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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -7.6883151432789902 \cdot 10^{21} \lor \neg \left(z \le 6.2617027895573594 \cdot 10^{42}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]

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 -7.6883151432789902 \cdot 10^{21} \lor \neg \left(z \le 6.2617027895573594 \cdot 10^{42}\right):\\
\;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\

\mathbf{else}:\\
\;\;\;\;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}\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r382321 = x;
        double r382322 = y;
        double r382323 = z;
        double r382324 = 3.13060547623;
        double r382325 = r382323 * r382324;
        double r382326 = 11.1667541262;
        double r382327 = r382325 + r382326;
        double r382328 = r382327 * r382323;
        double r382329 = t;
        double r382330 = r382328 + r382329;
        double r382331 = r382330 * r382323;
        double r382332 = a;
        double r382333 = r382331 + r382332;
        double r382334 = r382333 * r382323;
        double r382335 = b;
        double r382336 = r382334 + r382335;
        double r382337 = r382322 * r382336;
        double r382338 = 15.234687407;
        double r382339 = r382323 + r382338;
        double r382340 = r382339 * r382323;
        double r382341 = 31.4690115749;
        double r382342 = r382340 + r382341;
        double r382343 = r382342 * r382323;
        double r382344 = 11.9400905721;
        double r382345 = r382343 + r382344;
        double r382346 = r382345 * r382323;
        double r382347 = 0.607771387771;
        double r382348 = r382346 + r382347;
        double r382349 = r382337 / r382348;
        double r382350 = r382321 + r382349;
        return r382350;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r382351 = z;
        double r382352 = -7.68831514327899e+21;
        bool r382353 = r382351 <= r382352;
        double r382354 = 6.26170278955736e+42;
        bool r382355 = r382351 <= r382354;
        double r382356 = !r382355;
        bool r382357 = r382353 || r382356;
        double r382358 = y;
        double r382359 = 3.13060547623;
        double r382360 = t;
        double r382361 = 2.0;
        double r382362 = pow(r382351, r382361);
        double r382363 = r382360 / r382362;
        double r382364 = r382359 + r382363;
        double r382365 = x;
        double r382366 = fma(r382358, r382364, r382365);
        double r382367 = r382351 * r382359;
        double r382368 = 11.1667541262;
        double r382369 = r382367 + r382368;
        double r382370 = r382369 * r382351;
        double r382371 = r382370 + r382360;
        double r382372 = r382371 * r382351;
        double r382373 = a;
        double r382374 = r382372 + r382373;
        double r382375 = r382374 * r382351;
        double r382376 = b;
        double r382377 = r382375 + r382376;
        double r382378 = r382358 * r382377;
        double r382379 = 15.234687407;
        double r382380 = r382351 + r382379;
        double r382381 = r382380 * r382351;
        double r382382 = 31.4690115749;
        double r382383 = r382381 + r382382;
        double r382384 = r382383 * r382351;
        double r382385 = 11.9400905721;
        double r382386 = r382384 + r382385;
        double r382387 = r382386 * r382351;
        double r382388 = 0.607771387771;
        double r382389 = r382387 + r382388;
        double r382390 = r382378 / r382389;
        double r382391 = r382365 + r382390;
        double r382392 = r382357 ? r382366 : r382391;
        return r382392;
}

Original	29.5
Target	0.9
Herbie	1.4

Derivation

Split input into 2 regimes
if z < -7.68831514327899e+21 or 6.26170278955736e+42 < z
1. Initial program 59.2
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified56.9
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Taylor expanded around inf 8.7
  \[\leadsto \color{blue}{x + \left(\frac{t \cdot y}{{z}^{2}} + 3.13060547622999996 \cdot y\right)}\]
4. Simplified1.5
  \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)}\]
if -7.68831514327899e+21 < z < 6.26170278955736e+42
1. Initial program 1.3
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
Recombined 2 regimes into one program.
Final simplification1.4
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -7.6883151432789902 \cdot 10^{21} \lor \neg \left(z \le 6.2617027895573594 \cdot 10^{42}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(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))))

Error

Target

Derivation

`if z < -7.68831514327899e+21 or 6.26170278955736e+42 < z`

`if -7.68831514327899e+21 < z < 6.26170278955736e+42`

Reproduce