Average Error: 29.5 → 4.6
Time: 6.2s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.65848663070093563 \cdot 10^{27} \lor \neg \left(z \le 130676711668149.234\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]
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 -3.65848663070093563 \cdot 10^{27} \lor \neg \left(z \le 130676711668149.234\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 r440155 = x;
        double r440156 = y;
        double r440157 = z;
        double r440158 = 3.13060547623;
        double r440159 = r440157 * r440158;
        double r440160 = 11.1667541262;
        double r440161 = r440159 + r440160;
        double r440162 = r440161 * r440157;
        double r440163 = t;
        double r440164 = r440162 + r440163;
        double r440165 = r440164 * r440157;
        double r440166 = a;
        double r440167 = r440165 + r440166;
        double r440168 = r440167 * r440157;
        double r440169 = b;
        double r440170 = r440168 + r440169;
        double r440171 = r440156 * r440170;
        double r440172 = 15.234687407;
        double r440173 = r440157 + r440172;
        double r440174 = r440173 * r440157;
        double r440175 = 31.4690115749;
        double r440176 = r440174 + r440175;
        double r440177 = r440176 * r440157;
        double r440178 = 11.9400905721;
        double r440179 = r440177 + r440178;
        double r440180 = r440179 * r440157;
        double r440181 = 0.607771387771;
        double r440182 = r440180 + r440181;
        double r440183 = r440171 / r440182;
        double r440184 = r440155 + r440183;
        return r440184;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r440185 = z;
        double r440186 = -3.6584866307009356e+27;
        bool r440187 = r440185 <= r440186;
        double r440188 = 130676711668149.23;
        bool r440189 = r440185 <= r440188;
        double r440190 = !r440189;
        bool r440191 = r440187 || r440190;
        double r440192 = x;
        double r440193 = 3.13060547623;
        double r440194 = y;
        double r440195 = r440193 * r440194;
        double r440196 = t;
        double r440197 = r440196 * r440194;
        double r440198 = 2.0;
        double r440199 = pow(r440185, r440198);
        double r440200 = r440197 / r440199;
        double r440201 = r440195 + r440200;
        double r440202 = 36.527041698806414;
        double r440203 = r440194 / r440185;
        double r440204 = r440202 * r440203;
        double r440205 = r440201 - r440204;
        double r440206 = r440192 + r440205;
        double r440207 = r440185 * r440193;
        double r440208 = 11.1667541262;
        double r440209 = r440207 + r440208;
        double r440210 = r440209 * r440185;
        double r440211 = r440210 + r440196;
        double r440212 = r440211 * r440185;
        double r440213 = a;
        double r440214 = r440212 + r440213;
        double r440215 = r440214 * r440185;
        double r440216 = b;
        double r440217 = r440215 + r440216;
        double r440218 = 15.234687407;
        double r440219 = r440185 + r440218;
        double r440220 = r440219 * r440185;
        double r440221 = 31.4690115749;
        double r440222 = r440220 + r440221;
        double r440223 = r440222 * r440185;
        double r440224 = 11.9400905721;
        double r440225 = r440223 + r440224;
        double r440226 = r440225 * r440185;
        double r440227 = 0.607771387771;
        double r440228 = r440226 + r440227;
        double r440229 = r440217 / r440228;
        double r440230 = r440194 * r440229;
        double r440231 = r440192 + r440230;
        double r440232 = r440191 ? r440206 : r440231;
        return r440232;
}

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

Original29.5
Target1.1
Herbie4.6
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.6584866307009356e+27 or 130676711668149.23 < z

    1. Initial program 57.6

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

    2. Taylor expanded around inf 8.8

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

    if -3.6584866307009356e+27 < z < 130676711668149.23

    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. Using strategy rm

    3. Applied *-un-lft-identity0.5

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

    4. Applied times-frac0.3

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

    5. Simplified0.3

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

  4. Final simplification4.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.65848663070093563 \cdot 10^{27} \lor \neg \left(z \le 130676711668149.234\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 
(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))))