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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -7.6883151432789902 \cdot 10^{21} \lor \neg \left(z \le 6.2617027895573594 \cdot 10^{42}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]

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 -7.6883151432789902 \cdot 10^{21} \lor \neg \left(z \le 6.2617027895573594 \cdot 10^{42}\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 r324044 = x;
        double r324045 = y;
        double r324046 = z;
        double r324047 = 3.13060547623;
        double r324048 = r324046 * r324047;
        double r324049 = 11.1667541262;
        double r324050 = r324048 + r324049;
        double r324051 = r324050 * r324046;
        double r324052 = t;
        double r324053 = r324051 + r324052;
        double r324054 = r324053 * r324046;
        double r324055 = a;
        double r324056 = r324054 + r324055;
        double r324057 = r324056 * r324046;
        double r324058 = b;
        double r324059 = r324057 + r324058;
        double r324060 = r324045 * r324059;
        double r324061 = 15.234687407;
        double r324062 = r324046 + r324061;
        double r324063 = r324062 * r324046;
        double r324064 = 31.4690115749;
        double r324065 = r324063 + r324064;
        double r324066 = r324065 * r324046;
        double r324067 = 11.9400905721;
        double r324068 = r324066 + r324067;
        double r324069 = r324068 * r324046;
        double r324070 = 0.607771387771;
        double r324071 = r324069 + r324070;
        double r324072 = r324060 / r324071;
        double r324073 = r324044 + r324072;
        return r324073;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r324074 = z;
        double r324075 = -7.68831514327899e+21;
        bool r324076 = r324074 <= r324075;
        double r324077 = 6.26170278955736e+42;
        bool r324078 = r324074 <= r324077;
        double r324079 = !r324078;
        bool r324080 = r324076 || r324079;
        double r324081 = y;
        double r324082 = 3.13060547623;
        double r324083 = t;
        double r324084 = 2.0;
        double r324085 = pow(r324074, r324084);
        double r324086 = r324083 / r324085;
        double r324087 = r324082 + r324086;
        double r324088 = x;
        double r324089 = fma(r324081, r324087, r324088);
        double r324090 = r324074 * r324082;
        double r324091 = 11.1667541262;
        double r324092 = r324090 + r324091;
        double r324093 = r324092 * r324074;
        double r324094 = r324093 + r324083;
        double r324095 = r324094 * r324074;
        double r324096 = a;
        double r324097 = r324095 + r324096;
        double r324098 = r324097 * r324074;
        double r324099 = b;
        double r324100 = r324098 + r324099;
        double r324101 = r324081 * r324100;
        double r324102 = 15.234687407;
        double r324103 = r324074 + r324102;
        double r324104 = r324103 * r324074;
        double r324105 = 31.4690115749;
        double r324106 = r324104 + r324105;
        double r324107 = r324106 * r324074;
        double r324108 = 11.9400905721;
        double r324109 = r324107 + r324108;
        double r324110 = r324109 * r324074;
        double r324111 = 0.607771387771;
        double r324112 = r324110 + r324111;
        double r324113 = r324101 / r324112;
        double r324114 = r324088 + r324113;
        double r324115 = r324080 ? r324089 : r324114;
        return r324115;
}

Original	29.5
Target	0.9
Herbie	1.4

Derivation

Split input into 2 regimes
if z < -7.68831514327899e+21 or 6.26170278955736e+42 < z
1. Initial program 59.2
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified56.9
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Taylor expanded around inf 8.7
  \[\leadsto \color{blue}{x + \left(\frac{t \cdot y}{{z}^{2}} + 3.13060547622999996 \cdot y\right)}\]
4. Simplified1.5
  \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)}\]
if -7.68831514327899e+21 < z < 6.26170278955736e+42
1. Initial program 1.3
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
Recombined 2 regimes into one program.
Final simplification1.4
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -7.6883151432789902 \cdot 10^{21} \lor \neg \left(z \le 6.2617027895573594 \cdot 10^{42}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 +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 < -7.68831514327899e+21 or 6.26170278955736e+42 < z`

`if -7.68831514327899e+21 < z < 6.26170278955736e+42`

Reproduce