Average Error: 4.0 → 3.1
Time: 38.1s
Precision: 64
\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -7.898436796540733 \cdot 10^{-89}:\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\ \mathbf{elif}\;t \le 1.4924055999405827 \cdot 10^{-228}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{\left(\left(\sqrt{t + a} \cdot z\right)\right)}{t} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\ \end{array}\]
\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 -7.898436796540733 \cdot 10^{-89}:\\
\;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\

\mathbf{elif}\;t \le 1.4924055999405827 \cdot 10^{-228}:\\
\;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{\left(\left(\sqrt{t + a} \cdot z\right)\right)}{t} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right)}}\\

\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{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r1727448 = x;
        double r1727449 = y;
        double r1727450 = 2.0;
        double r1727451 = z;
        double r1727452 = t;
        double r1727453 = a;
        double r1727454 = r1727452 + r1727453;
        double r1727455 = sqrt(r1727454);
        double r1727456 = r1727451 * r1727455;
        double r1727457 = r1727456 / r1727452;
        double r1727458 = b;
        double r1727459 = c;
        double r1727460 = r1727458 - r1727459;
        double r1727461 = 5.0;
        double r1727462 = 6.0;
        double r1727463 = r1727461 / r1727462;
        double r1727464 = r1727453 + r1727463;
        double r1727465 = 3.0;
        double r1727466 = r1727452 * r1727465;
        double r1727467 = r1727450 / r1727466;
        double r1727468 = r1727464 - r1727467;
        double r1727469 = r1727460 * r1727468;
        double r1727470 = r1727457 - r1727469;
        double r1727471 = r1727450 * r1727470;
        double r1727472 = exp(r1727471);
        double r1727473 = r1727449 * r1727472;
        double r1727474 = r1727448 + r1727473;
        double r1727475 = r1727448 / r1727474;
        return r1727475;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r1727476 = t;
        double r1727477 = -7.898436796540733e-89;
        bool r1727478 = r1727476 <= r1727477;
        double r1727479 = x;
        double r1727480 = z;
        double r1727481 = cbrt(r1727476);
        double r1727482 = r1727481 * r1727481;
        double r1727483 = r1727480 / r1727482;
        double r1727484 = a;
        double r1727485 = r1727476 + r1727484;
        double r1727486 = sqrt(r1727485);
        double r1727487 = r1727486 / r1727481;
        double r1727488 = r1727483 * r1727487;
        double r1727489 = 5.0;
        double r1727490 = 6.0;
        double r1727491 = r1727489 / r1727490;
        double r1727492 = r1727491 + r1727484;
        double r1727493 = 2.0;
        double r1727494 = 3.0;
        double r1727495 = r1727476 * r1727494;
        double r1727496 = r1727493 / r1727495;
        double r1727497 = r1727492 - r1727496;
        double r1727498 = b;
        double r1727499 = c;
        double r1727500 = r1727498 - r1727499;
        double r1727501 = r1727497 * r1727500;
        double r1727502 = r1727488 - r1727501;
        double r1727503 = r1727502 * r1727493;
        double r1727504 = exp(r1727503);
        double r1727505 = y;
        double r1727506 = r1727504 * r1727505;
        double r1727507 = r1727506 + r1727479;
        double r1727508 = r1727479 / r1727507;
        double r1727509 = 1.4924055999405827e-228;
        bool r1727510 = r1727476 <= r1727509;
        double r1727511 = r1727486 * r1727480;
        double r1727512 = /* ERROR: no posit support in C */;
        double r1727513 = /* ERROR: no posit support in C */;
        double r1727514 = r1727513 / r1727476;
        double r1727515 = r1727514 - r1727501;
        double r1727516 = r1727493 * r1727515;
        double r1727517 = exp(r1727516);
        double r1727518 = r1727505 * r1727517;
        double r1727519 = r1727479 + r1727518;
        double r1727520 = r1727479 / r1727519;
        double r1727521 = r1727510 ? r1727520 : r1727508;
        double r1727522 = r1727478 ? r1727508 : r1727521;
        return r1727522;
}

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 2 regimes

  2. if t < -7.898436796540733e-89 or 1.4924055999405827e-228 < t

    1. Initial program 2.9

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

    3. Applied add-cube-cbrt2.9

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

    4. Applied times-frac1.4

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

    if -7.898436796540733e-89 < t < 1.4924055999405827e-228

    1. Initial program 8.1

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

    3. Applied insert-posit169.1

      \[\leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{\color{blue}{\left(\left(z \cdot \sqrt{t + a}\right)\right)}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -7.898436796540733 \cdot 10^{-89}:\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\ \mathbf{elif}\;t \le 1.4924055999405827 \cdot 10^{-228}:\\ \;\;\;\;\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{\left(\left(\sqrt{t + a} \cdot z\right)\right)}{t} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{e^{\left(\frac{z}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{\sqrt{t + a}}{\sqrt[3]{t}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{t \cdot 3.0}\right) \cdot \left(b - c\right)\right) \cdot 2.0} \cdot y + x}\\ \end{array}\]

Reproduce

herbie shell --seed 2019153 
(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)))))))))))