdot 823}}} \cdot \sqrt[3]{e^{\frac{1.77 - \frac{2}{\frac{\sqrt[3]{\left(\left(i + 1\right) \cdot \frac{1.205 \cdot 10^{-29}}{\pi}\right) \cdot \frac{3}{4}}}{1.205 \cdot 10^{-29}}} \cdot 6.25 \cdot 10^{+18}}{8.625 \cdot 10^{-05} \cdot 823}}}\right) \cdot \sqrt[3]{e^{\frac{1.77 - \frac{2}{\frac{\sqrt[3]{\left(\left(i + 1\right) \cdot \frac{1.205 \cdot 10^{-29}}{\pi}\right) \cdot \frac{3}{4}}}{1.205 \cdot 10^{-29}}} \cdot 6.25 \cdot 10^{+18}}{8.625 \cdot 10^{-05} \cdot 823}}}}\]

Reproduce

herbie shell --seed 1 
(FPCore (i)
  :name "(pow((48*PI*PI/1.205e-29/1.205e-29),1/3)*( 1.0e-6*exp(-1.1/(8.625e-5 * 823))))*pow((i+1),1/3)*exp(-(1.77-2* 6.25e18 *1.205e-29/(pow((3*(i+1)*1.205e-29/(4*PI)),1/3)))/( 8.625e-5 * 823))"
  (* (* (* (pow (/ (/ (* (* 48 PI) PI) 1.205e-29) 1.205e-29) (/ 1 3)) (* 1e-06 (exp (/ (- 1.1) (* 8.625e-05 823))))) (pow (+ i 1) (/ 1 3))) (exp (/ (- (- 1.77 (/ (* (* 2 6.25e+18) 1.205e-29) (pow (/ (* (* 3 (+ i 1)) 1.205e-29) (* 4 PI)) (/ 1 3))))) (* 8.625e-05 823)))))