Average Error: 4.1 → 7.4
Time: 50.5s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.261181977315073190059434568255866235012 \cdot 10^{103}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\log \left(e^{\sqrt[3]{t}}\right)} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) \cdot 2}}\\ \mathbf{elif}\;a \le 1.392355474446630492888563594513676627677 \cdot 10^{109}:\\ \;\;\;\;\frac{x}{y \cdot e^{2 \cdot \frac{\left(\sqrt{t + a} \cdot z\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot 3\right) - \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot 3 - \left(a - \frac{5}{6}\right) \cdot \frac{2}{t}\right) \cdot \left(\left(b - c\right) \cdot t\right)}{3 \cdot \left(t \cdot \left(a - \frac{5}{6}\right)\right)}} + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\log \left(e^{\sqrt[3]{t}}\right)} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right) \cdot 2}}\\ \end{array}\]
\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}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\log \left(e^{\sqrt[3]{t}}\right)} - \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}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\log \left(e^{\sqrt[3]{t}}\right)} - \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 r4222488 = x;
        double r4222489 = y;
        double r4222490 = 2.0;
        double r4222491 = z;
        double r4222492 = t;
        double r4222493 = a;
        double r4222494 = r4222492 + r4222493;
        double r4222495 = sqrt(r4222494);
        double r4222496 = r4222491 * r4222495;
        double r4222497 = r4222496 / r4222492;
        double r4222498 = b;
        double r4222499 = c;
        double r4222500 = r4222498 - r4222499;
        double r4222501 = 5.0;
        double r4222502 = 6.0;
        double r4222503 = r4222501 / r4222502;
        double r4222504 = r4222493 + r4222503;
        double r4222505 = 3.0;
        double r4222506 = r4222492 * r4222505;
        double r4222507 = r4222490 / r4222506;
        double r4222508 = r4222504 - r4222507;
        double r4222509 = r4222500 * r4222508;
        double r4222510 = r4222497 - r4222509;
        double r4222511 = r4222490 * r4222510;
        double r4222512 = exp(r4222511);
        double r4222513 = r4222489 * r4222512;
        double r4222514 = r4222488 + r4222513;
        double r4222515 = r4222488 / r4222514;
        return r4222515;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r4222516 = a;
        double r4222517 = -1.2611819773150732e+103;
        bool r4222518 = r4222516 <= r4222517;
        double r4222519 = x;
        double r4222520 = y;
        double r4222521 = z;
        double r4222522 = t;
        double r4222523 = cbrt(r4222522);
        double r4222524 = r4222523 * r4222523;
        double r4222525 = r4222521 / r4222524;
        double r4222526 = r4222522 + r4222516;
        double r4222527 = sqrt(r4222526);
        double r4222528 = exp(r4222523);
        double r4222529 = log(r4222528);
        double r4222530 = r4222527 / r4222529;
        double r4222531 = r4222525 * r4222530;
        double r4222532 = b;
        double r4222533 = c;
        double r4222534 = r4222532 - r4222533;
        double r4222535 = 5.0;
        double r4222536 = 6.0;
        double r4222537 = r4222535 / r4222536;
        double r4222538 = r4222516 + r4222537;
        double r4222539 = 2.0;
        double r4222540 = 3.0;
        double r4222541 = r4222522 * r4222540;
        double r4222542 = r4222539 / r4222541;
        double r4222543 = r4222538 - r4222542;
        double r4222544 = r4222534 * r4222543;
        double r4222545 = r4222531 - r4222544;
        double r4222546 = r4222545 * r4222539;
        double r4222547 = exp(r4222546);
        double r4222548 = r4222520 * r4222547;
        double r4222549 = r4222519 + r4222548;
        double r4222550 = r4222519 / r4222549;
        double r4222551 = 1.3923554744466305e+109;
        bool r4222552 = r4222516 <= r4222551;
        double r4222553 = r4222527 * r4222521;
        double r4222554 = r4222516 - r4222537;
        double r4222555 = r4222554 * r4222540;
        double r4222556 = r4222553 * r4222555;
        double r4222557 = r4222516 * r4222516;
        double r4222558 = r4222537 * r4222537;
        double r4222559 = r4222557 - r4222558;
        double r4222560 = r4222559 * r4222540;
        double r4222561 = r4222539 / r4222522;
        double r4222562 = r4222554 * r4222561;
        double r4222563 = r4222560 - r4222562;
        double r4222564 = r4222534 * r4222522;
        double r4222565 = r4222563 * r4222564;
        double r4222566 = r4222556 - r4222565;
        double r4222567 = r4222522 * r4222554;
        double r4222568 = r4222540 * r4222567;
        double r4222569 = r4222566 / r4222568;
        double r4222570 = r4222539 * r4222569;
        double r4222571 = exp(r4222570);
        double r4222572 = r4222520 * r4222571;
        double r4222573 = r4222572 + r4222519;
        double r4222574 = r4222519 / r4222573;
        double r4222575 = r4222552 ? r4222574 : r4222550;
        double r4222576 = r4222518 ? r4222550 : r4222575;
        return r4222576;
}

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

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

    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

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

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)))))))))))