Average Error: 29.8 → 1.2
Time: 17.6s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.60358813459331432 \cdot 10^{48} \lor \neg \left(z \le 5.7420122539198766 \cdot 10^{73}\right):\\ \;\;\;\;x + y \cdot \left(\left(\frac{t}{{z}^{2}} + 3.13060547622999996\right) - \frac{36.527041698806414}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.60358813459331432 \cdot 10^{48} \lor \neg \left(z \le 5.7420122539198766 \cdot 10^{73}\right):\\
\;\;\;\;x + y \cdot \left(\left(\frac{t}{{z}^{2}} + 3.13060547622999996\right) - \frac{36.527041698806414}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r422613 = x;
        double r422614 = y;
        double r422615 = z;
        double r422616 = 3.13060547623;
        double r422617 = r422615 * r422616;
        double r422618 = 11.1667541262;
        double r422619 = r422617 + r422618;
        double r422620 = r422619 * r422615;
        double r422621 = t;
        double r422622 = r422620 + r422621;
        double r422623 = r422622 * r422615;
        double r422624 = a;
        double r422625 = r422623 + r422624;
        double r422626 = r422625 * r422615;
        double r422627 = b;
        double r422628 = r422626 + r422627;
        double r422629 = r422614 * r422628;
        double r422630 = 15.234687407;
        double r422631 = r422615 + r422630;
        double r422632 = r422631 * r422615;
        double r422633 = 31.4690115749;
        double r422634 = r422632 + r422633;
        double r422635 = r422634 * r422615;
        double r422636 = 11.9400905721;
        double r422637 = r422635 + r422636;
        double r422638 = r422637 * r422615;
        double r422639 = 0.607771387771;
        double r422640 = r422638 + r422639;
        double r422641 = r422629 / r422640;
        double r422642 = r422613 + r422641;
        return r422642;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r422643 = z;
        double r422644 = -1.6035881345933143e+48;
        bool r422645 = r422643 <= r422644;
        double r422646 = 5.742012253919877e+73;
        bool r422647 = r422643 <= r422646;
        double r422648 = !r422647;
        bool r422649 = r422645 || r422648;
        double r422650 = x;
        double r422651 = y;
        double r422652 = t;
        double r422653 = 2.0;
        double r422654 = pow(r422643, r422653);
        double r422655 = r422652 / r422654;
        double r422656 = 3.13060547623;
        double r422657 = r422655 + r422656;
        double r422658 = 36.527041698806414;
        double r422659 = r422658 / r422643;
        double r422660 = r422657 - r422659;
        double r422661 = r422651 * r422660;
        double r422662 = r422650 + r422661;
        double r422663 = r422643 * r422656;
        double r422664 = 11.1667541262;
        double r422665 = r422663 + r422664;
        double r422666 = r422665 * r422643;
        double r422667 = r422666 + r422652;
        double r422668 = r422667 * r422643;
        double r422669 = a;
        double r422670 = r422668 + r422669;
        double r422671 = r422670 * r422643;
        double r422672 = b;
        double r422673 = r422671 + r422672;
        double r422674 = 15.234687407;
        double r422675 = r422643 + r422674;
        double r422676 = r422675 * r422643;
        double r422677 = 31.4690115749;
        double r422678 = r422676 + r422677;
        double r422679 = r422678 * r422643;
        double r422680 = 11.9400905721;
        double r422681 = r422679 + r422680;
        double r422682 = r422681 * r422643;
        double r422683 = 0.607771387771;
        double r422684 = r422682 + r422683;
        double r422685 = r422673 / r422684;
        double r422686 = r422651 * r422685;
        double r422687 = r422650 + r422686;
        double r422688 = r422649 ? r422662 : r422687;
        return r422688;
}

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

Original29.8
Target1.0
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.6035881345933143e+48 or 5.742012253919877e+73 < z

    1. Initial program 62.2

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity62.2

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004\right)}}\]

    4. Applied times-frac61.0

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}}\]

    5. Simplified61.0

      \[\leadsto x + \color{blue}{y} \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]

    6. Taylor expanded around inf 0.8

      \[\leadsto x + y \cdot \color{blue}{\left(\left(\frac{t}{{z}^{2}} + 3.13060547622999996\right) - 36.527041698806414 \cdot \frac{1}{z}\right)}\]

    7. Simplified0.8

      \[\leadsto x + y \cdot \color{blue}{\left(\left(\frac{t}{{z}^{2}} + 3.13060547622999996\right) - \frac{36.527041698806414}{z}\right)}\]

    if -1.6035881345933143e+48 < z < 5.742012253919877e+73

    1. Initial program 3.6

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity3.6

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004\right)}}\]

    4. Applied times-frac1.5

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}}\]

    5. Simplified1.5

      \[\leadsto x + \color{blue}{y} \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.60358813459331432 \cdot 10^{48} \lor \neg \left(z \le 5.7420122539198766 \cdot 10^{73}\right):\\ \;\;\;\;x + y \cdot \left(\left(\frac{t}{{z}^{2}} + 3.13060547622999996\right) - \frac{36.527041698806414}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :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))))