Average Error: 3.7 → 2.6
Time: 36.1s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le \frac{-3044132996692187}{1.852673427797059126777135760139006525652 \cdot 10^{78}} \lor \neg \left(t \le \frac{8271322624711839}{1.774508604237321510130185077851573570199 \cdot 10^{131}}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) + \left(-\sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)\right)\right)}{\sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)\right)}}}\\ \end{array}\]
\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}
↓
\begin{array}{l}
\mathbf{if}\;t \le \frac{-3044132996692187}{1.852673427797059126777135760139006525652 \cdot 10^{78}} \lor \neg \left(t \le \frac{8271322624711839}{1.774508604237321510130185077851573570199 \cdot 10^{131}}\right):\\
\;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) + \left(-\sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)\right)\right)}{\sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)\right)}}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r111332 = x;
        double r111333 = y;
        double r111334 = 2.0;
        double r111335 = z;
        double r111336 = t;
        double r111337 = a;
        double r111338 = r111336 + r111337;
        double r111339 = sqrt(r111338);
        double r111340 = r111335 * r111339;
        double r111341 = r111340 / r111336;
        double r111342 = b;
        double r111343 = c;
        double r111344 = r111342 - r111343;
        double r111345 = 5.0;
        double r111346 = 6.0;
        double r111347 = r111345 / r111346;
        double r111348 = r111337 + r111347;
        double r111349 = 3.0;
        double r111350 = r111336 * r111349;
        double r111351 = r111334 / r111350;
        double r111352 = r111348 - r111351;
        double r111353 = r111344 * r111352;
        double r111354 = r111341 - r111353;
        double r111355 = r111334 * r111354;
        double r111356 = exp(r111355);
        double r111357 = r111333 * r111356;
        double r111358 = r111332 + r111357;
        double r111359 = r111332 / r111358;
        return r111359;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r111360 = t;
        double r111361 = -3044132996692187.0;
        double r111362 = 1.8526734277970591e+78;
        double r111363 = r111361 / r111362;
        bool r111364 = r111360 <= r111363;
        double r111365 = 8271322624711839.0;
        double r111366 = 1.7745086042373215e+131;
        double r111367 = r111365 / r111366;
        bool r111368 = r111360 <= r111367;
        double r111369 = !r111368;
        bool r111370 = r111364 || r111369;
        double r111371 = x;
        double r111372 = y;
        double r111373 = 2.0;
        double r111374 = z;
        double r111375 = cbrt(r111360);
        double r111376 = r111375 * r111375;
        double r111377 = r111374 / r111376;
        double r111378 = a;
        double r111379 = r111360 + r111378;
        double r111380 = sqrt(r111379);
        double r111381 = r111380 / r111375;
        double r111382 = r111377 * r111381;
        double r111383 = b;
        double r111384 = c;
        double r111385 = r111383 - r111384;
        double r111386 = 5.0;
        double r111387 = 6.0;
        double r111388 = r111386 / r111387;
        double r111389 = r111378 + r111388;
        double r111390 = 3.0;
        double r111391 = r111360 * r111390;
        double r111392 = r111373 / r111391;
        double r111393 = r111389 - r111392;
        double r111394 = r111385 * r111393;
        double r111395 = r111382 - r111394;
        double r111396 = r111373 * r111395;
        double r111397 = exp(r111396);
        double r111398 = r111372 * r111397;
        double r111399 = r111371 + r111398;
        double r111400 = r111371 / r111399;
        double r111401 = r111374 * r111381;
        double r111402 = r111378 - r111388;
        double r111403 = r111402 * r111391;
        double r111404 = r111401 * r111403;
        double r111405 = r111378 * r111378;
        double r111406 = r111388 * r111388;
        double r111407 = r111405 - r111406;
        double r111408 = r111407 * r111391;
        double r111409 = r111402 * r111373;
        double r111410 = r111408 - r111409;
        double r111411 = r111385 * r111410;
        double r111412 = r111375 * r111411;
        double r111413 = r111375 * r111412;
        double r111414 = -r111413;
        double r111415 = r111404 + r111414;
        double r111416 = r111375 * r111403;
        double r111417 = r111375 * r111416;
        double r111418 = r111415 / r111417;
        double r111419 = r111373 * r111418;
        double r111420 = exp(r111419);
        double r111421 = r111372 * r111420;
        double r111422 = r111371 + r111421;
        double r111423 = r111371 / r111422;
        double r111424 = r111370 ? r111400 : r111423;
        return r111424;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if t < -1.6431028539724054e-63 or 4.661190486741443e-116 < t

    1. Initial program 2.3

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt2.3

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

    4. Applied times-frac0.5

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

    if -1.6431028539724054e-63 < t < 4.661190486741443e-116

    1. Initial program 6.6

      \[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt6.6

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]

    4. Applied times-frac6.8

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
    5. Using strategy rm

    6. Applied add-log-exp33.0

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \color{blue}{\log \left(e^{\sqrt[3]{t}}\right)}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
    7. Using strategy rm

    8. Applied flip-+34.8

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \log \left(e^{\sqrt[3]{t}}\right)} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\color{blue}{\frac{a \cdot a - \frac{5}{6} \cdot \frac{5}{6}}{a - \frac{5}{6}}} - \frac{2}{t \cdot 3}\right)\right)}}\]

    9. Applied frac-sub34.8

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \log \left(e^{\sqrt[3]{t}}\right)} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \color{blue}{\frac{\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2}{\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)}}\right)}}\]

    10. Applied associate-*r/34.8

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \log \left(e^{\sqrt[3]{t}}\right)} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \color{blue}{\frac{\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)}{\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)}}\right)}}\]

    11. Applied associate-*l/34.9

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \left(\color{blue}{\frac{z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}}{\sqrt[3]{t} \cdot \log \left(e^{\sqrt[3]{t}}\right)}} - \frac{\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)}{\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)}\right)}}\]

    12. Applied frac-sub46.1

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\frac{\left(z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(\sqrt[3]{t} \cdot \log \left(e^{\sqrt[3]{t}}\right)\right) \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\left(\sqrt[3]{t} \cdot \log \left(e^{\sqrt[3]{t}}\right)\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}}\]

    13. Simplified32.1

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \frac{\color{blue}{\left(z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) + \left(-\sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)\right)\right)}}{\left(\sqrt[3]{t} \cdot \log \left(e^{\sqrt[3]{t}}\right)\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\]

    14. Simplified6.7

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) + \left(-\sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)\right)\right)}{\color{blue}{\sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)\right)}}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le \frac{-3044132996692187}{1.852673427797059126777135760139006525652 \cdot 10^{78}} \lor \neg \left(t \le \frac{8271322624711839}{1.774508604237321510130185077851573570199 \cdot 10^{131}}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) + \left(-\sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)\right)\right)}{\sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)\right)}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2"
  :precision binary64
  (/ x (+ x (* y (exp (* 2 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5 6)) (/ 2 (* t 3)))))))))))