Average Error: 28.2 → 1.1
Time: 35.7s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -5.657439373470419 \cdot 10^{+35}:\\ \;\;\;\;\left(y \cdot 3.13060547623 + \left(\frac{t}{\frac{z \cdot z}{y}} - \frac{y}{z} \cdot 36.527041698806414\right)\right) + x\\ \mathbf{elif}\;z \le 4.025561367592441 \cdot 10^{+50}:\\ \;\;\;\;x + y \cdot \frac{b + \left(z \cdot \left(z \cdot \left(3.13060547623 \cdot z + 11.1667541262\right) + t\right) + a\right) \cdot z}{0.607771387771 + \left(\left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right) \cdot z + 11.9400905721\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 3.13060547623 + \left(\frac{t}{\frac{z \cdot z}{y}} - \frac{y}{z} \cdot 36.527041698806414\right)\right) + x\\ \end{array}\]
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}
↓
\begin{array}{l}
\mathbf{if}\;z \le -5.657439373470419 \cdot 10^{+35}:\\
\;\;\;\;\left(y \cdot 3.13060547623 + \left(\frac{t}{\frac{z \cdot z}{y}} - \frac{y}{z} \cdot 36.527041698806414\right)\right) + x\\

\mathbf{elif}\;z \le 4.025561367592441 \cdot 10^{+50}:\\
\;\;\;\;x + y \cdot \frac{b + \left(z \cdot \left(z \cdot \left(3.13060547623 \cdot z + 11.1667541262\right) + t\right) + a\right) \cdot z}{0.607771387771 + \left(\left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right) \cdot z + 11.9400905721\right) \cdot z}\\

\mathbf{else}:\\
\;\;\;\;\left(y \cdot 3.13060547623 + \left(\frac{t}{\frac{z \cdot z}{y}} - \frac{y}{z} \cdot 36.527041698806414\right)\right) + x\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r20992286 = x;
        double r20992287 = y;
        double r20992288 = z;
        double r20992289 = 3.13060547623;
        double r20992290 = r20992288 * r20992289;
        double r20992291 = 11.1667541262;
        double r20992292 = r20992290 + r20992291;
        double r20992293 = r20992292 * r20992288;
        double r20992294 = t;
        double r20992295 = r20992293 + r20992294;
        double r20992296 = r20992295 * r20992288;
        double r20992297 = a;
        double r20992298 = r20992296 + r20992297;
        double r20992299 = r20992298 * r20992288;
        double r20992300 = b;
        double r20992301 = r20992299 + r20992300;
        double r20992302 = r20992287 * r20992301;
        double r20992303 = 15.234687407;
        double r20992304 = r20992288 + r20992303;
        double r20992305 = r20992304 * r20992288;
        double r20992306 = 31.4690115749;
        double r20992307 = r20992305 + r20992306;
        double r20992308 = r20992307 * r20992288;
        double r20992309 = 11.9400905721;
        double r20992310 = r20992308 + r20992309;
        double r20992311 = r20992310 * r20992288;
        double r20992312 = 0.607771387771;
        double r20992313 = r20992311 + r20992312;
        double r20992314 = r20992302 / r20992313;
        double r20992315 = r20992286 + r20992314;
        return r20992315;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r20992316 = z;
        double r20992317 = -5.657439373470419e+35;
        bool r20992318 = r20992316 <= r20992317;
        double r20992319 = y;
        double r20992320 = 3.13060547623;
        double r20992321 = r20992319 * r20992320;
        double r20992322 = t;
        double r20992323 = r20992316 * r20992316;
        double r20992324 = r20992323 / r20992319;
        double r20992325 = r20992322 / r20992324;
        double r20992326 = r20992319 / r20992316;
        double r20992327 = 36.527041698806414;
        double r20992328 = r20992326 * r20992327;
        double r20992329 = r20992325 - r20992328;
        double r20992330 = r20992321 + r20992329;
        double r20992331 = x;
        double r20992332 = r20992330 + r20992331;
        double r20992333 = 4.025561367592441e+50;
        bool r20992334 = r20992316 <= r20992333;
        double r20992335 = b;
        double r20992336 = r20992320 * r20992316;
        double r20992337 = 11.1667541262;
        double r20992338 = r20992336 + r20992337;
        double r20992339 = r20992316 * r20992338;
        double r20992340 = r20992339 + r20992322;
        double r20992341 = r20992316 * r20992340;
        double r20992342 = a;
        double r20992343 = r20992341 + r20992342;
        double r20992344 = r20992343 * r20992316;
        double r20992345 = r20992335 + r20992344;
        double r20992346 = 0.607771387771;
        double r20992347 = 31.4690115749;
        double r20992348 = 15.234687407;
        double r20992349 = r20992316 + r20992348;
        double r20992350 = r20992316 * r20992349;
        double r20992351 = r20992347 + r20992350;
        double r20992352 = r20992351 * r20992316;
        double r20992353 = 11.9400905721;
        double r20992354 = r20992352 + r20992353;
        double r20992355 = r20992354 * r20992316;
        double r20992356 = r20992346 + r20992355;
        double r20992357 = r20992345 / r20992356;
        double r20992358 = r20992319 * r20992357;
        double r20992359 = r20992331 + r20992358;
        double r20992360 = r20992334 ? r20992359 : r20992332;
        double r20992361 = r20992318 ? r20992332 : r20992360;
        return r20992361;
}

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

Original28.2
Target1.0
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -5.657439373470419e+35 or 4.025561367592441e+50 < z

    1. Initial program 58.9

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
    2. Using strategy rm

    3. Applied associate-/l*56.9

      \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\]
    4. Using strategy rm

    5. Applied div-inv56.9

      \[\leadsto x + \color{blue}{y \cdot \frac{1}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\]

    6. Simplified56.9

      \[\leadsto x + y \cdot \color{blue}{\frac{b + z \cdot \left(z \cdot \left(z \cdot \left(3.13060547623 \cdot z + 11.1667541262\right) + t\right) + a\right)}{0.607771387771 + \left(11.9400905721 + \left(z \cdot \left(15.234687407 + z\right) + 31.4690115749\right) \cdot z\right) \cdot z}}\]

    7. Taylor expanded around inf 7.4

      \[\leadsto x + \color{blue}{\left(\left(\frac{t \cdot y}{{z}^{2}} + 3.13060547623 \cdot y\right) - 36.527041698806414 \cdot \frac{y}{z}\right)}\]

    8. Simplified1.3

      \[\leadsto x + \color{blue}{\left(y \cdot 3.13060547623 + \left(\frac{t}{\frac{z \cdot z}{y}} - \frac{y}{z} \cdot 36.527041698806414\right)\right)}\]

    if -5.657439373470419e+35 < z < 4.025561367592441e+50

    1. Initial program 2.0

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
    2. Using strategy rm

    3. Applied associate-/l*0.9

      \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\]
    4. Using strategy rm

    5. Applied div-inv0.9

      \[\leadsto x + \color{blue}{y \cdot \frac{1}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\]

    6. Simplified0.9

      \[\leadsto x + y \cdot \color{blue}{\frac{b + z \cdot \left(z \cdot \left(z \cdot \left(3.13060547623 \cdot z + 11.1667541262\right) + t\right) + a\right)}{0.607771387771 + \left(11.9400905721 + \left(z \cdot \left(15.234687407 + z\right) + 31.4690115749\right) \cdot z\right) \cdot z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.657439373470419 \cdot 10^{+35}:\\ \;\;\;\;\left(y \cdot 3.13060547623 + \left(\frac{t}{\frac{z \cdot z}{y}} - \frac{y}{z} \cdot 36.527041698806414\right)\right) + x\\ \mathbf{elif}\;z \le 4.025561367592441 \cdot 10^{+50}:\\ \;\;\;\;x + y \cdot \frac{b + \left(z \cdot \left(z \cdot \left(3.13060547623 \cdot z + 11.1667541262\right) + t\right) + a\right) \cdot z}{0.607771387771 + \left(\left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right) \cdot z + 11.9400905721\right) \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot 3.13060547623 + \left(\frac{t}{\frac{z \cdot z}{y}} - \frac{y}{z} \cdot 36.527041698806414\right)\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019158 
(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))) (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))))