Average Error: 29.7 → 4.4
Time: 5.4s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.9939183141103301 \cdot 10^{53} \lor \neg \left(z \le 1.84976842774575583 \cdot 10^{58}\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]
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 -6.9939183141103301 \cdot 10^{53} \lor \neg \left(z \le 1.84976842774575583 \cdot 10^{58}\right):\\
\;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\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 r381109 = x;
        double r381110 = y;
        double r381111 = z;
        double r381112 = 3.13060547623;
        double r381113 = r381111 * r381112;
        double r381114 = 11.1667541262;
        double r381115 = r381113 + r381114;
        double r381116 = r381115 * r381111;
        double r381117 = t;
        double r381118 = r381116 + r381117;
        double r381119 = r381118 * r381111;
        double r381120 = a;
        double r381121 = r381119 + r381120;
        double r381122 = r381121 * r381111;
        double r381123 = b;
        double r381124 = r381122 + r381123;
        double r381125 = r381110 * r381124;
        double r381126 = 15.234687407;
        double r381127 = r381111 + r381126;
        double r381128 = r381127 * r381111;
        double r381129 = 31.4690115749;
        double r381130 = r381128 + r381129;
        double r381131 = r381130 * r381111;
        double r381132 = 11.9400905721;
        double r381133 = r381131 + r381132;
        double r381134 = r381133 * r381111;
        double r381135 = 0.607771387771;
        double r381136 = r381134 + r381135;
        double r381137 = r381125 / r381136;
        double r381138 = r381109 + r381137;
        return r381138;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r381139 = z;
        double r381140 = -6.99391831411033e+53;
        bool r381141 = r381139 <= r381140;
        double r381142 = 1.8497684277457558e+58;
        bool r381143 = r381139 <= r381142;
        double r381144 = !r381143;
        bool r381145 = r381141 || r381144;
        double r381146 = x;
        double r381147 = 3.13060547623;
        double r381148 = y;
        double r381149 = r381147 * r381148;
        double r381150 = t;
        double r381151 = r381150 * r381148;
        double r381152 = 2.0;
        double r381153 = pow(r381139, r381152);
        double r381154 = r381151 / r381153;
        double r381155 = r381149 + r381154;
        double r381156 = 36.527041698806414;
        double r381157 = r381148 / r381139;
        double r381158 = r381156 * r381157;
        double r381159 = r381155 - r381158;
        double r381160 = r381146 + r381159;
        double r381161 = r381139 * r381147;
        double r381162 = 11.1667541262;
        double r381163 = r381161 + r381162;
        double r381164 = r381163 * r381139;
        double r381165 = r381164 + r381150;
        double r381166 = r381165 * r381139;
        double r381167 = a;
        double r381168 = r381166 + r381167;
        double r381169 = r381168 * r381139;
        double r381170 = b;
        double r381171 = r381169 + r381170;
        double r381172 = 15.234687407;
        double r381173 = r381139 + r381172;
        double r381174 = r381173 * r381139;
        double r381175 = 31.4690115749;
        double r381176 = r381174 + r381175;
        double r381177 = r381176 * r381139;
        double r381178 = 11.9400905721;
        double r381179 = r381177 + r381178;
        double r381180 = r381179 * r381139;
        double r381181 = 0.607771387771;
        double r381182 = r381180 + r381181;
        double r381183 = r381171 / r381182;
        double r381184 = r381148 * r381183;
        double r381185 = r381146 + r381184;
        double r381186 = r381145 ? r381160 : r381185;
        return r381186;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.7
Target1.0
Herbie4.4
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -6.99391831411033e+53 or 1.8497684277457558e+58 < z

    1. Initial program 61.9

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

    2. Taylor expanded around inf 8.3

      \[\leadsto x + \color{blue}{\left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)}\]

    if -6.99391831411033e+53 < z < 1.8497684277457558e+58

    1. Initial program 3.0

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

    3. Applied *-un-lft-identity3.0

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004\right)}}\]

    4. Applied times-frac1.2

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}}\]

    5. Simplified1.2

      \[\leadsto x + \color{blue}{y} \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification4.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.9939183141103301 \cdot 10^{53} \lor \neg \left(z \le 1.84976842774575583 \cdot 10^{58}\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]

Reproduce

herbie shell --seed 2020018 
(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))))