Average Error: 3.8 → 7.0
Time: 11.4s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le 3.45477252400855375 \cdot 10^{233}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \sqrt[3]{{\left(\frac{2}{t \cdot 3}\right)}^{3}}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + 0.83333333333333337\right) - a \cdot b\right)}}\\ \end{array}\]
\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}\;a \le 3.45477252400855375 \cdot 10^{233}:\\
\;\;\;\;\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]{{\left(\frac{2}{t \cdot 3}\right)}^{3}}\right)\right)}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + 0.83333333333333337\right) - a \cdot b\right)}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r113483 = x;
        double r113484 = y;
        double r113485 = 2.0;
        double r113486 = z;
        double r113487 = t;
        double r113488 = a;
        double r113489 = r113487 + r113488;
        double r113490 = sqrt(r113489);
        double r113491 = r113486 * r113490;
        double r113492 = r113491 / r113487;
        double r113493 = b;
        double r113494 = c;
        double r113495 = r113493 - r113494;
        double r113496 = 5.0;
        double r113497 = 6.0;
        double r113498 = r113496 / r113497;
        double r113499 = r113488 + r113498;
        double r113500 = 3.0;
        double r113501 = r113487 * r113500;
        double r113502 = r113485 / r113501;
        double r113503 = r113499 - r113502;
        double r113504 = r113495 * r113503;
        double r113505 = r113492 - r113504;
        double r113506 = r113485 * r113505;
        double r113507 = exp(r113506);
        double r113508 = r113484 * r113507;
        double r113509 = r113483 + r113508;
        double r113510 = r113483 / r113509;
        return r113510;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r113511 = a;
        double r113512 = 3.4547725240085537e+233;
        bool r113513 = r113511 <= r113512;
        double r113514 = x;
        double r113515 = y;
        double r113516 = 2.0;
        double r113517 = z;
        double r113518 = t;
        double r113519 = r113518 + r113511;
        double r113520 = sqrt(r113519);
        double r113521 = r113517 * r113520;
        double r113522 = r113521 / r113518;
        double r113523 = b;
        double r113524 = c;
        double r113525 = r113523 - r113524;
        double r113526 = 5.0;
        double r113527 = 6.0;
        double r113528 = r113526 / r113527;
        double r113529 = r113511 + r113528;
        double r113530 = 3.0;
        double r113531 = r113518 * r113530;
        double r113532 = r113516 / r113531;
        double r113533 = 3.0;
        double r113534 = pow(r113532, r113533);
        double r113535 = cbrt(r113534);
        double r113536 = r113529 - r113535;
        double r113537 = r113525 * r113536;
        double r113538 = r113522 - r113537;
        double r113539 = r113516 * r113538;
        double r113540 = exp(r113539);
        double r113541 = r113515 * r113540;
        double r113542 = r113514 + r113541;
        double r113543 = r113514 / r113542;
        double r113544 = 0.8333333333333334;
        double r113545 = r113511 + r113544;
        double r113546 = r113524 * r113545;
        double r113547 = r113511 * r113523;
        double r113548 = r113546 - r113547;
        double r113549 = r113516 * r113548;
        double r113550 = exp(r113549);
        double r113551 = r113515 * r113550;
        double r113552 = r113514 + r113551;
        double r113553 = r113514 / r113552;
        double r113554 = r113513 ? r113543 : r113553;
        return r113554;
}

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 < 3.4547725240085537e+233

    1. Initial program 3.2

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

    3. Applied add-cbrt-cube3.2

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

    4. Applied add-cbrt-cube6.0

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

    5. Applied cbrt-unprod6.0

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

    6. Applied add-cbrt-cube6.0

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

    7. Applied cbrt-undiv6.1

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

    8. Simplified6.1

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

    if 3.4547725240085537e+233 < a

    1. Initial program 8.1

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

    2. Taylor expanded around inf 14.0

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(\left(a \cdot c + 0.83333333333333337 \cdot c\right) - a \cdot b\right)}}}\]

    3. Simplified14.0

      \[\leadsto \frac{x}{x + y \cdot e^{2 \cdot \color{blue}{\left(c \cdot \left(a + 0.83333333333333337\right) - a \cdot b\right)}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification7.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le 3.45477252400855375 \cdot 10^{233}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \sqrt[3]{{\left(\frac{2}{t \cdot 3}\right)}^{3}}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(c \cdot \left(a + 0.83333333333333337\right) - a \cdot b\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(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)))))))))))