Average Error: 3.6 → 1.8
Time: 1.3m
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -4.382061142785191097588738309999822145457 \cdot 10^{-96}:\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5}{6} + a\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2} \cdot y + x}\\ \mathbf{elif}\;t \le 4.339752338022243962882841013808555445154 \cdot 10^{-171}:\\ \;\;\;\;\frac{x}{y \cdot e^{\frac{\left(\sqrt{t + a} \cdot z\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - t \cdot \left(\left(\left(\frac{5}{6} + a\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(a - \frac{5}{6}\right) \cdot 2\right) \cdot \left(b - c\right)\right)}{\left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) \cdot t} \cdot 2} + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5}{6} + a\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2} \cdot y + x}\\ \end{array}\]
\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 -4.382061142785191097588738309999822145457 \cdot 10^{-96}:\\
\;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5}{6} + a\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2} \cdot y + x}\\

\mathbf{elif}\;t \le 4.339752338022243962882841013808555445154 \cdot 10^{-171}:\\
\;\;\;\;\frac{x}{y \cdot e^{\frac{\left(\sqrt{t + a} \cdot z\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - t \cdot \left(\left(\left(\frac{5}{6} + a\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(a - \frac{5}{6}\right) \cdot 2\right) \cdot \left(b - c\right)\right)}{\left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) \cdot t} \cdot 2} + x}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r5687387 = x;
        double r5687388 = y;
        double r5687389 = 2.0;
        double r5687390 = z;
        double r5687391 = t;
        double r5687392 = a;
        double r5687393 = r5687391 + r5687392;
        double r5687394 = sqrt(r5687393);
        double r5687395 = r5687390 * r5687394;
        double r5687396 = r5687395 / r5687391;
        double r5687397 = b;
        double r5687398 = c;
        double r5687399 = r5687397 - r5687398;
        double r5687400 = 5.0;
        double r5687401 = 6.0;
        double r5687402 = r5687400 / r5687401;
        double r5687403 = r5687392 + r5687402;
        double r5687404 = 3.0;
        double r5687405 = r5687391 * r5687404;
        double r5687406 = r5687389 / r5687405;
        double r5687407 = r5687403 - r5687406;
        double r5687408 = r5687399 * r5687407;
        double r5687409 = r5687396 - r5687408;
        double r5687410 = r5687389 * r5687409;
        double r5687411 = exp(r5687410);
        double r5687412 = r5687388 * r5687411;
        double r5687413 = r5687387 + r5687412;
        double r5687414 = r5687387 / r5687413;
        return r5687414;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r5687415 = t;
        double r5687416 = -4.382061142785191e-96;
        bool r5687417 = r5687415 <= r5687416;
        double r5687418 = x;
        double r5687419 = z;
        double r5687420 = cbrt(r5687415);
        double r5687421 = r5687420 * r5687420;
        double r5687422 = r5687419 / r5687421;
        double r5687423 = a;
        double r5687424 = r5687415 + r5687423;
        double r5687425 = sqrt(r5687424);
        double r5687426 = r5687425 / r5687420;
        double r5687427 = r5687422 * r5687426;
        double r5687428 = 5.0;
        double r5687429 = 6.0;
        double r5687430 = r5687428 / r5687429;
        double r5687431 = r5687430 + r5687423;
        double r5687432 = 2.0;
        double r5687433 = 3.0;
        double r5687434 = r5687415 * r5687433;
        double r5687435 = r5687432 / r5687434;
        double r5687436 = r5687431 - r5687435;
        double r5687437 = b;
        double r5687438 = c;
        double r5687439 = r5687437 - r5687438;
        double r5687440 = r5687436 * r5687439;
        double r5687441 = r5687427 - r5687440;
        double r5687442 = r5687441 * r5687432;
        double r5687443 = exp(r5687442);
        double r5687444 = y;
        double r5687445 = r5687443 * r5687444;
        double r5687446 = r5687445 + r5687418;
        double r5687447 = r5687418 / r5687446;
        double r5687448 = 4.339752338022244e-171;
        bool r5687449 = r5687415 <= r5687448;
        double r5687450 = r5687425 * r5687419;
        double r5687451 = r5687423 - r5687430;
        double r5687452 = r5687451 * r5687434;
        double r5687453 = r5687450 * r5687452;
        double r5687454 = r5687431 * r5687452;
        double r5687455 = r5687451 * r5687432;
        double r5687456 = r5687454 - r5687455;
        double r5687457 = r5687456 * r5687439;
        double r5687458 = r5687415 * r5687457;
        double r5687459 = r5687453 - r5687458;
        double r5687460 = r5687452 * r5687415;
        double r5687461 = r5687459 / r5687460;
        double r5687462 = r5687461 * r5687432;
        double r5687463 = exp(r5687462);
        double r5687464 = r5687444 * r5687463;
        double r5687465 = r5687464 + r5687418;
        double r5687466 = r5687418 / r5687465;
        double r5687467 = r5687449 ? r5687466 : r5687447;
        double r5687468 = r5687417 ? r5687447 : r5687467;
        return r5687468;
}

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 < -4.382061142785191e-96 or 4.339752338022244e-171 < t

    1. Initial program 2.2

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

    3. Applied add-cube-cbrt2.2

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

    4. Applied times-frac0.8

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

    if -4.382061142785191e-96 < t < 4.339752338022244e-171

    1. Initial program 7.6

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

    3. Applied flip-+10.7

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

    4. Applied frac-sub10.7

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

    5. Applied associate-*r/10.8

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

    6. Applied frac-sub7.7

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

    8. Applied difference-of-squares7.7

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

    9. Applied associate-*l*4.6

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

  4. Final simplification1.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -4.382061142785191097588738309999822145457 \cdot 10^{-96}:\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5}{6} + a\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2} \cdot y + x}\\ \mathbf{elif}\;t \le 4.339752338022243962882841013808555445154 \cdot 10^{-171}:\\ \;\;\;\;\frac{x}{y \cdot e^{\frac{\left(\sqrt{t + a} \cdot z\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - t \cdot \left(\left(\left(\frac{5}{6} + a\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(a - \frac{5}{6}\right) \cdot 2\right) \cdot \left(b - c\right)\right)}{\left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) \cdot t} \cdot 2} + x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5}{6} + a\right) - \frac{2}{t \cdot 3}\right) \cdot \left(b - c\right)\right) \cdot 2} \cdot y + x}\\ \end{array}\]

Reproduce

herbie shell --seed 2019170 
(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)))))))))))