Average Error: 3.8 → 3.2
Time: 38.4s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.3988457469696705 \cdot 10^{-242} \lor \neg \left(t \le 3.22201208794726605 \cdot 10^{-194}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{\left(\left|\sqrt[3]{t + a}\right| \cdot z\right) \cdot \sqrt{\sqrt[3]{t + a}}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(\left(\left|\sqrt[3]{t + a}\right| \cdot z\right) \cdot \sqrt{\sqrt[3]{t + a}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{t \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \end{array}\]
\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 -1.3988457469696705 \cdot 10^{-242} \lor \neg \left(t \le 3.22201208794726605 \cdot 10^{-194}\right):\\
\;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{\left(\left|\sqrt[3]{t + a}\right| \cdot z\right) \cdot \sqrt{\sqrt[3]{t + a}}}{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(\left(\left|\sqrt[3]{t + a}\right| \cdot z\right) \cdot \sqrt{\sqrt[3]{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 + \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)}}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r199319 = x;
        double r199320 = y;
        double r199321 = 2.0;
        double r199322 = z;
        double r199323 = t;
        double r199324 = a;
        double r199325 = r199323 + r199324;
        double r199326 = sqrt(r199325);
        double r199327 = r199322 * r199326;
        double r199328 = r199327 / r199323;
        double r199329 = b;
        double r199330 = c;
        double r199331 = r199329 - r199330;
        double r199332 = 5.0;
        double r199333 = 6.0;
        double r199334 = r199332 / r199333;
        double r199335 = r199324 + r199334;
        double r199336 = 3.0;
        double r199337 = r199323 * r199336;
        double r199338 = r199321 / r199337;
        double r199339 = r199335 - r199338;
        double r199340 = r199331 * r199339;
        double r199341 = r199328 - r199340;
        double r199342 = r199321 * r199341;
        double r199343 = exp(r199342);
        double r199344 = r199320 * r199343;
        double r199345 = r199319 + r199344;
        double r199346 = r199319 / r199345;
        return r199346;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r199347 = t;
        double r199348 = -1.3988457469696705e-242;
        bool r199349 = r199347 <= r199348;
        double r199350 = 3.222012087947266e-194;
        bool r199351 = r199347 <= r199350;
        double r199352 = !r199351;
        bool r199353 = r199349 || r199352;
        double r199354 = x;
        double r199355 = y;
        double r199356 = 2.0;
        double r199357 = a;
        double r199358 = r199347 + r199357;
        double r199359 = cbrt(r199358);
        double r199360 = fabs(r199359);
        double r199361 = z;
        double r199362 = r199360 * r199361;
        double r199363 = sqrt(r199359);
        double r199364 = r199362 * r199363;
        double r199365 = r199364 / r199347;
        double r199366 = b;
        double r199367 = c;
        double r199368 = r199366 - r199367;
        double r199369 = 5.0;
        double r199370 = 6.0;
        double r199371 = r199369 / r199370;
        double r199372 = r199357 + r199371;
        double r199373 = 3.0;
        double r199374 = r199347 * r199373;
        double r199375 = r199356 / r199374;
        double r199376 = r199372 - r199375;
        double r199377 = r199368 * r199376;
        double r199378 = r199365 - r199377;
        double r199379 = r199356 * r199378;
        double r199380 = exp(r199379);
        double r199381 = r199355 * r199380;
        double r199382 = r199354 + r199381;
        double r199383 = r199354 / r199382;
        double r199384 = r199357 - r199371;
        double r199385 = r199384 * r199374;
        double r199386 = r199364 * r199385;
        double r199387 = r199372 * r199385;
        double r199388 = r199384 * r199356;
        double r199389 = r199387 - r199388;
        double r199390 = r199368 * r199389;
        double r199391 = r199347 * r199390;
        double r199392 = r199386 - r199391;
        double r199393 = r199347 * r199385;
        double r199394 = r199392 / r199393;
        double r199395 = r199356 * r199394;
        double r199396 = exp(r199395);
        double r199397 = r199355 * r199396;
        double r199398 = r199354 + r199397;
        double r199399 = r199354 / r199398;
        double r199400 = r199353 ? r199383 : r199399;
        return r199400;
}

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 < -1.3988457469696705e-242 or 3.222012087947266e-194 < t

    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-cube-cbrt2.9

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

    4. Applied sqrt-prod2.9

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

    5. Applied associate-*r*2.9

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

    6. Simplified2.9

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

    if -1.3988457469696705e-242 < t < 3.222012087947266e-194

    1. Initial program 9.2

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

    3. Applied add-cube-cbrt9.2

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

    4. Applied sqrt-prod9.2

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

    5. Applied associate-*r*9.2

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

    6. Simplified9.2

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

    8. Applied flip-+13.9

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

    9. Applied frac-sub13.9

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

    10. Applied associate-*r/13.9

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

    11. Applied frac-sub9.8

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

    13. Applied difference-of-squares9.8

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

    14. Applied associate-*l*4.9

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

  4. Final simplification3.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.3988457469696705 \cdot 10^{-242} \lor \neg \left(t \le 3.22201208794726605 \cdot 10^{-194}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{\left(\left|\sqrt[3]{t + a}\right| \cdot z\right) \cdot \sqrt{\sqrt[3]{t + a}}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{\left(\left(\left|\sqrt[3]{t + a}\right| \cdot z\right) \cdot \sqrt{\sqrt[3]{t + a}}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{t \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 
(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)))))))))))