Average Error: 28.8 → 1.1
Time: 21.7s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.895393240846026 \cdot 10^{+34}:\\ \;\;\;\;\left(y \cdot \left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{36.527041698806414 \cdot y}{z}\right) + x\\ \mathbf{elif}\;z \le 3.866410402714096 \cdot 10^{+43}:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot \left(a + z \cdot \left(z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right) + t\right)\right)}{0.607771387771 + \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{36.527041698806414 \cdot y}{z}\right) + x\\ \end{array}\]
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.895393240846026 \cdot 10^{+34}:\\
\;\;\;\;\left(y \cdot \left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{36.527041698806414 \cdot y}{z}\right) + x\\

\mathbf{elif}\;z \le 3.866410402714096 \cdot 10^{+43}:\\
\;\;\;\;x + y \cdot \frac{b + z \cdot \left(a + z \cdot \left(z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right) + t\right)\right)}{0.607771387771 + \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right) \cdot z}\\

\mathbf{else}:\\
\;\;\;\;\left(y \cdot \left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{36.527041698806414 \cdot y}{z}\right) + x\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r21225446 = x;
        double r21225447 = y;
        double r21225448 = z;
        double r21225449 = 3.13060547623;
        double r21225450 = r21225448 * r21225449;
        double r21225451 = 11.1667541262;
        double r21225452 = r21225450 + r21225451;
        double r21225453 = r21225452 * r21225448;
        double r21225454 = t;
        double r21225455 = r21225453 + r21225454;
        double r21225456 = r21225455 * r21225448;
        double r21225457 = a;
        double r21225458 = r21225456 + r21225457;
        double r21225459 = r21225458 * r21225448;
        double r21225460 = b;
        double r21225461 = r21225459 + r21225460;
        double r21225462 = r21225447 * r21225461;
        double r21225463 = 15.234687407;
        double r21225464 = r21225448 + r21225463;
        double r21225465 = r21225464 * r21225448;
        double r21225466 = 31.4690115749;
        double r21225467 = r21225465 + r21225466;
        double r21225468 = r21225467 * r21225448;
        double r21225469 = 11.9400905721;
        double r21225470 = r21225468 + r21225469;
        double r21225471 = r21225470 * r21225448;
        double r21225472 = 0.607771387771;
        double r21225473 = r21225471 + r21225472;
        double r21225474 = r21225462 / r21225473;
        double r21225475 = r21225446 + r21225474;
        return r21225475;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r21225476 = z;
        double r21225477 = -2.895393240846026e+34;
        bool r21225478 = r21225476 <= r21225477;
        double r21225479 = y;
        double r21225480 = 3.13060547623;
        double r21225481 = t;
        double r21225482 = r21225476 * r21225476;
        double r21225483 = r21225481 / r21225482;
        double r21225484 = r21225480 + r21225483;
        double r21225485 = r21225479 * r21225484;
        double r21225486 = 36.527041698806414;
        double r21225487 = r21225486 * r21225479;
        double r21225488 = r21225487 / r21225476;
        double r21225489 = r21225485 - r21225488;
        double r21225490 = x;
        double r21225491 = r21225489 + r21225490;
        double r21225492 = 3.866410402714096e+43;
        bool r21225493 = r21225476 <= r21225492;
        double r21225494 = b;
        double r21225495 = a;
        double r21225496 = 11.1667541262;
        double r21225497 = r21225480 * r21225476;
        double r21225498 = r21225496 + r21225497;
        double r21225499 = r21225476 * r21225498;
        double r21225500 = r21225499 + r21225481;
        double r21225501 = r21225476 * r21225500;
        double r21225502 = r21225495 + r21225501;
        double r21225503 = r21225476 * r21225502;
        double r21225504 = r21225494 + r21225503;
        double r21225505 = 0.607771387771;
        double r21225506 = 11.9400905721;
        double r21225507 = 31.4690115749;
        double r21225508 = 15.234687407;
        double r21225509 = r21225508 + r21225476;
        double r21225510 = r21225476 * r21225509;
        double r21225511 = r21225507 + r21225510;
        double r21225512 = r21225476 * r21225511;
        double r21225513 = r21225506 + r21225512;
        double r21225514 = r21225513 * r21225476;
        double r21225515 = r21225505 + r21225514;
        double r21225516 = r21225504 / r21225515;
        double r21225517 = r21225479 * r21225516;
        double r21225518 = r21225490 + r21225517;
        double r21225519 = r21225493 ? r21225518 : r21225491;
        double r21225520 = r21225478 ? r21225491 : r21225519;
        return r21225520;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original28.8
Target1.0
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.895393240846026e+34 or 3.866410402714096e+43 < z

    1. Initial program 58.2

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]

    2. Taylor expanded around inf 8.0

      \[\leadsto x + \color{blue}{\left(\left(\frac{t \cdot y}{{z}^{2}} + 3.13060547623 \cdot y\right) - 36.527041698806414 \cdot \frac{y}{z}\right)}\]

    3. Simplified1.5

      \[\leadsto x + \color{blue}{\left(3.13060547623 \cdot y + \left(\frac{t}{z} \cdot \frac{y}{z} - 36.527041698806414 \cdot \frac{y}{z}\right)\right)}\]

    4. Taylor expanded around 0 8.0

      \[\leadsto x + \color{blue}{\left(\left(\frac{t \cdot y}{{z}^{2}} + 3.13060547623 \cdot y\right) - 36.527041698806414 \cdot \frac{y}{z}\right)}\]

    5. Simplified2.6

      \[\leadsto x + \color{blue}{\left(\frac{y \cdot \left(\frac{t}{z} - 36.527041698806414\right)}{z} + y \cdot 3.13060547623\right)}\]

    6. Taylor expanded around 0 8.0

      \[\leadsto x + \color{blue}{\left(\left(\frac{t \cdot y}{{z}^{2}} + 3.13060547623 \cdot y\right) - 36.527041698806414 \cdot \frac{y}{z}\right)}\]

    7. Simplified1.4

      \[\leadsto x + \color{blue}{\left(y \cdot \left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{y \cdot 36.527041698806414}{z}\right)}\]

    if -2.895393240846026e+34 < z < 3.866410402714096e+43

    1. Initial program 1.4

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity1.4

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771\right)}}\]

    4. Applied times-frac0.7

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}}\]

    5. Simplified0.7

      \[\leadsto x + \color{blue}{y} \cdot \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.895393240846026 \cdot 10^{+34}:\\ \;\;\;\;\left(y \cdot \left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{36.527041698806414 \cdot y}{z}\right) + x\\ \mathbf{elif}\;z \le 3.866410402714096 \cdot 10^{+43}:\\ \;\;\;\;x + y \cdot \frac{b + z \cdot \left(a + z \cdot \left(z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right) + t\right)\right)}{0.607771387771 + \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(15.234687407 + z\right)\right)\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{36.527041698806414 \cdot y}{z}\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"

  :herbie-target
  (if (< z -6.499344996252632e+53) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1))) (if (< z 7.066965436914287e+59) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771) (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)))) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1)))))

  (+ x (/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))