Average Error: 29.0 → 4.9
Time: 12.3s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.74079175780789884 \cdot 10^{36} \lor \neg \left(z \le 10094.0500466464382\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]
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):\\
\;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;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}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r365103 = x;
        double r365104 = y;
        double r365105 = z;
        double r365106 = 3.13060547623;
        double r365107 = r365105 * r365106;
        double r365108 = 11.1667541262;
        double r365109 = r365107 + r365108;
        double r365110 = r365109 * r365105;
        double r365111 = t;
        double r365112 = r365110 + r365111;
        double r365113 = r365112 * r365105;
        double r365114 = a;
        double r365115 = r365113 + r365114;
        double r365116 = r365115 * r365105;
        double r365117 = b;
        double r365118 = r365116 + r365117;
        double r365119 = r365104 * r365118;
        double r365120 = 15.234687407;
        double r365121 = r365105 + r365120;
        double r365122 = r365121 * r365105;
        double r365123 = 31.4690115749;
        double r365124 = r365122 + r365123;
        double r365125 = r365124 * r365105;
        double r365126 = 11.9400905721;
        double r365127 = r365125 + r365126;
        double r365128 = r365127 * r365105;
        double r365129 = 0.607771387771;
        double r365130 = r365128 + r365129;
        double r365131 = r365119 / r365130;
        double r365132 = r365103 + r365131;
        return r365132;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r365133 = z;
        double r365134 = -1.7407917578078988e+36;
        bool r365135 = r365133 <= r365134;
        double r365136 = 10094.050046646438;
        bool r365137 = r365133 <= r365136;
        double r365138 = !r365137;
        bool r365139 = r365135 || r365138;
        double r365140 = x;
        double r365141 = 3.13060547623;
        double r365142 = y;
        double r365143 = r365141 * r365142;
        double r365144 = t;
        double r365145 = r365144 * r365142;
        double r365146 = 2.0;
        double r365147 = pow(r365133, r365146);
        double r365148 = r365145 / r365147;
        double r365149 = r365143 + r365148;
        double r365150 = 36.527041698806414;
        double r365151 = r365142 / r365133;
        double r365152 = r365150 * r365151;
        double r365153 = r365149 - r365152;
        double r365154 = r365140 + r365153;
        double r365155 = 15.234687407;
        double r365156 = r365133 + r365155;
        double r365157 = r365156 * r365133;
        double r365158 = 31.4690115749;
        double r365159 = r365157 + r365158;
        double r365160 = r365159 * r365133;
        double r365161 = 11.9400905721;
        double r365162 = r365160 + r365161;
        double r365163 = r365162 * r365133;
        double r365164 = 0.607771387771;
        double r365165 = r365163 + r365164;
        double r365166 = r365133 * r365141;
        double r365167 = 11.1667541262;
        double r365168 = r365166 + r365167;
        double r365169 = r365168 * r365133;
        double r365170 = r365169 + r365144;
        double r365171 = r365170 * r365133;
        double r365172 = a;
        double r365173 = r365171 + r365172;
        double r365174 = r365173 * r365133;
        double r365175 = b;
        double r365176 = r365174 + r365175;
        double r365177 = r365165 / r365176;
        double r365178 = r365142 / r365177;
        double r365179 = r365140 + r365178;
        double r365180 = r365139 ? r365154 : r365179;
        return r365180;
}

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

Original29.0
Target1.1
Herbie4.9
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -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. Taylor expanded around inf 9.3

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

    if -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. Using strategy rm

    3. Applied associate-/l*0.4

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

  4. Final simplification4.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.74079175780789884 \cdot 10^{36} \lor \neg \left(z \le 10094.0500466464382\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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))))