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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -83720619159694770000 \lor \neg \left(z \le 57541922403869164000\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]

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 -83720619159694770000 \lor \neg \left(z \le 57541922403869164000\right):\\
\;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\

\mathbf{else}:\\
\;\;\;\;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}\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r371617 = x;
        double r371618 = y;
        double r371619 = z;
        double r371620 = 3.13060547623;
        double r371621 = r371619 * r371620;
        double r371622 = 11.1667541262;
        double r371623 = r371621 + r371622;
        double r371624 = r371623 * r371619;
        double r371625 = t;
        double r371626 = r371624 + r371625;
        double r371627 = r371626 * r371619;
        double r371628 = a;
        double r371629 = r371627 + r371628;
        double r371630 = r371629 * r371619;
        double r371631 = b;
        double r371632 = r371630 + r371631;
        double r371633 = r371618 * r371632;
        double r371634 = 15.234687407;
        double r371635 = r371619 + r371634;
        double r371636 = r371635 * r371619;
        double r371637 = 31.4690115749;
        double r371638 = r371636 + r371637;
        double r371639 = r371638 * r371619;
        double r371640 = 11.9400905721;
        double r371641 = r371639 + r371640;
        double r371642 = r371641 * r371619;
        double r371643 = 0.607771387771;
        double r371644 = r371642 + r371643;
        double r371645 = r371633 / r371644;
        double r371646 = r371617 + r371645;
        return r371646;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r371647 = z;
        double r371648 = -8.372061915969477e+19;
        bool r371649 = r371647 <= r371648;
        double r371650 = 5.754192240386916e+19;
        bool r371651 = r371647 <= r371650;
        double r371652 = !r371651;
        bool r371653 = r371649 || r371652;
        double r371654 = y;
        double r371655 = 3.13060547623;
        double r371656 = t;
        double r371657 = 2.0;
        double r371658 = pow(r371647, r371657);
        double r371659 = r371656 / r371658;
        double r371660 = r371655 + r371659;
        double r371661 = x;
        double r371662 = fma(r371654, r371660, r371661);
        double r371663 = r371647 * r371655;
        double r371664 = 11.1667541262;
        double r371665 = r371663 + r371664;
        double r371666 = r371665 * r371647;
        double r371667 = r371666 + r371656;
        double r371668 = r371667 * r371647;
        double r371669 = a;
        double r371670 = r371668 + r371669;
        double r371671 = r371670 * r371647;
        double r371672 = b;
        double r371673 = r371671 + r371672;
        double r371674 = r371654 * r371673;
        double r371675 = 15.234687407;
        double r371676 = r371647 + r371675;
        double r371677 = r371676 * r371647;
        double r371678 = 31.4690115749;
        double r371679 = r371677 + r371678;
        double r371680 = r371679 * r371647;
        double r371681 = 11.9400905721;
        double r371682 = r371680 + r371681;
        double r371683 = r371682 * r371647;
        double r371684 = 0.607771387771;
        double r371685 = r371683 + r371684;
        double r371686 = r371674 / r371685;
        double r371687 = r371661 + r371686;
        double r371688 = r371653 ? r371662 : r371687;
        return r371688;
}

Original	29.6
Target	1.1
Herbie	1.4

Derivation

Split input into 2 regimes
if z < -8.372061915969477e+19 or 5.754192240386916e+19 < z
1. Initial program 57.8
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified55.2
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Taylor expanded around inf 9.5
  \[\leadsto \color{blue}{x + \left(\frac{t \cdot y}{{z}^{2}} + 3.13060547622999996 \cdot y\right)}\]
4. Simplified2.1
  \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)}\]
if -8.372061915969477e+19 < z < 5.754192240386916e+19
1. Initial program 0.7
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
Recombined 2 regimes into one program.
Final simplification1.4
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -83720619159694770000 \lor \neg \left(z \le 57541922403869164000\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(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))))

Error

Target

Derivation

`if z < -8.372061915969477e+19 or 5.754192240386916e+19 < z`

`if -8.372061915969477e+19 < z < 5.754192240386916e+19`

Reproduce