Average Error: 4.0 → 2.5
Time: 20.8s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -9.8445712940939801 \cdot 10^{-106} \lor \neg \left(t \le 1.1526597656514836 \cdot 10^{-304}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \end{array}\]
\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 -9.8445712940939801 \cdot 10^{-106} \lor \neg \left(t \le 1.1526597656514836 \cdot 10^{-304}\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 \sqrt[3]{t}\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 \sqrt[3]{t}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r136440 = x;
        double r136441 = y;
        double r136442 = 2.0;
        double r136443 = z;
        double r136444 = t;
        double r136445 = a;
        double r136446 = r136444 + r136445;
        double r136447 = sqrt(r136446);
        double r136448 = r136443 * r136447;
        double r136449 = r136448 / r136444;
        double r136450 = b;
        double r136451 = c;
        double r136452 = r136450 - r136451;
        double r136453 = 5.0;
        double r136454 = 6.0;
        double r136455 = r136453 / r136454;
        double r136456 = r136445 + r136455;
        double r136457 = 3.0;
        double r136458 = r136444 * r136457;
        double r136459 = r136442 / r136458;
        double r136460 = r136456 - r136459;
        double r136461 = r136452 * r136460;
        double r136462 = r136449 - r136461;
        double r136463 = r136442 * r136462;
        double r136464 = exp(r136463);
        double r136465 = r136441 * r136464;
        double r136466 = r136440 + r136465;
        double r136467 = r136440 / r136466;
        return r136467;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r136468 = t;
        double r136469 = -9.84457129409398e-106;
        bool r136470 = r136468 <= r136469;
        double r136471 = 1.1526597656514836e-304;
        bool r136472 = r136468 <= r136471;
        double r136473 = !r136472;
        bool r136474 = r136470 || r136473;
        double r136475 = x;
        double r136476 = y;
        double r136477 = 2.0;
        double r136478 = z;
        double r136479 = cbrt(r136468);
        double r136480 = r136479 * r136479;
        double r136481 = r136478 / r136480;
        double r136482 = a;
        double r136483 = r136468 + r136482;
        double r136484 = sqrt(r136483);
        double r136485 = r136484 / r136479;
        double r136486 = r136481 * r136485;
        double r136487 = b;
        double r136488 = c;
        double r136489 = r136487 - r136488;
        double r136490 = 5.0;
        double r136491 = 6.0;
        double r136492 = r136490 / r136491;
        double r136493 = r136482 + r136492;
        double r136494 = 3.0;
        double r136495 = r136468 * r136494;
        double r136496 = r136477 / r136495;
        double r136497 = r136493 - r136496;
        double r136498 = r136489 * r136497;
        double r136499 = r136486 - r136498;
        double r136500 = r136477 * r136499;
        double r136501 = exp(r136500);
        double r136502 = r136476 * r136501;
        double r136503 = r136475 + r136502;
        double r136504 = r136475 / r136503;
        double r136505 = r136478 * r136485;
        double r136506 = r136482 - r136492;
        double r136507 = r136506 * r136495;
        double r136508 = r136505 * r136507;
        double r136509 = r136482 * r136482;
        double r136510 = r136492 * r136492;
        double r136511 = r136509 - r136510;
        double r136512 = r136511 * r136495;
        double r136513 = r136506 * r136477;
        double r136514 = r136512 - r136513;
        double r136515 = r136489 * r136514;
        double r136516 = r136480 * r136515;
        double r136517 = r136508 - r136516;
        double r136518 = r136480 * r136507;
        double r136519 = r136517 / r136518;
        double r136520 = r136477 * r136519;
        double r136521 = exp(r136520);
        double r136522 = r136476 * r136521;
        double r136523 = r136475 + r136522;
        double r136524 = r136475 / r136523;
        double r136525 = r136474 ? r136504 : r136524;
        return r136525;
}

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 < -9.84457129409398e-106 or 1.1526597656514836e-304 < t

    1. Initial program 3.3

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

    3. Applied add-cube-cbrt3.3

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

    4. Applied times-frac2.1

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

    if -9.84457129409398e-106 < t < 1.1526597656514836e-304

    1. Initial program 8.4

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

    3. Applied add-cube-cbrt8.4

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

    4. Applied times-frac8.5

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

    6. Applied flip-+10.7

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

    7. Applied frac-sub10.7

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

    8. Applied associate-*r/10.7

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

    9. Applied associate-*l/10.7

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

    10. Applied frac-sub5.7

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

  4. Final simplification2.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -9.8445712940939801 \cdot 10^{-106} \lor \neg \left(t \le 1.1526597656514836 \cdot 10^{-304}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(z \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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)))))))))))