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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1.7503197233736622 \cdot 10^{25} \lor \neg \left(z \le 14972530473052320000\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{{z}^{2}}, y, \mathsf{fma}\left(3.13060547622999996, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]

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 -1.7503197233736622 \cdot 10^{25} \lor \neg \left(z \le 14972530473052320000\right):\\
\;\;\;\;\mathsf{fma}\left(\frac{t}{{z}^{2}}, y, \mathsf{fma}\left(3.13060547622999996, y, x\right)\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 r427328 = x;
        double r427329 = y;
        double r427330 = z;
        double r427331 = 3.13060547623;
        double r427332 = r427330 * r427331;
        double r427333 = 11.1667541262;
        double r427334 = r427332 + r427333;
        double r427335 = r427334 * r427330;
        double r427336 = t;
        double r427337 = r427335 + r427336;
        double r427338 = r427337 * r427330;
        double r427339 = a;
        double r427340 = r427338 + r427339;
        double r427341 = r427340 * r427330;
        double r427342 = b;
        double r427343 = r427341 + r427342;
        double r427344 = r427329 * r427343;
        double r427345 = 15.234687407;
        double r427346 = r427330 + r427345;
        double r427347 = r427346 * r427330;
        double r427348 = 31.4690115749;
        double r427349 = r427347 + r427348;
        double r427350 = r427349 * r427330;
        double r427351 = 11.9400905721;
        double r427352 = r427350 + r427351;
        double r427353 = r427352 * r427330;
        double r427354 = 0.607771387771;
        double r427355 = r427353 + r427354;
        double r427356 = r427344 / r427355;
        double r427357 = r427328 + r427356;
        return r427357;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r427358 = z;
        double r427359 = -1.7503197233736622e+25;
        bool r427360 = r427358 <= r427359;
        double r427361 = 1.497253047305232e+19;
        bool r427362 = r427358 <= r427361;
        double r427363 = !r427362;
        bool r427364 = r427360 || r427363;
        double r427365 = t;
        double r427366 = 2.0;
        double r427367 = pow(r427358, r427366);
        double r427368 = r427365 / r427367;
        double r427369 = y;
        double r427370 = 3.13060547623;
        double r427371 = x;
        double r427372 = fma(r427370, r427369, r427371);
        double r427373 = fma(r427368, r427369, r427372);
        double r427374 = r427358 * r427370;
        double r427375 = 11.1667541262;
        double r427376 = r427374 + r427375;
        double r427377 = r427376 * r427358;
        double r427378 = r427377 + r427365;
        double r427379 = r427378 * r427358;
        double r427380 = a;
        double r427381 = r427379 + r427380;
        double r427382 = r427381 * r427358;
        double r427383 = b;
        double r427384 = r427382 + r427383;
        double r427385 = r427369 * r427384;
        double r427386 = 15.234687407;
        double r427387 = r427358 + r427386;
        double r427388 = r427387 * r427358;
        double r427389 = 31.4690115749;
        double r427390 = r427388 + r427389;
        double r427391 = r427390 * r427358;
        double r427392 = 11.9400905721;
        double r427393 = r427391 + r427392;
        double r427394 = r427393 * r427358;
        double r427395 = 0.607771387771;
        double r427396 = r427394 + r427395;
        double r427397 = r427385 / r427396;
        double r427398 = r427371 + r427397;
        double r427399 = r427364 ? r427373 : r427398;
        return r427399;
}

Original	30.1
Target	0.9
Herbie	1.1

Derivation

Split input into 2 regimes
if z < -1.7503197233736622e+25 or 1.497253047305232e+19 < z
1. Initial program 58.6
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified56.3
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Taylor expanded around inf 8.7
  \[\leadsto \color{blue}{x + \left(\frac{t \cdot y}{{z}^{2}} + 3.13060547622999996 \cdot y\right)}\]
4. Simplified1.7
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t}{{z}^{2}}, y, \mathsf{fma}\left(3.13060547622999996, y, x\right)\right)}\]
if -1.7503197233736622e+25 < z < 1.497253047305232e+19
1. Initial program 0.6
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
Recombined 2 regimes into one program.
Final simplification1.1
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.7503197233736622 \cdot 10^{25} \lor \neg \left(z \le 14972530473052320000\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{{z}^{2}}, y, \mathsf{fma}\left(3.13060547622999996, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +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))))

Falling back on racket egraph because egg-herbie package not installed (more)

Error

Target

Derivation

`if z < -1.7503197233736622e+25 or 1.497253047305232e+19 < z`

`if -1.7503197233736622e+25 < z < 1.497253047305232e+19`

Reproduce