Average Error: 29.2 → 1.6
Time: 25.0s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2552320556936620790683030666608640 \lor \neg \left(z \le 871.6899146722846580814803019165992736816\right):\\ \;\;\;\;\left(y \cdot 3.130605476229999961645944495103321969509 + \left(\frac{t}{z} \cdot \frac{y}{z} - \frac{36.52704169880641416057187598198652267456 \cdot y}{z}\right)\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{b + \left(z \cdot a + \left(z \cdot z\right) \cdot \left(t + z \cdot \left(3.130605476229999961645944495103321969509 \cdot z + 11.16675412620000074070958362426608800888\right)\right)\right)}{\left(\left(\left(15.2346874069999991263557603815570473671 + z\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227} \cdot y\\ \end{array}\]
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 -2552320556936620790683030666608640 \lor \neg \left(z \le 871.6899146722846580814803019165992736816\right):\\
\;\;\;\;\left(y \cdot 3.130605476229999961645944495103321969509 + \left(\frac{t}{z} \cdot \frac{y}{z} - \frac{36.52704169880641416057187598198652267456 \cdot y}{z}\right)\right) + x\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r323302 = x;
        double r323303 = y;
        double r323304 = z;
        double r323305 = 3.13060547623;
        double r323306 = r323304 * r323305;
        double r323307 = 11.1667541262;
        double r323308 = r323306 + r323307;
        double r323309 = r323308 * r323304;
        double r323310 = t;
        double r323311 = r323309 + r323310;
        double r323312 = r323311 * r323304;
        double r323313 = a;
        double r323314 = r323312 + r323313;
        double r323315 = r323314 * r323304;
        double r323316 = b;
        double r323317 = r323315 + r323316;
        double r323318 = r323303 * r323317;
        double r323319 = 15.234687407;
        double r323320 = r323304 + r323319;
        double r323321 = r323320 * r323304;
        double r323322 = 31.4690115749;
        double r323323 = r323321 + r323322;
        double r323324 = r323323 * r323304;
        double r323325 = 11.9400905721;
        double r323326 = r323324 + r323325;
        double r323327 = r323326 * r323304;
        double r323328 = 0.607771387771;
        double r323329 = r323327 + r323328;
        double r323330 = r323318 / r323329;
        double r323331 = r323302 + r323330;
        return r323331;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r323332 = z;
        double r323333 = -2.5523205569366208e+33;
        bool r323334 = r323332 <= r323333;
        double r323335 = 871.6899146722847;
        bool r323336 = r323332 <= r323335;
        double r323337 = !r323336;
        bool r323338 = r323334 || r323337;
        double r323339 = y;
        double r323340 = 3.13060547623;
        double r323341 = r323339 * r323340;
        double r323342 = t;
        double r323343 = r323342 / r323332;
        double r323344 = r323339 / r323332;
        double r323345 = r323343 * r323344;
        double r323346 = 36.527041698806414;
        double r323347 = r323346 * r323339;
        double r323348 = r323347 / r323332;
        double r323349 = r323345 - r323348;
        double r323350 = r323341 + r323349;
        double r323351 = x;
        double r323352 = r323350 + r323351;
        double r323353 = b;
        double r323354 = a;
        double r323355 = r323332 * r323354;
        double r323356 = r323332 * r323332;
        double r323357 = r323340 * r323332;
        double r323358 = 11.1667541262;
        double r323359 = r323357 + r323358;
        double r323360 = r323332 * r323359;
        double r323361 = r323342 + r323360;
        double r323362 = r323356 * r323361;
        double r323363 = r323355 + r323362;
        double r323364 = r323353 + r323363;
        double r323365 = 15.234687407;
        double r323366 = r323365 + r323332;
        double r323367 = r323366 * r323332;
        double r323368 = 31.4690115749;
        double r323369 = r323367 + r323368;
        double r323370 = r323369 * r323332;
        double r323371 = 11.9400905721;
        double r323372 = r323370 + r323371;
        double r323373 = r323372 * r323332;
        double r323374 = 0.607771387771;
        double r323375 = r323373 + r323374;
        double r323376 = r323364 / r323375;
        double r323377 = r323376 * r323339;
        double r323378 = r323351 + r323377;
        double r323379 = r323338 ? r323352 : r323378;
        return r323379;
}

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

Original29.2
Target0.9
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252631754123144978817242590467 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914286795694558389038333165002 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.5523205569366208e+33 or 871.6899146722847 < z

    1. Initial program 57.1

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

    2. Simplified54.0

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

    3. Taylor expanded around inf 8.7

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

    4. Simplified2.5

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

    if -2.5523205569366208e+33 < z < 871.6899146722847

    1. Initial program 0.7

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

    2. Simplified0.3

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

    4. Applied distribute-lft-in0.3

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

    5. Simplified0.7

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2552320556936620790683030666608640 \lor \neg \left(z \le 871.6899146722846580814803019165992736816\right):\\ \;\;\;\;\left(y \cdot 3.130605476229999961645944495103321969509 + \left(\frac{t}{z} \cdot \frac{y}{z} - \frac{36.52704169880641416057187598198652267456 \cdot y}{z}\right)\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{b + \left(z \cdot a + \left(z \cdot z\right) \cdot \left(t + z \cdot \left(3.130605476229999961645944495103321969509 \cdot z + 11.16675412620000074070958362426608800888\right)\right)\right)}{\left(\left(\left(15.2346874069999991263557603815570473671 + z\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(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))))