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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1.74079175780789884 \cdot 10^{36} \lor \neg \left(z \le 10094.0500466464382\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

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 -1.74079175780789884 \cdot 10^{36} \lor \neg \left(z \le 10094.0500466464382\right):\\
\;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(y \cdot \frac{1}{\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)\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r318999 = x;
        double r319000 = y;
        double r319001 = z;
        double r319002 = 3.13060547623;
        double r319003 = r319001 * r319002;
        double r319004 = 11.1667541262;
        double r319005 = r319003 + r319004;
        double r319006 = r319005 * r319001;
        double r319007 = t;
        double r319008 = r319006 + r319007;
        double r319009 = r319008 * r319001;
        double r319010 = a;
        double r319011 = r319009 + r319010;
        double r319012 = r319011 * r319001;
        double r319013 = b;
        double r319014 = r319012 + r319013;
        double r319015 = r319000 * r319014;
        double r319016 = 15.234687407;
        double r319017 = r319001 + r319016;
        double r319018 = r319017 * r319001;
        double r319019 = 31.4690115749;
        double r319020 = r319018 + r319019;
        double r319021 = r319020 * r319001;
        double r319022 = 11.9400905721;
        double r319023 = r319021 + r319022;
        double r319024 = r319023 * r319001;
        double r319025 = 0.607771387771;
        double r319026 = r319024 + r319025;
        double r319027 = r319015 / r319026;
        double r319028 = r318999 + r319027;
        return r319028;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r319029 = z;
        double r319030 = -1.7407917578078988e+36;
        bool r319031 = r319029 <= r319030;
        double r319032 = 10094.050046646438;
        bool r319033 = r319029 <= r319032;
        double r319034 = !r319033;
        bool r319035 = r319031 || r319034;
        double r319036 = y;
        double r319037 = 3.13060547623;
        double r319038 = t;
        double r319039 = 2.0;
        double r319040 = pow(r319029, r319039);
        double r319041 = r319038 / r319040;
        double r319042 = r319037 + r319041;
        double r319043 = x;
        double r319044 = fma(r319036, r319042, r319043);
        double r319045 = 1.0;
        double r319046 = 15.234687407;
        double r319047 = r319029 + r319046;
        double r319048 = 31.4690115749;
        double r319049 = fma(r319047, r319029, r319048);
        double r319050 = 11.9400905721;
        double r319051 = fma(r319049, r319029, r319050);
        double r319052 = 0.607771387771;
        double r319053 = fma(r319051, r319029, r319052);
        double r319054 = r319045 / r319053;
        double r319055 = r319036 * r319054;
        double r319056 = 11.1667541262;
        double r319057 = fma(r319029, r319037, r319056);
        double r319058 = fma(r319057, r319029, r319038);
        double r319059 = a;
        double r319060 = fma(r319058, r319029, r319059);
        double r319061 = b;
        double r319062 = fma(r319060, r319029, r319061);
        double r319063 = fma(r319055, r319062, r319043);
        double r319064 = r319035 ? r319044 : r319063;
        return r319064;
}

Original	29.0
Target	1.1
Herbie	1.4

Derivation

Split input into 2 regimes
if z < -1.7407917578078988e+36 or 10094.050046646438 < z
1. Initial program 57.3
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified55.4
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Taylor expanded around inf 9.3
  \[\leadsto \color{blue}{x + \left(\frac{t \cdot y}{{z}^{2}} + 3.13060547622999996 \cdot y\right)}\]
4. Simplified2.2
  \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)}\]
if -1.7407917578078988e+36 < z < 10094.050046646438
1. Initial program 0.7
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified0.5
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Using strategy rm
4. Applied div-inv0.6
  \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\]
Recombined 2 regimes into one program.
Final simplification1.4
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.74079175780789884 \cdot 10^{36} \lor \neg \left(z \le 10094.0500466464382\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 +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 < -1.7407917578078988e+36 or 10094.050046646438 < z`

`if -1.7407917578078988e+36 < z < 10094.050046646438`

Reproduce