Average Error: 3.8 → 4.4
Time: 35.3s
Precision: 64
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -5.347055751992442 \cdot 10^{-277}:\\ \;\;\;\;\frac{x}{x + e^{\left(\frac{\left(\left(\sqrt{t + a} \cdot z\right)\right)}{t} - \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{3.0 \cdot t}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y}\\ \mathbf{elif}\;t \le 1.1946639376173716 \cdot 10^{-306}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \left(\left(\frac{z}{t} \cdot \sqrt{t + a} - \left(\frac{5.0}{6.0} + \left(a - \frac{\frac{2.0}{t}}{3.0}\right)\right) \cdot \left(b - c\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \log \left(e^{\frac{z}{t} \cdot \sqrt{t + a} - \left(\frac{5.0}{6.0} + \left(a - \frac{\frac{2.0}{t}}{3.0}\right)\right) \cdot \left(b - c\right)}\right)}}\\ \end{array}\]
\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}
↓
\begin{array}{l}
\mathbf{if}\;t \le -5.347055751992442 \cdot 10^{-277}:\\
\;\;\;\;\frac{x}{x + e^{\left(\frac{\left(\left(\sqrt{t + a} \cdot z\right)\right)}{t} - \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{3.0 \cdot t}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y}\\

\mathbf{elif}\;t \le 1.1946639376173716 \cdot 10^{-306}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \left(\left(\frac{z}{t} \cdot \sqrt{t + a} - \left(\frac{5.0}{6.0} + \left(a - \frac{\frac{2.0}{t}}{3.0}\right)\right) \cdot \left(b - c\right)\right)\right)}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \log \left(e^{\frac{z}{t} \cdot \sqrt{t + a} - \left(\frac{5.0}{6.0} + \left(a - \frac{\frac{2.0}{t}}{3.0}\right)\right) \cdot \left(b - c\right)}\right)}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r4478476 = x;
        double r4478477 = y;
        double r4478478 = 2.0;
        double r4478479 = z;
        double r4478480 = t;
        double r4478481 = a;
        double r4478482 = r4478480 + r4478481;
        double r4478483 = sqrt(r4478482);
        double r4478484 = r4478479 * r4478483;
        double r4478485 = r4478484 / r4478480;
        double r4478486 = b;
        double r4478487 = c;
        double r4478488 = r4478486 - r4478487;
        double r4478489 = 5.0;
        double r4478490 = 6.0;
        double r4478491 = r4478489 / r4478490;
        double r4478492 = r4478481 + r4478491;
        double r4478493 = 3.0;
        double r4478494 = r4478480 * r4478493;
        double r4478495 = r4478478 / r4478494;
        double r4478496 = r4478492 - r4478495;
        double r4478497 = r4478488 * r4478496;
        double r4478498 = r4478485 - r4478497;
        double r4478499 = r4478478 * r4478498;
        double r4478500 = exp(r4478499);
        double r4478501 = r4478477 * r4478500;
        double r4478502 = r4478476 + r4478501;
        double r4478503 = r4478476 / r4478502;
        return r4478503;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r4478504 = t;
        double r4478505 = -5.347055751992442e-277;
        bool r4478506 = r4478504 <= r4478505;
        double r4478507 = x;
        double r4478508 = a;
        double r4478509 = r4478504 + r4478508;
        double r4478510 = sqrt(r4478509);
        double r4478511 = z;
        double r4478512 = r4478510 * r4478511;
        double r4478513 = /* ERROR: no posit support in C */;
        double r4478514 = /* ERROR: no posit support in C */;
        double r4478515 = r4478514 / r4478504;
        double r4478516 = 5.0;
        double r4478517 = 6.0;
        double r4478518 = r4478516 / r4478517;
        double r4478519 = r4478508 + r4478518;
        double r4478520 = 2.0;
        double r4478521 = 3.0;
        double r4478522 = r4478521 * r4478504;
        double r4478523 = r4478520 / r4478522;
        double r4478524 = r4478519 - r4478523;
        double r4478525 = b;
        double r4478526 = c;
        double r4478527 = r4478525 - r4478526;
        double r4478528 = r4478524 * r4478527;
        double r4478529 = r4478515 - r4478528;
        double r4478530 = r4478529 * r4478520;
        double r4478531 = exp(r4478530);
        double r4478532 = y;
        double r4478533 = r4478531 * r4478532;
        double r4478534 = r4478507 + r4478533;
        double r4478535 = r4478507 / r4478534;
        double r4478536 = 1.1946639376173716e-306;
        bool r4478537 = r4478504 <= r4478536;
        double r4478538 = r4478511 / r4478504;
        double r4478539 = r4478538 * r4478510;
        double r4478540 = r4478520 / r4478504;
        double r4478541 = r4478540 / r4478521;
        double r4478542 = r4478508 - r4478541;
        double r4478543 = r4478518 + r4478542;
        double r4478544 = r4478543 * r4478527;
        double r4478545 = r4478539 - r4478544;
        double r4478546 = /* ERROR: no posit support in C */;
        double r4478547 = /* ERROR: no posit support in C */;
        double r4478548 = r4478520 * r4478547;
        double r4478549 = exp(r4478548);
        double r4478550 = r4478532 * r4478549;
        double r4478551 = r4478507 + r4478550;
        double r4478552 = r4478507 / r4478551;
        double r4478553 = exp(r4478545);
        double r4478554 = log(r4478553);
        double r4478555 = r4478520 * r4478554;
        double r4478556 = exp(r4478555);
        double r4478557 = r4478532 * r4478556;
        double r4478558 = r4478507 + r4478557;
        double r4478559 = r4478507 / r4478558;
        double r4478560 = r4478537 ? r4478552 : r4478559;
        double r4478561 = r4478506 ? r4478535 : r4478560;
        return r4478561;
}

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

Derivation

  1. Split input into 3 regimes

  2. if t < -5.347055751992442e-277

    1. Initial program 4.3

      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
    2. Using strategy rm

    3. Applied insert-posit168.8

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{\color{blue}{\left(\left(z \cdot \sqrt{t + a}\right)\right)}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]

    if -5.347055751992442e-277 < t < 1.1946639376173716e-306

    1. Initial program 13.5

      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
    2. Using strategy rm

    3. Applied add-log-exp17.1

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\log \left(e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}\right)}\right)}}\]

    4. Applied add-log-exp28.8

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\log \left(e^{\frac{z \cdot \sqrt{t + a}}{t}}\right)} - \log \left(e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}\right)\right)}}\]

    5. Applied diff-log28.8

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\log \left(\frac{e^{\frac{z \cdot \sqrt{t + a}}{t}}}{e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}}\right)}}}\]

    6. Simplified15.3

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \log \color{blue}{\left(e^{\frac{z}{t} \cdot \sqrt{t + a} - \left(\frac{5.0}{6.0} + \left(a - \frac{\frac{2.0}{t}}{3.0}\right)\right) \cdot \left(b - c\right)}\right)}}}\]
    7. Using strategy rm

    8. Applied insert-posit1626.8

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\left(\left(\log \left(e^{\frac{z}{t} \cdot \sqrt{t + a} - \left(\frac{5.0}{6.0} + \left(a - \frac{\frac{2.0}{t}}{3.0}\right)\right) \cdot \left(b - c\right)}\right)\right)\right)}}}\]

    9. Simplified23.7

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\left(\left(\frac{z}{t} \cdot \sqrt{t + a} - \left(\frac{5.0}{6.0} + \left(a - \frac{\frac{2.0}{t}}{3.0}\right)\right) \cdot \left(b - c\right)\right)\right)}}}\]

    if 1.1946639376173716e-306 < t

    1. Initial program 3.2

      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
    2. Using strategy rm

    3. Applied add-log-exp7.4

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\log \left(e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}\right)}\right)}}\]

    4. Applied add-log-exp14.3

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\log \left(e^{\frac{z \cdot \sqrt{t + a}}{t}}\right)} - \log \left(e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}\right)\right)}}\]

    5. Applied diff-log14.3

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\log \left(\frac{e^{\frac{z \cdot \sqrt{t + a}}{t}}}{e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}}\right)}}}\]

    6. Simplified2.3

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \log \color{blue}{\left(e^{\frac{z}{t} \cdot \sqrt{t + a} - \left(\frac{5.0}{6.0} + \left(a - \frac{\frac{2.0}{t}}{3.0}\right)\right) \cdot \left(b - c\right)}\right)}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification4.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -5.347055751992442 \cdot 10^{-277}:\\ \;\;\;\;\frac{x}{x + e^{\left(\frac{\left(\left(\sqrt{t + a} \cdot z\right)\right)}{t} - \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{3.0 \cdot t}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y}\\ \mathbf{elif}\;t \le 1.1946639376173716 \cdot 10^{-306}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \left(\left(\frac{z}{t} \cdot \sqrt{t + a} - \left(\frac{5.0}{6.0} + \left(a - \frac{\frac{2.0}{t}}{3.0}\right)\right) \cdot \left(b - c\right)\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \log \left(e^{\frac{z}{t} \cdot \sqrt{t + a} - \left(\frac{5.0}{6.0} + \left(a - \frac{\frac{2.0}{t}}{3.0}\right)\right) \cdot \left(b - c\right)}\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(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)))))))))))