Average Error: 30.1 → 4.5
Time: 5.2s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.39389244567685115 \cdot 10^{38} \lor \neg \left(z \le 1751680100761613370000\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]
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 -3.39389244567685115 \cdot 10^{38} \lor \neg \left(z \le 1751680100761613370000\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 r395173 = x;
        double r395174 = y;
        double r395175 = z;
        double r395176 = 3.13060547623;
        double r395177 = r395175 * r395176;
        double r395178 = 11.1667541262;
        double r395179 = r395177 + r395178;
        double r395180 = r395179 * r395175;
        double r395181 = t;
        double r395182 = r395180 + r395181;
        double r395183 = r395182 * r395175;
        double r395184 = a;
        double r395185 = r395183 + r395184;
        double r395186 = r395185 * r395175;
        double r395187 = b;
        double r395188 = r395186 + r395187;
        double r395189 = r395174 * r395188;
        double r395190 = 15.234687407;
        double r395191 = r395175 + r395190;
        double r395192 = r395191 * r395175;
        double r395193 = 31.4690115749;
        double r395194 = r395192 + r395193;
        double r395195 = r395194 * r395175;
        double r395196 = 11.9400905721;
        double r395197 = r395195 + r395196;
        double r395198 = r395197 * r395175;
        double r395199 = 0.607771387771;
        double r395200 = r395198 + r395199;
        double r395201 = r395189 / r395200;
        double r395202 = r395173 + r395201;
        return r395202;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r395203 = z;
        double r395204 = -3.393892445676851e+38;
        bool r395205 = r395203 <= r395204;
        double r395206 = 1.7516801007616134e+21;
        bool r395207 = r395203 <= r395206;
        double r395208 = !r395207;
        bool r395209 = r395205 || r395208;
        double r395210 = x;
        double r395211 = 3.13060547623;
        double r395212 = y;
        double r395213 = r395211 * r395212;
        double r395214 = t;
        double r395215 = r395214 * r395212;
        double r395216 = 2.0;
        double r395217 = pow(r395203, r395216);
        double r395218 = r395215 / r395217;
        double r395219 = r395213 + r395218;
        double r395220 = 36.527041698806414;
        double r395221 = r395212 / r395203;
        double r395222 = r395220 * r395221;
        double r395223 = r395219 - r395222;
        double r395224 = r395210 + r395223;
        double r395225 = 15.234687407;
        double r395226 = r395203 + r395225;
        double r395227 = r395226 * r395203;
        double r395228 = 31.4690115749;
        double r395229 = r395227 + r395228;
        double r395230 = r395229 * r395203;
        double r395231 = 11.9400905721;
        double r395232 = r395230 + r395231;
        double r395233 = r395232 * r395203;
        double r395234 = 0.607771387771;
        double r395235 = r395233 + r395234;
        double r395236 = r395203 * r395211;
        double r395237 = 11.1667541262;
        double r395238 = r395236 + r395237;
        double r395239 = r395238 * r395203;
        double r395240 = r395239 + r395214;
        double r395241 = r395240 * r395203;
        double r395242 = a;
        double r395243 = r395241 + r395242;
        double r395244 = r395243 * r395203;
        double r395245 = b;
        double r395246 = r395244 + r395245;
        double r395247 = r395235 / r395246;
        double r395248 = r395212 / r395247;
        double r395249 = r395210 + r395248;
        double r395250 = r395209 ? r395224 : r395249;
        return r395250;
}

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

Original30.1
Target0.9
Herbie4.5
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.393892445676851e+38 or 1.7516801007616134e+21 < z

    1. Initial program 59.3

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

    2. Taylor expanded around inf 8.5

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

    if -3.393892445676851e+38 < z < 1.7516801007616134e+21

    1. Initial program 1.2

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

    3. Applied associate-/l*0.6

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

  4. Final simplification4.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.39389244567685115 \cdot 10^{38} \lor \neg \left(z \le 1751680100761613370000\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 
(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))))