Average Error: 28.5 → 1.9
Time: 19.2s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.343660081947173 \cdot 10^{+38}:\\ \;\;\;\;x + \left(\left(\left(y \cdot \frac{t}{z}\right) \cdot \frac{1}{z} + 3.13060547623 \cdot y\right) - \frac{y}{z} \cdot 36.527041698806414\right)\\ \mathbf{elif}\;z \le 2533004793734.77:\\ \;\;\;\;x + y \cdot \frac{z \cdot \left(a + z \cdot \left(t + \left(11.1667541262 + 3.13060547623 \cdot z\right) \cdot z\right)\right) + b}{0.607771387771 + z \cdot \left(11.9400905721 + \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right) \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\left(y \cdot \frac{t}{z}\right) \cdot \frac{1}{z} + 3.13060547623 \cdot y\right) - \frac{y}{z} \cdot 36.527041698806414\right)\\ \end{array}\]
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 -1.343660081947173 \cdot 10^{+38}:\\
\;\;\;\;x + \left(\left(\left(y \cdot \frac{t}{z}\right) \cdot \frac{1}{z} + 3.13060547623 \cdot y\right) - \frac{y}{z} \cdot 36.527041698806414\right)\\

\mathbf{elif}\;z \le 2533004793734.77:\\
\;\;\;\;x + y \cdot \frac{z \cdot \left(a + z \cdot \left(t + \left(11.1667541262 + 3.13060547623 \cdot z\right) \cdot z\right)\right) + b}{0.607771387771 + z \cdot \left(11.9400905721 + \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right) \cdot z\right)}\\

\mathbf{else}:\\
\;\;\;\;x + \left(\left(\left(y \cdot \frac{t}{z}\right) \cdot \frac{1}{z} + 3.13060547623 \cdot y\right) - \frac{y}{z} \cdot 36.527041698806414\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r20587494 = x;
        double r20587495 = y;
        double r20587496 = z;
        double r20587497 = 3.13060547623;
        double r20587498 = r20587496 * r20587497;
        double r20587499 = 11.1667541262;
        double r20587500 = r20587498 + r20587499;
        double r20587501 = r20587500 * r20587496;
        double r20587502 = t;
        double r20587503 = r20587501 + r20587502;
        double r20587504 = r20587503 * r20587496;
        double r20587505 = a;
        double r20587506 = r20587504 + r20587505;
        double r20587507 = r20587506 * r20587496;
        double r20587508 = b;
        double r20587509 = r20587507 + r20587508;
        double r20587510 = r20587495 * r20587509;
        double r20587511 = 15.234687407;
        double r20587512 = r20587496 + r20587511;
        double r20587513 = r20587512 * r20587496;
        double r20587514 = 31.4690115749;
        double r20587515 = r20587513 + r20587514;
        double r20587516 = r20587515 * r20587496;
        double r20587517 = 11.9400905721;
        double r20587518 = r20587516 + r20587517;
        double r20587519 = r20587518 * r20587496;
        double r20587520 = 0.607771387771;
        double r20587521 = r20587519 + r20587520;
        double r20587522 = r20587510 / r20587521;
        double r20587523 = r20587494 + r20587522;
        return r20587523;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r20587524 = z;
        double r20587525 = -1.343660081947173e+38;
        bool r20587526 = r20587524 <= r20587525;
        double r20587527 = x;
        double r20587528 = y;
        double r20587529 = t;
        double r20587530 = r20587529 / r20587524;
        double r20587531 = r20587528 * r20587530;
        double r20587532 = 1.0;
        double r20587533 = r20587532 / r20587524;
        double r20587534 = r20587531 * r20587533;
        double r20587535 = 3.13060547623;
        double r20587536 = r20587535 * r20587528;
        double r20587537 = r20587534 + r20587536;
        double r20587538 = r20587528 / r20587524;
        double r20587539 = 36.527041698806414;
        double r20587540 = r20587538 * r20587539;
        double r20587541 = r20587537 - r20587540;
        double r20587542 = r20587527 + r20587541;
        double r20587543 = 2533004793734.77;
        bool r20587544 = r20587524 <= r20587543;
        double r20587545 = a;
        double r20587546 = 11.1667541262;
        double r20587547 = r20587535 * r20587524;
        double r20587548 = r20587546 + r20587547;
        double r20587549 = r20587548 * r20587524;
        double r20587550 = r20587529 + r20587549;
        double r20587551 = r20587524 * r20587550;
        double r20587552 = r20587545 + r20587551;
        double r20587553 = r20587524 * r20587552;
        double r20587554 = b;
        double r20587555 = r20587553 + r20587554;
        double r20587556 = 0.607771387771;
        double r20587557 = 11.9400905721;
        double r20587558 = 31.4690115749;
        double r20587559 = 15.234687407;
        double r20587560 = r20587524 + r20587559;
        double r20587561 = r20587524 * r20587560;
        double r20587562 = r20587558 + r20587561;
        double r20587563 = r20587562 * r20587524;
        double r20587564 = r20587557 + r20587563;
        double r20587565 = r20587524 * r20587564;
        double r20587566 = r20587556 + r20587565;
        double r20587567 = r20587555 / r20587566;
        double r20587568 = r20587528 * r20587567;
        double r20587569 = r20587527 + r20587568;
        double r20587570 = r20587544 ? r20587569 : r20587542;
        double r20587571 = r20587526 ? r20587542 : r20587570;
        return r20587571;
}

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

Original28.5
Target1.0
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.343660081947173e+38 or 2533004793734.77 < z

    1. Initial program 56.7

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

    2. Taylor expanded around inf 9.1

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

    3. Simplified2.0

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

    5. Applied *-un-lft-identity2.0

      \[\leadsto x + \left(\left(3.13060547623 \cdot y + \frac{\color{blue}{1 \cdot t}}{z \cdot z} \cdot y\right) - \frac{y \cdot 36.527041698806414}{z}\right)\]

    6. Applied times-frac2.0

      \[\leadsto x + \left(\left(3.13060547623 \cdot y + \color{blue}{\left(\frac{1}{z} \cdot \frac{t}{z}\right)} \cdot y\right) - \frac{y \cdot 36.527041698806414}{z}\right)\]

    7. Applied associate-*l*3.4

      \[\leadsto x + \left(\left(3.13060547623 \cdot y + \color{blue}{\frac{1}{z} \cdot \left(\frac{t}{z} \cdot y\right)}\right) - \frac{y \cdot 36.527041698806414}{z}\right)\]

    8. Taylor expanded around 0 3.4

      \[\leadsto x + \left(\left(3.13060547623 \cdot y + \frac{1}{z} \cdot \left(\frac{t}{z} \cdot y\right)\right) - \color{blue}{36.527041698806414 \cdot \frac{y}{z}}\right)\]

    if -1.343660081947173e+38 < z < 2533004793734.77

    1. Initial program 0.9

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

    3. Applied *-un-lft-identity0.9

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

    4. Applied times-frac0.4

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

    5. Simplified0.4

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.343660081947173 \cdot 10^{+38}:\\ \;\;\;\;x + \left(\left(\left(y \cdot \frac{t}{z}\right) \cdot \frac{1}{z} + 3.13060547623 \cdot y\right) - \frac{y}{z} \cdot 36.527041698806414\right)\\ \mathbf{elif}\;z \le 2533004793734.77:\\ \;\;\;\;x + y \cdot \frac{z \cdot \left(a + z \cdot \left(t + \left(11.1667541262 + 3.13060547623 \cdot z\right) \cdot z\right)\right) + b}{0.607771387771 + z \cdot \left(11.9400905721 + \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right) \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\left(y \cdot \frac{t}{z}\right) \cdot \frac{1}{z} + 3.13060547623 \cdot y\right) - \frac{y}{z} \cdot 36.527041698806414\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(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))))