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

↓

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

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):\\
\;\;\;\;\mathsf{fma}\left(\frac{t}{{z}^{2}}, y, \mathsf{fma}\left(3.13060547622999996, y, x\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{\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)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)} \cdot y + x\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r442672 = x;
        double r442673 = y;
        double r442674 = z;
        double r442675 = 3.13060547623;
        double r442676 = r442674 * r442675;
        double r442677 = 11.1667541262;
        double r442678 = r442676 + r442677;
        double r442679 = r442678 * r442674;
        double r442680 = t;
        double r442681 = r442679 + r442680;
        double r442682 = r442681 * r442674;
        double r442683 = a;
        double r442684 = r442682 + r442683;
        double r442685 = r442684 * r442674;
        double r442686 = b;
        double r442687 = r442685 + r442686;
        double r442688 = r442673 * r442687;
        double r442689 = 15.234687407;
        double r442690 = r442674 + r442689;
        double r442691 = r442690 * r442674;
        double r442692 = 31.4690115749;
        double r442693 = r442691 + r442692;
        double r442694 = r442693 * r442674;
        double r442695 = 11.9400905721;
        double r442696 = r442694 + r442695;
        double r442697 = r442696 * r442674;
        double r442698 = 0.607771387771;
        double r442699 = r442697 + r442698;
        double r442700 = r442688 / r442699;
        double r442701 = r442672 + r442700;
        return r442701;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r442702 = z;
        double r442703 = -1.6035881345933143e+48;
        bool r442704 = r442702 <= r442703;
        double r442705 = 5.742012253919877e+73;
        bool r442706 = r442702 <= r442705;
        double r442707 = !r442706;
        bool r442708 = r442704 || r442707;
        double r442709 = t;
        double r442710 = 2.0;
        double r442711 = pow(r442702, r442710);
        double r442712 = r442709 / r442711;
        double r442713 = y;
        double r442714 = 3.13060547623;
        double r442715 = x;
        double r442716 = fma(r442714, r442713, r442715);
        double r442717 = fma(r442712, r442713, r442716);
        double r442718 = 11.1667541262;
        double r442719 = fma(r442702, r442714, r442718);
        double r442720 = fma(r442719, r442702, r442709);
        double r442721 = a;
        double r442722 = fma(r442720, r442702, r442721);
        double r442723 = b;
        double r442724 = fma(r442722, r442702, r442723);
        double r442725 = 15.234687407;
        double r442726 = r442702 + r442725;
        double r442727 = 31.4690115749;
        double r442728 = fma(r442726, r442702, r442727);
        double r442729 = 11.9400905721;
        double r442730 = fma(r442728, r442702, r442729);
        double r442731 = 0.607771387771;
        double r442732 = fma(r442730, r442702, r442731);
        double r442733 = r442724 / r442732;
        double r442734 = r442733 * r442713;
        double r442735 = r442734 + r442715;
        double r442736 = r442708 ? r442717 : r442735;
        return r442736;
}

Original	29.8
Target	1.0
Herbie	1.2

Derivation

Split input into 2 regimes
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. Simplified61.4
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Taylor expanded around inf 8.4
  \[\leadsto \color{blue}{x + \left(\frac{t \cdot y}{{z}^{2}} + 3.13060547622999996 \cdot y\right)}\]
4. Simplified0.8
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{{z}^{2}}, y, \mathsf{fma}\left(3.13060547622999996, y, x\right)\right)}\]
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. Simplified1.8
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Using strategy rm
4. Applied clear-num2.0
  \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}{y}}}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\]
5. Using strategy rm
6. Applied fma-udef2.0
  \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}{y}} \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right) + x}\]
7. Simplified1.5
  \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)} \cdot y} + x\]
Recombined 2 regimes into one program.
Final simplification1.2
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.60358813459331432 \cdot 10^{48} \lor \neg \left(z \le 5.7420122539198766 \cdot 10^{73}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{{z}^{2}}, y, \mathsf{fma}\left(3.13060547622999996, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)} \cdot y + x\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 +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))))

Falling back on racket egraph because egg-herbie package not installed (more)

Error

Target

Derivation

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

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

Reproduce