Average Error: 6.3 → 1.8
Time: 1.1m
Precision: 64
\[i \gt 0\]
\[\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}\]
\[\frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\frac{\sqrt[3]{\left(48 \cdot \pi\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{\sqrt[3]{1.205 \cdot 10^{-29}}}}{\frac{e^{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}}}}{e^{\frac{\frac{2 \cdot 1.205 \cdot 10^{-29}}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}\]
\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{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\frac{\sqrt[3]{\left(48 \cdot \pi\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{\sqrt[3]{1.205 \cdot 10^{-29}}}}{\frac{e^{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}}}}{e^{\frac{\frac{2 \cdot 1.205 \cdot 10^{-29}}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}
double f(double i) {
        double r27237361 = 48.0;
        double r27237362 = atan2(1.0, 0.0);
        double r27237363 = r27237361 * r27237362;
        double r27237364 = r27237363 * r27237362;
        double r27237365 = 1.205e-29;
        double r27237366 = r27237364 / r27237365;
        double r27237367 = r27237366 / r27237365;
        double r27237368 = 1.0;
        double r27237369 = 3.0;
        double r27237370 = r27237368 / r27237369;
        double r27237371 = pow(r27237367, r27237370);
        double r27237372 = 1e-06;
        double r27237373 = 1.1;
        double r27237374 = -r27237373;
        double r27237375 = 8.625e-05;
        double r27237376 = 823.0;
        double r27237377 = r27237375 * r27237376;
        double r27237378 = r27237374 / r27237377;
        double r27237379 = exp(r27237378);
        double r27237380 = r27237372 * r27237379;
        double r27237381 = r27237371 * r27237380;
        double r27237382 = i;
        double r27237383 = r27237382 + r27237368;
        double r27237384 = pow(r27237383, r27237370);
        double r27237385 = r27237381 * r27237384;
        double r27237386 = 1.77;
        double r27237387 = 2.0;
        double r27237388 = 6.25e+18;
        double r27237389 = r27237387 * r27237388;
        double r27237390 = r27237389 * r27237365;
        double r27237391 = r27237369 * r27237383;
        double r27237392 = r27237391 * r27237365;
        double r27237393 = 4.0;
        double r27237394 = r27237393 * r27237362;
        double r27237395 = r27237392 / r27237394;
        double r27237396 = pow(r27237395, r27237370);
        double r27237397 = r27237390 / r27237396;
        double r27237398 = r27237386 - r27237397;
        double r27237399 = -r27237398;
        double r27237400 = r27237399 / r27237377;
        double r27237401 = exp(r27237400);
        double r27237402 = r27237385 * r27237401;
        return r27237402;
}

double f(double i) {
        double r27237403 = 1.0;
        double r27237404 = i;
        double r27237405 = r27237403 + r27237404;
        double r27237406 = cbrt(r27237405);
        double r27237407 = 1e-06;
        double r27237408 = r27237406 * r27237407;
        double r27237409 = 1.1;
        double r27237410 = 823.0;
        double r27237411 = 8.625e-05;
        double r27237412 = r27237410 * r27237411;
        double r27237413 = r27237409 / r27237412;
        double r27237414 = exp(r27237413);
        double r27237415 = r27237408 / r27237414;
        double r27237416 = 48.0;
        double r27237417 = atan2(1.0, 0.0);
        double r27237418 = r27237416 * r27237417;
        double r27237419 = 1.205e-29;
        double r27237420 = r27237417 / r27237419;
        double r27237421 = r27237418 * r27237420;
        double r27237422 = cbrt(r27237421);
        double r27237423 = cbrt(r27237419);
        double r27237424 = r27237422 / r27237423;
        double r27237425 = 1.77;
        double r27237426 = r27237425 / r27237412;
        double r27237427 = exp(r27237426);
        double r27237428 = 2.0;
        double r27237429 = r27237428 * r27237419;
        double r27237430 = 1.3333333333333333;
        double r27237431 = r27237419 / r27237417;
        double r27237432 = r27237430 / r27237431;
        double r27237433 = r27237405 / r27237432;
        double r27237434 = cbrt(r27237433);
        double r27237435 = 6.25e+18;
        double r27237436 = r27237434 / r27237435;
        double r27237437 = r27237429 / r27237436;
        double r27237438 = r27237437 / r27237412;
        double r27237439 = exp(r27237438);
        double r27237440 = r27237427 / r27237439;
        double r27237441 = r27237424 / r27237440;
        double r27237442 = r27237415 * r27237441;
        return r27237442;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 6.3

    \[\left(\left({\left(\frac{\frac{\left(48 \cdot \pi\right) \cdot \pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}\right)}^{\left(\frac{1}{3}\right)} \cdot \left(10^{-06} \cdot e^{\frac{-1.1}{8.625 \cdot 10^{-05} \cdot 823}}\right)\right) \cdot {\left(i + 1\right)}^{\left(\frac{1}{3}\right)}\right) \cdot e^{\frac{-\left(1.77 - \frac{\left(2 \cdot 6.25 \cdot 10^{+18}\right) \cdot 1.205 \cdot 10^{-29}}{{\left(\frac{\left(3 \cdot \left(i + 1\right)\right) \cdot 1.205 \cdot 10^{-29}}{4 \cdot \pi}\right)}^{\left(\frac{1}{3}\right)}}\right)}{8.625 \cdot 10^{-05} \cdot 823}}\]
  2. Simplified2.0

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\sqrt[3]{\left(\frac{\pi}{1.205 \cdot 10^{-29}} \cdot 48\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{e^{\frac{1.77 - \frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}\]
  3. Using strategy rm
  4. Applied div-sub2.0

    \[\leadsto \frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\sqrt[3]{\left(\frac{\pi}{1.205 \cdot 10^{-29}} \cdot 48\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{e^{\color{blue}{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}} - \frac{\frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}\]
  5. Applied exp-diff1.9

    \[\leadsto \frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\sqrt[3]{\left(\frac{\pi}{1.205 \cdot 10^{-29}} \cdot 48\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{\color{blue}{\frac{e^{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}}}}{e^{\frac{\frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}}\]
  6. Using strategy rm
  7. Applied associate-*l/1.9

    \[\leadsto \frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\sqrt[3]{\color{blue}{\frac{\pi \cdot 48}{1.205 \cdot 10^{-29}}} \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{\frac{e^{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}}}}{e^{\frac{\frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}\]
  8. Applied associate-*l/1.9

    \[\leadsto \frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\sqrt[3]{\color{blue}{\frac{\left(\pi \cdot 48\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}{1.205 \cdot 10^{-29}}}}}{\frac{e^{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}}}}{e^{\frac{\frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}\]
  9. Applied cbrt-div1.8

    \[\leadsto \frac{\sqrt[3]{1 + i} \cdot 10^{-06}}{e^{\frac{1.1}{823 \cdot 8.625 \cdot 10^{-05}}}} \cdot \frac{\color{blue}{\frac{\sqrt[3]{\left(\pi \cdot 48\right) \cdot \frac{\pi}{1.205 \cdot 10^{-29}}}}{\sqrt[3]{1.205 \cdot 10^{-29}}}}}{\frac{e^{\frac{1.77}{823 \cdot 8.625 \cdot 10^{-05}}}}{e^{\frac{\frac{1.205 \cdot 10^{-29} \cdot 2}{\frac{\sqrt[3]{\frac{1 + i}{\frac{\frac{4}{3}}{\frac{1.205 \cdot 10^{-29}}{\pi}}}}}{6.25 \cdot 10^{+18}}}}{823 \cdot 8.625 \cdot 10^{-05}}}}}\]
  10. Final simplification1.8

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

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))"
  :pre (> i 0)
  (* (* (* (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)))))