Average Error: 29.3 → 4.4
Time: 5.1s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.7622742072428377 \cdot 10^{61} \lor \neg \left(z \le 6.5875831388733411 \cdot 10^{55}\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]
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 -5.7622742072428377 \cdot 10^{61} \lor \neg \left(z \le 6.5875831388733411 \cdot 10^{55}\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 r318179 = x;
        double r318180 = y;
        double r318181 = z;
        double r318182 = 3.13060547623;
        double r318183 = r318181 * r318182;
        double r318184 = 11.1667541262;
        double r318185 = r318183 + r318184;
        double r318186 = r318185 * r318181;
        double r318187 = t;
        double r318188 = r318186 + r318187;
        double r318189 = r318188 * r318181;
        double r318190 = a;
        double r318191 = r318189 + r318190;
        double r318192 = r318191 * r318181;
        double r318193 = b;
        double r318194 = r318192 + r318193;
        double r318195 = r318180 * r318194;
        double r318196 = 15.234687407;
        double r318197 = r318181 + r318196;
        double r318198 = r318197 * r318181;
        double r318199 = 31.4690115749;
        double r318200 = r318198 + r318199;
        double r318201 = r318200 * r318181;
        double r318202 = 11.9400905721;
        double r318203 = r318201 + r318202;
        double r318204 = r318203 * r318181;
        double r318205 = 0.607771387771;
        double r318206 = r318204 + r318205;
        double r318207 = r318195 / r318206;
        double r318208 = r318179 + r318207;
        return r318208;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r318209 = z;
        double r318210 = -5.762274207242838e+61;
        bool r318211 = r318209 <= r318210;
        double r318212 = 6.587583138873341e+55;
        bool r318213 = r318209 <= r318212;
        double r318214 = !r318213;
        bool r318215 = r318211 || r318214;
        double r318216 = x;
        double r318217 = 3.13060547623;
        double r318218 = y;
        double r318219 = r318217 * r318218;
        double r318220 = t;
        double r318221 = r318220 * r318218;
        double r318222 = 2.0;
        double r318223 = pow(r318209, r318222);
        double r318224 = r318221 / r318223;
        double r318225 = r318219 + r318224;
        double r318226 = 36.527041698806414;
        double r318227 = r318218 / r318209;
        double r318228 = r318226 * r318227;
        double r318229 = r318225 - r318228;
        double r318230 = r318216 + r318229;
        double r318231 = 15.234687407;
        double r318232 = r318209 + r318231;
        double r318233 = r318232 * r318209;
        double r318234 = 31.4690115749;
        double r318235 = r318233 + r318234;
        double r318236 = r318235 * r318209;
        double r318237 = 11.9400905721;
        double r318238 = r318236 + r318237;
        double r318239 = r318238 * r318209;
        double r318240 = 0.607771387771;
        double r318241 = r318239 + r318240;
        double r318242 = r318209 * r318217;
        double r318243 = 11.1667541262;
        double r318244 = r318242 + r318243;
        double r318245 = r318244 * r318209;
        double r318246 = r318245 + r318220;
        double r318247 = r318246 * r318209;
        double r318248 = a;
        double r318249 = r318247 + r318248;
        double r318250 = r318249 * r318209;
        double r318251 = b;
        double r318252 = r318250 + r318251;
        double r318253 = r318241 / r318252;
        double r318254 = r318218 / r318253;
        double r318255 = r318216 + r318254;
        double r318256 = r318215 ? r318230 : r318255;
        return r318256;
}

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

Original29.3
Target0.9
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 < -5.762274207242838e+61 or 6.587583138873341e+55 < z

    1. Initial program 62.3

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

    2. Taylor expanded around inf 8.3

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

    if -5.762274207242838e+61 < z < 6.587583138873341e+55

    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 associate-/l*1.2

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

  4. Final simplification4.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.7622742072428377 \cdot 10^{61} \lor \neg \left(z \le 6.5875831388733411 \cdot 10^{55}\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 
(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))))