Average Error: 4.1 → 7.4
Time: 54.7s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.261181977315073190059434568255866235012 \cdot 10^{103}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(\frac{z}{\log \left(e^{\sqrt[3]{t}}\right) \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) \cdot 2}}\\ \mathbf{elif}\;a \le 1.392355474446630492888563594513676627677 \cdot 10^{109}:\\ \;\;\;\;\frac{x}{y \cdot e^{2 \cdot \frac{\left(\sqrt{t + a} \cdot z\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot 3\right) - \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot 3 - \left(a - \frac{5}{6}\right) \cdot \frac{2}{t}\right) \cdot \left(\left(b - c\right) \cdot t\right)}{3 \cdot \left(t \cdot \left(a - \frac{5}{6}\right)\right)}} + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(\frac{z}{\log \left(e^{\sqrt[3]{t}}\right) \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) \cdot 2}}\\ \end{array}\]
\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}\;a \le -1.261181977315073190059434568255866235012 \cdot 10^{103}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{\left(\frac{z}{\log \left(e^{\sqrt[3]{t}}\right) \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) \cdot 2}}\\

\mathbf{elif}\;a \le 1.392355474446630492888563594513676627677 \cdot 10^{109}:\\
\;\;\;\;\frac{x}{y \cdot e^{2 \cdot \frac{\left(\sqrt{t + a} \cdot z\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot 3\right) - \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot 3 - \left(a - \frac{5}{6}\right) \cdot \frac{2}{t}\right) \cdot \left(\left(b - c\right) \cdot t\right)}{3 \cdot \left(t \cdot \left(a - \frac{5}{6}\right)\right)}} + x}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{\left(\frac{z}{\log \left(e^{\sqrt[3]{t}}\right) \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) \cdot 2}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r4217503 = x;
        double r4217504 = y;
        double r4217505 = 2.0;
        double r4217506 = z;
        double r4217507 = t;
        double r4217508 = a;
        double r4217509 = r4217507 + r4217508;
        double r4217510 = sqrt(r4217509);
        double r4217511 = r4217506 * r4217510;
        double r4217512 = r4217511 / r4217507;
        double r4217513 = b;
        double r4217514 = c;
        double r4217515 = r4217513 - r4217514;
        double r4217516 = 5.0;
        double r4217517 = 6.0;
        double r4217518 = r4217516 / r4217517;
        double r4217519 = r4217508 + r4217518;
        double r4217520 = 3.0;
        double r4217521 = r4217507 * r4217520;
        double r4217522 = r4217505 / r4217521;
        double r4217523 = r4217519 - r4217522;
        double r4217524 = r4217515 * r4217523;
        double r4217525 = r4217512 - r4217524;
        double r4217526 = r4217505 * r4217525;
        double r4217527 = exp(r4217526);
        double r4217528 = r4217504 * r4217527;
        double r4217529 = r4217503 + r4217528;
        double r4217530 = r4217503 / r4217529;
        return r4217530;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r4217531 = a;
        double r4217532 = -1.2611819773150732e+103;
        bool r4217533 = r4217531 <= r4217532;
        double r4217534 = x;
        double r4217535 = y;
        double r4217536 = z;
        double r4217537 = t;
        double r4217538 = cbrt(r4217537);
        double r4217539 = exp(r4217538);
        double r4217540 = log(r4217539);
        double r4217541 = r4217540 * r4217538;
        double r4217542 = r4217536 / r4217541;
        double r4217543 = r4217537 + r4217531;
        double r4217544 = sqrt(r4217543);
        double r4217545 = r4217544 / r4217538;
        double r4217546 = r4217542 * r4217545;
        double r4217547 = b;
        double r4217548 = c;
        double r4217549 = r4217547 - r4217548;
        double r4217550 = 5.0;
        double r4217551 = 6.0;
        double r4217552 = r4217550 / r4217551;
        double r4217553 = r4217531 + r4217552;
        double r4217554 = 2.0;
        double r4217555 = 3.0;
        double r4217556 = r4217537 * r4217555;
        double r4217557 = r4217554 / r4217556;
        double r4217558 = r4217553 - r4217557;
        double r4217559 = r4217549 * r4217558;
        double r4217560 = r4217546 - r4217559;
        double r4217561 = r4217560 * r4217554;
        double r4217562 = exp(r4217561);
        double r4217563 = r4217535 * r4217562;
        double r4217564 = r4217534 + r4217563;
        double r4217565 = r4217534 / r4217564;
        double r4217566 = 1.3923554744466305e+109;
        bool r4217567 = r4217531 <= r4217566;
        double r4217568 = r4217544 * r4217536;
        double r4217569 = r4217531 - r4217552;
        double r4217570 = r4217569 * r4217555;
        double r4217571 = r4217568 * r4217570;
        double r4217572 = r4217531 * r4217531;
        double r4217573 = r4217552 * r4217552;
        double r4217574 = r4217572 - r4217573;
        double r4217575 = r4217574 * r4217555;
        double r4217576 = r4217554 / r4217537;
        double r4217577 = r4217569 * r4217576;
        double r4217578 = r4217575 - r4217577;
        double r4217579 = r4217549 * r4217537;
        double r4217580 = r4217578 * r4217579;
        double r4217581 = r4217571 - r4217580;
        double r4217582 = r4217537 * r4217569;
        double r4217583 = r4217555 * r4217582;
        double r4217584 = r4217581 / r4217583;
        double r4217585 = r4217554 * r4217584;
        double r4217586 = exp(r4217585);
        double r4217587 = r4217535 * r4217586;
        double r4217588 = r4217587 + r4217534;
        double r4217589 = r4217534 / r4217588;
        double r4217590 = r4217567 ? r4217589 : r4217565;
        double r4217591 = r4217533 ? r4217565 : r4217590;
        return r4217591;
}

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 a < -1.2611819773150732e+103 or 1.3923554744466305e+109 < a

    1. Initial program 6.7

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

    3. Applied add-cube-cbrt6.7

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

    4. Applied times-frac4.7

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

    6. Applied add-log-exp15.6

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

    if -1.2611819773150732e+103 < a < 1.3923554744466305e+109

    1. Initial program 2.9

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

    3. Applied add-cbrt-cube2.9

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

    4. Applied add-cbrt-cube5.0

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

    5. Applied cbrt-unprod5.0

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

    6. Applied add-cbrt-cube5.0

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

    7. Applied cbrt-undiv5.1

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

    8. Simplified5.1

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

    10. Applied frac-times5.1

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

    11. Applied frac-times5.1

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

    12. Applied cbrt-div5.1

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

    13. Applied flip-+5.1

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

    14. Applied frac-sub5.1

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

    15. Applied associate-*r/5.2

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

    16. Applied frac-sub5.7

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

    17. Simplified3.5

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

    18. Simplified3.5

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

  4. Final simplification7.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.261181977315073190059434568255866235012 \cdot 10^{103}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(\frac{z}{\log \left(e^{\sqrt[3]{t}}\right) \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) \cdot 2}}\\ \mathbf{elif}\;a \le 1.392355474446630492888563594513676627677 \cdot 10^{109}:\\ \;\;\;\;\frac{x}{y \cdot e^{2 \cdot \frac{\left(\sqrt{t + a} \cdot z\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot 3\right) - \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot 3 - \left(a - \frac{5}{6}\right) \cdot \frac{2}{t}\right) \cdot \left(\left(b - c\right) \cdot t\right)}{3 \cdot \left(t \cdot \left(a - \frac{5}{6}\right)\right)}} + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(\frac{z}{\log \left(e^{\sqrt[3]{t}}\right) \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) \cdot 2}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z t a b c)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2"
  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))