Average Error: 28.9 → 1.0
Time: 24.6s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -11377676592436386882634106867972293791840000:\\ \;\;\;\;x + \left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\frac{y}{z} \cdot \frac{\sqrt[3]{t}}{z}\right) + \left(3.130605476229999961645944495103321969509 \cdot y - \frac{y}{z} \cdot 36.52704169880641416057187598198652267456\right)\right)\\ \mathbf{elif}\;z \le 854771490603964610616754176:\\ \;\;\;\;x + \frac{y}{\frac{0.6077713877710000378584709324059076607227 + z \cdot \left(11.94009057210000079862766142468899488449 + \left(z \cdot \left(15.2346874069999991263557603815570473671 + z\right) + 31.46901157490000144889563671313226222992\right) \cdot z\right)}{z \cdot \left(\left(\left(11.16675412620000074070958362426608800888 + 3.130605476229999961645944495103321969509 \cdot z\right) \cdot z + t\right) \cdot z + a\right) + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\frac{y}{z} \cdot \frac{\sqrt[3]{t}}{z}\right) + \left(3.130605476229999961645944495103321969509 \cdot y - \frac{y}{z} \cdot 36.52704169880641416057187598198652267456\right)\right)\\ \end{array}\]
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}
↓
\begin{array}{l}
\mathbf{if}\;z \le -11377676592436386882634106867972293791840000:\\
\;\;\;\;x + \left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\frac{y}{z} \cdot \frac{\sqrt[3]{t}}{z}\right) + \left(3.130605476229999961645944495103321969509 \cdot y - \frac{y}{z} \cdot 36.52704169880641416057187598198652267456\right)\right)\\

\mathbf{elif}\;z \le 854771490603964610616754176:\\
\;\;\;\;x + \frac{y}{\frac{0.6077713877710000378584709324059076607227 + z \cdot \left(11.94009057210000079862766142468899488449 + \left(z \cdot \left(15.2346874069999991263557603815570473671 + z\right) + 31.46901157490000144889563671313226222992\right) \cdot z\right)}{z \cdot \left(\left(\left(11.16675412620000074070958362426608800888 + 3.130605476229999961645944495103321969509 \cdot z\right) \cdot z + t\right) \cdot z + a\right) + b}}\\

\mathbf{else}:\\
\;\;\;\;x + \left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\frac{y}{z} \cdot \frac{\sqrt[3]{t}}{z}\right) + \left(3.130605476229999961645944495103321969509 \cdot y - \frac{y}{z} \cdot 36.52704169880641416057187598198652267456\right)\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r19690273 = x;
        double r19690274 = y;
        double r19690275 = z;
        double r19690276 = 3.13060547623;
        double r19690277 = r19690275 * r19690276;
        double r19690278 = 11.1667541262;
        double r19690279 = r19690277 + r19690278;
        double r19690280 = r19690279 * r19690275;
        double r19690281 = t;
        double r19690282 = r19690280 + r19690281;
        double r19690283 = r19690282 * r19690275;
        double r19690284 = a;
        double r19690285 = r19690283 + r19690284;
        double r19690286 = r19690285 * r19690275;
        double r19690287 = b;
        double r19690288 = r19690286 + r19690287;
        double r19690289 = r19690274 * r19690288;
        double r19690290 = 15.234687407;
        double r19690291 = r19690275 + r19690290;
        double r19690292 = r19690291 * r19690275;
        double r19690293 = 31.4690115749;
        double r19690294 = r19690292 + r19690293;
        double r19690295 = r19690294 * r19690275;
        double r19690296 = 11.9400905721;
        double r19690297 = r19690295 + r19690296;
        double r19690298 = r19690297 * r19690275;
        double r19690299 = 0.607771387771;
        double r19690300 = r19690298 + r19690299;
        double r19690301 = r19690289 / r19690300;
        double r19690302 = r19690273 + r19690301;
        return r19690302;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r19690303 = z;
        double r19690304 = -1.1377676592436387e+43;
        bool r19690305 = r19690303 <= r19690304;
        double r19690306 = x;
        double r19690307 = t;
        double r19690308 = cbrt(r19690307);
        double r19690309 = r19690308 * r19690308;
        double r19690310 = y;
        double r19690311 = r19690310 / r19690303;
        double r19690312 = r19690308 / r19690303;
        double r19690313 = r19690311 * r19690312;
        double r19690314 = r19690309 * r19690313;
        double r19690315 = 3.13060547623;
        double r19690316 = r19690315 * r19690310;
        double r19690317 = 36.527041698806414;
        double r19690318 = r19690311 * r19690317;
        double r19690319 = r19690316 - r19690318;
        double r19690320 = r19690314 + r19690319;
        double r19690321 = r19690306 + r19690320;
        double r19690322 = 8.547714906039646e+26;
        bool r19690323 = r19690303 <= r19690322;
        double r19690324 = 0.607771387771;
        double r19690325 = 11.9400905721;
        double r19690326 = 15.234687407;
        double r19690327 = r19690326 + r19690303;
        double r19690328 = r19690303 * r19690327;
        double r19690329 = 31.4690115749;
        double r19690330 = r19690328 + r19690329;
        double r19690331 = r19690330 * r19690303;
        double r19690332 = r19690325 + r19690331;
        double r19690333 = r19690303 * r19690332;
        double r19690334 = r19690324 + r19690333;
        double r19690335 = 11.1667541262;
        double r19690336 = r19690315 * r19690303;
        double r19690337 = r19690335 + r19690336;
        double r19690338 = r19690337 * r19690303;
        double r19690339 = r19690338 + r19690307;
        double r19690340 = r19690339 * r19690303;
        double r19690341 = a;
        double r19690342 = r19690340 + r19690341;
        double r19690343 = r19690303 * r19690342;
        double r19690344 = b;
        double r19690345 = r19690343 + r19690344;
        double r19690346 = r19690334 / r19690345;
        double r19690347 = r19690310 / r19690346;
        double r19690348 = r19690306 + r19690347;
        double r19690349 = r19690323 ? r19690348 : r19690321;
        double r19690350 = r19690305 ? r19690321 : r19690349;
        return r19690350;
}

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

Original28.9
Target0.8
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252631754123144978817242590467 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914286795694558389038333165002 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.1377676592436387e+43 or 8.547714906039646e+26 < z

    1. Initial program 59.2

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]

    2. Taylor expanded around inf 9.0

      \[\leadsto x + \color{blue}{\left(\left(\frac{t \cdot y}{{z}^{2}} + 3.130605476229999961645944495103321969509 \cdot y\right) - 36.52704169880641416057187598198652267456 \cdot \frac{y}{z}\right)}\]

    3. Simplified1.5

      \[\leadsto x + \color{blue}{\left(\left(3.130605476229999961645944495103321969509 \cdot y - \frac{y}{z} \cdot 36.52704169880641416057187598198652267456\right) + \frac{t}{z} \cdot \frac{y}{z}\right)}\]
    4. Using strategy rm

    5. Applied *-un-lft-identity1.5

      \[\leadsto x + \left(\left(3.130605476229999961645944495103321969509 \cdot y - \frac{y}{z} \cdot 36.52704169880641416057187598198652267456\right) + \frac{t}{\color{blue}{1 \cdot z}} \cdot \frac{y}{z}\right)\]

    6. Applied add-cube-cbrt1.6

      \[\leadsto x + \left(\left(3.130605476229999961645944495103321969509 \cdot y - \frac{y}{z} \cdot 36.52704169880641416057187598198652267456\right) + \frac{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}{1 \cdot z} \cdot \frac{y}{z}\right)\]

    7. Applied times-frac1.6

      \[\leadsto x + \left(\left(3.130605476229999961645944495103321969509 \cdot y - \frac{y}{z} \cdot 36.52704169880641416057187598198652267456\right) + \color{blue}{\left(\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{1} \cdot \frac{\sqrt[3]{t}}{z}\right)} \cdot \frac{y}{z}\right)\]

    8. Applied associate-*l*1.6

      \[\leadsto x + \left(\left(3.130605476229999961645944495103321969509 \cdot y - \frac{y}{z} \cdot 36.52704169880641416057187598198652267456\right) + \color{blue}{\frac{\sqrt[3]{t} \cdot \sqrt[3]{t}}{1} \cdot \left(\frac{\sqrt[3]{t}}{z} \cdot \frac{y}{z}\right)}\right)\]

    if -1.1377676592436387e+43 < z < 8.547714906039646e+26

    1. Initial program 1.3

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]
    2. Using strategy rm

    3. Applied associate-/l*0.5

      \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -11377676592436386882634106867972293791840000:\\ \;\;\;\;x + \left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\frac{y}{z} \cdot \frac{\sqrt[3]{t}}{z}\right) + \left(3.130605476229999961645944495103321969509 \cdot y - \frac{y}{z} \cdot 36.52704169880641416057187598198652267456\right)\right)\\ \mathbf{elif}\;z \le 854771490603964610616754176:\\ \;\;\;\;x + \frac{y}{\frac{0.6077713877710000378584709324059076607227 + z \cdot \left(11.94009057210000079862766142468899488449 + \left(z \cdot \left(15.2346874069999991263557603815570473671 + z\right) + 31.46901157490000144889563671313226222992\right) \cdot z\right)}{z \cdot \left(\left(\left(11.16675412620000074070958362426608800888 + 3.130605476229999961645944495103321969509 \cdot z\right) \cdot z + t\right) \cdot z + a\right) + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\frac{y}{z} \cdot \frac{\sqrt[3]{t}}{z}\right) + \left(3.130605476229999961645944495103321969509 \cdot y - \frac{y}{z} \cdot 36.52704169880641416057187598198652267456\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(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))))