Average Error: 3.6 → 5.6
Time: 12.6s
Precision: 64
\[\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \frac{2}{t \cdot 3}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.82240491841941235 \cdot 10^{25} \lor \neg \left(t \le 9.4038599868785742 \cdot 10^{-4}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \log \left(e^{\frac{2}{t \cdot 3}}\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \frac{t}{\sqrt{t + a}} \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\frac{t}{\sqrt{t + a}} \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \end{array}\]
\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 -1.82240491841941235 \cdot 10^{25} \lor \neg \left(t \le 9.4038599868785742 \cdot 10^{-4}\right):\\
\;\;\;\;\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) - \log \left(e^{\frac{2}{t \cdot 3}}\right)\right)\right)}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \frac{t}{\sqrt{t + a}} \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)}{\frac{t}{\sqrt{t + a}} \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 r107341 = x;
        double r107342 = y;
        double r107343 = 2.0;
        double r107344 = z;
        double r107345 = t;
        double r107346 = a;
        double r107347 = r107345 + r107346;
        double r107348 = sqrt(r107347);
        double r107349 = r107344 * r107348;
        double r107350 = r107349 / r107345;
        double r107351 = b;
        double r107352 = c;
        double r107353 = r107351 - r107352;
        double r107354 = 5.0;
        double r107355 = 6.0;
        double r107356 = r107354 / r107355;
        double r107357 = r107346 + r107356;
        double r107358 = 3.0;
        double r107359 = r107345 * r107358;
        double r107360 = r107343 / r107359;
        double r107361 = r107357 - r107360;
        double r107362 = r107353 * r107361;
        double r107363 = r107350 - r107362;
        double r107364 = r107343 * r107363;
        double r107365 = exp(r107364);
        double r107366 = r107342 * r107365;
        double r107367 = r107341 + r107366;
        double r107368 = r107341 / r107367;
        return r107368;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r107369 = t;
        double r107370 = -1.8224049184194124e+25;
        bool r107371 = r107369 <= r107370;
        double r107372 = 0.0009403859986878574;
        bool r107373 = r107369 <= r107372;
        double r107374 = !r107373;
        bool r107375 = r107371 || r107374;
        double r107376 = x;
        double r107377 = y;
        double r107378 = 2.0;
        double r107379 = z;
        double r107380 = a;
        double r107381 = r107369 + r107380;
        double r107382 = sqrt(r107381);
        double r107383 = r107379 * r107382;
        double r107384 = r107383 / r107369;
        double r107385 = b;
        double r107386 = c;
        double r107387 = r107385 - r107386;
        double r107388 = 5.0;
        double r107389 = 6.0;
        double r107390 = r107388 / r107389;
        double r107391 = r107380 + r107390;
        double r107392 = 3.0;
        double r107393 = r107369 * r107392;
        double r107394 = r107378 / r107393;
        double r107395 = exp(r107394);
        double r107396 = log(r107395);
        double r107397 = r107391 - r107396;
        double r107398 = r107387 * r107397;
        double r107399 = r107384 - r107398;
        double r107400 = r107378 * r107399;
        double r107401 = exp(r107400);
        double r107402 = r107377 * r107401;
        double r107403 = r107376 + r107402;
        double r107404 = r107376 / r107403;
        double r107405 = r107380 - r107390;
        double r107406 = r107405 * r107393;
        double r107407 = r107379 * r107406;
        double r107408 = r107369 / r107382;
        double r107409 = r107380 * r107380;
        double r107410 = r107390 * r107390;
        double r107411 = r107409 - r107410;
        double r107412 = r107411 * r107393;
        double r107413 = r107405 * r107378;
        double r107414 = r107412 - r107413;
        double r107415 = r107387 * r107414;
        double r107416 = r107408 * r107415;
        double r107417 = r107407 - r107416;
        double r107418 = r107408 * r107406;
        double r107419 = r107417 / r107418;
        double r107420 = r107378 * r107419;
        double r107421 = exp(r107420);
        double r107422 = r107377 * r107421;
        double r107423 = r107376 + r107422;
        double r107424 = r107376 / r107423;
        double r107425 = r107375 ? r107404 : r107424;
        return r107425;
}

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 < -1.8224049184194124e+25 or 0.0009403859986878574 < t

    1. Initial program 2.4

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

    3. Applied add-log-exp2.4

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

    if -1.8224049184194124e+25 < t < 0.0009403859986878574

    1. Initial program 4.8

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

    3. Applied associate-/l*5.9

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

    5. Applied flip-+8.4

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

    6. Applied frac-sub8.4

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

    7. Applied associate-*r/8.4

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

    8. Applied frac-sub8.8

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

  4. Final simplification5.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.82240491841941235 \cdot 10^{25} \lor \neg \left(t \le 9.4038599868785742 \cdot 10^{-4}\right):\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5}{6}\right) - \log \left(e^{\frac{2}{t \cdot 3}}\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2 \cdot \frac{z \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right) - \frac{t}{\sqrt{t + a}} \cdot \left(\left(b - c\right) \cdot \left(\left(a \cdot a - \frac{5}{6} \cdot \frac{5}{6}\right) \cdot \left(t \cdot 3\right) - \left(a - \frac{5}{6}\right) \cdot 2\right)\right)}{\frac{t}{\sqrt{t + a}} \cdot \left(\left(a - \frac{5}{6}\right) \cdot \left(t \cdot 3\right)\right)}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020056 
(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)))))))))))