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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1561166178717786600 \lor \neg \left(z \le 706881567136002.375\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996, \mathsf{fma}\left(t \cdot \frac{1}{{z}^{2}}, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

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 -1561166178717786600 \lor \neg \left(z \le 706881567136002.375\right):\\
\;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996, \mathsf{fma}\left(t \cdot \frac{1}{{z}^{2}}, y, x\right)\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 r466102 = x;
        double r466103 = y;
        double r466104 = z;
        double r466105 = 3.13060547623;
        double r466106 = r466104 * r466105;
        double r466107 = 11.1667541262;
        double r466108 = r466106 + r466107;
        double r466109 = r466108 * r466104;
        double r466110 = t;
        double r466111 = r466109 + r466110;
        double r466112 = r466111 * r466104;
        double r466113 = a;
        double r466114 = r466112 + r466113;
        double r466115 = r466114 * r466104;
        double r466116 = b;
        double r466117 = r466115 + r466116;
        double r466118 = r466103 * r466117;
        double r466119 = 15.234687407;
        double r466120 = r466104 + r466119;
        double r466121 = r466120 * r466104;
        double r466122 = 31.4690115749;
        double r466123 = r466121 + r466122;
        double r466124 = r466123 * r466104;
        double r466125 = 11.9400905721;
        double r466126 = r466124 + r466125;
        double r466127 = r466126 * r466104;
        double r466128 = 0.607771387771;
        double r466129 = r466127 + r466128;
        double r466130 = r466118 / r466129;
        double r466131 = r466102 + r466130;
        return r466131;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r466132 = z;
        double r466133 = -1.5611661787177866e+18;
        bool r466134 = r466132 <= r466133;
        double r466135 = 706881567136002.4;
        bool r466136 = r466132 <= r466135;
        double r466137 = !r466136;
        bool r466138 = r466134 || r466137;
        double r466139 = y;
        double r466140 = 3.13060547623;
        double r466141 = t;
        double r466142 = 1.0;
        double r466143 = 2.0;
        double r466144 = pow(r466132, r466143);
        double r466145 = r466142 / r466144;
        double r466146 = r466141 * r466145;
        double r466147 = x;
        double r466148 = fma(r466146, r466139, r466147);
        double r466149 = fma(r466139, r466140, r466148);
        double r466150 = 15.234687407;
        double r466151 = r466132 + r466150;
        double r466152 = 31.4690115749;
        double r466153 = fma(r466151, r466132, r466152);
        double r466154 = 11.9400905721;
        double r466155 = fma(r466153, r466132, r466154);
        double r466156 = 0.607771387771;
        double r466157 = fma(r466155, r466132, r466156);
        double r466158 = r466142 / r466157;
        double r466159 = r466139 * r466158;
        double r466160 = 11.1667541262;
        double r466161 = fma(r466132, r466140, r466160);
        double r466162 = fma(r466161, r466132, r466141);
        double r466163 = a;
        double r466164 = fma(r466162, r466132, r466163);
        double r466165 = b;
        double r466166 = fma(r466164, r466132, r466165);
        double r466167 = fma(r466159, r466166, r466147);
        double r466168 = r466138 ? r466149 : r466167;
        return r466168;
}

Original	29.4
Target	1.2
Herbie	1.4

Derivation

Split input into 2 regimes
if z < -1.5611661787177866e+18 or 706881567136002.4 < z
1. Initial program 56.9
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified54.5
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Taylor expanded around inf 9.3
  \[\leadsto \color{blue}{x + \left(\frac{t \cdot y}{{z}^{2}} + 3.13060547622999996 \cdot y\right)}\]
4. Simplified2.4
  \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547622999996, \mathsf{fma}\left(\frac{t}{{z}^{2}}, y, x\right)\right)}\]
5. Using strategy rm
6. Applied div-inv2.4
  \[\leadsto \mathsf{fma}\left(y, 3.13060547622999996, \mathsf{fma}\left(\color{blue}{t \cdot \frac{1}{{z}^{2}}}, y, x\right)\right)\]
if -1.5611661787177866e+18 < z < 706881567136002.4
1. Initial program 0.5
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified0.3
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Using strategy rm
4. Applied div-inv0.4
  \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\]
Recombined 2 regimes into one program.
Final simplification1.4
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1561166178717786600 \lor \neg \left(z \le 706881567136002.375\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996, \mathsf{fma}\left(t \cdot \frac{1}{{z}^{2}}, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 +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 < -1.5611661787177866e+18 or 706881567136002.4 < z`

`if -1.5611661787177866e+18 < z < 706881567136002.4`

Reproduce