Average Error: 29.1 → 4.4
Time: 17.9s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -9.556303061205325 \cdot 10^{56} \lor \neg \left(z \le 2.85934170495834728 \cdot 10^{71}\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]
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 -9.556303061205325 \cdot 10^{56} \lor \neg \left(z \le 2.85934170495834728 \cdot 10^{71}\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 r269204 = x;
        double r269205 = y;
        double r269206 = z;
        double r269207 = 3.13060547623;
        double r269208 = r269206 * r269207;
        double r269209 = 11.1667541262;
        double r269210 = r269208 + r269209;
        double r269211 = r269210 * r269206;
        double r269212 = t;
        double r269213 = r269211 + r269212;
        double r269214 = r269213 * r269206;
        double r269215 = a;
        double r269216 = r269214 + r269215;
        double r269217 = r269216 * r269206;
        double r269218 = b;
        double r269219 = r269217 + r269218;
        double r269220 = r269205 * r269219;
        double r269221 = 15.234687407;
        double r269222 = r269206 + r269221;
        double r269223 = r269222 * r269206;
        double r269224 = 31.4690115749;
        double r269225 = r269223 + r269224;
        double r269226 = r269225 * r269206;
        double r269227 = 11.9400905721;
        double r269228 = r269226 + r269227;
        double r269229 = r269228 * r269206;
        double r269230 = 0.607771387771;
        double r269231 = r269229 + r269230;
        double r269232 = r269220 / r269231;
        double r269233 = r269204 + r269232;
        return r269233;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r269234 = z;
        double r269235 = -9.556303061205325e+56;
        bool r269236 = r269234 <= r269235;
        double r269237 = 2.8593417049583473e+71;
        bool r269238 = r269234 <= r269237;
        double r269239 = !r269238;
        bool r269240 = r269236 || r269239;
        double r269241 = x;
        double r269242 = 3.13060547623;
        double r269243 = y;
        double r269244 = r269242 * r269243;
        double r269245 = t;
        double r269246 = r269245 * r269243;
        double r269247 = 2.0;
        double r269248 = pow(r269234, r269247);
        double r269249 = r269246 / r269248;
        double r269250 = r269244 + r269249;
        double r269251 = 36.527041698806414;
        double r269252 = r269243 / r269234;
        double r269253 = r269251 * r269252;
        double r269254 = r269250 - r269253;
        double r269255 = r269241 + r269254;
        double r269256 = 15.234687407;
        double r269257 = r269234 + r269256;
        double r269258 = r269257 * r269234;
        double r269259 = 31.4690115749;
        double r269260 = r269258 + r269259;
        double r269261 = r269260 * r269234;
        double r269262 = 11.9400905721;
        double r269263 = r269261 + r269262;
        double r269264 = r269263 * r269234;
        double r269265 = 0.607771387771;
        double r269266 = r269264 + r269265;
        double r269267 = r269234 * r269242;
        double r269268 = 11.1667541262;
        double r269269 = r269267 + r269268;
        double r269270 = r269269 * r269234;
        double r269271 = r269270 + r269245;
        double r269272 = r269271 * r269234;
        double r269273 = a;
        double r269274 = r269272 + r269273;
        double r269275 = r269274 * r269234;
        double r269276 = b;
        double r269277 = r269275 + r269276;
        double r269278 = r269266 / r269277;
        double r269279 = r269243 / r269278;
        double r269280 = r269241 + r269279;
        double r269281 = r269240 ? r269255 : r269280;
        return r269281;
}

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

Original29.1
Target1.1
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 < -9.556303061205325e+56 or 2.8593417049583473e+71 < z

    1. Initial program 62.8

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

    2. Taylor expanded around inf 8.0

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

    if -9.556303061205325e+56 < z < 2.8593417049583473e+71

    1. Initial program 3.5

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

    3. Applied associate-/l*1.6

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

  4. Final simplification4.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -9.556303061205325 \cdot 10^{56} \lor \neg \left(z \le 2.85934170495834728 \cdot 10^{71}\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"

  :herbie-target
  (if (< z -6.499344996252632e+53) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1.0))) (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 1.0)))))

  (+ 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))))