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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -3951683805489442300 \lor \neg \left(z \le 2.9291251479066061 \cdot 10^{36}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

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 -3951683805489442300 \lor \neg \left(z \le 2.9291251479066061 \cdot 10^{36}\right):\\
\;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(y \cdot \frac{1}{\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)\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r429443 = x;
        double r429444 = y;
        double r429445 = z;
        double r429446 = 3.13060547623;
        double r429447 = r429445 * r429446;
        double r429448 = 11.1667541262;
        double r429449 = r429447 + r429448;
        double r429450 = r429449 * r429445;
        double r429451 = t;
        double r429452 = r429450 + r429451;
        double r429453 = r429452 * r429445;
        double r429454 = a;
        double r429455 = r429453 + r429454;
        double r429456 = r429455 * r429445;
        double r429457 = b;
        double r429458 = r429456 + r429457;
        double r429459 = r429444 * r429458;
        double r429460 = 15.234687407;
        double r429461 = r429445 + r429460;
        double r429462 = r429461 * r429445;
        double r429463 = 31.4690115749;
        double r429464 = r429462 + r429463;
        double r429465 = r429464 * r429445;
        double r429466 = 11.9400905721;
        double r429467 = r429465 + r429466;
        double r429468 = r429467 * r429445;
        double r429469 = 0.607771387771;
        double r429470 = r429468 + r429469;
        double r429471 = r429459 / r429470;
        double r429472 = r429443 + r429471;
        return r429472;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r429473 = z;
        double r429474 = -3.9516838054894423e+18;
        bool r429475 = r429473 <= r429474;
        double r429476 = 2.929125147906606e+36;
        bool r429477 = r429473 <= r429476;
        double r429478 = !r429477;
        bool r429479 = r429475 || r429478;
        double r429480 = y;
        double r429481 = 3.13060547623;
        double r429482 = t;
        double r429483 = 2.0;
        double r429484 = pow(r429473, r429483);
        double r429485 = r429482 / r429484;
        double r429486 = r429481 + r429485;
        double r429487 = x;
        double r429488 = fma(r429480, r429486, r429487);
        double r429489 = 1.0;
        double r429490 = 15.234687407;
        double r429491 = r429473 + r429490;
        double r429492 = 31.4690115749;
        double r429493 = fma(r429491, r429473, r429492);
        double r429494 = 11.9400905721;
        double r429495 = fma(r429493, r429473, r429494);
        double r429496 = 0.607771387771;
        double r429497 = fma(r429495, r429473, r429496);
        double r429498 = r429489 / r429497;
        double r429499 = r429480 * r429498;
        double r429500 = 11.1667541262;
        double r429501 = fma(r429473, r429481, r429500);
        double r429502 = fma(r429501, r429473, r429482);
        double r429503 = a;
        double r429504 = fma(r429502, r429473, r429503);
        double r429505 = b;
        double r429506 = fma(r429504, r429473, r429505);
        double r429507 = fma(r429499, r429506, r429487);
        double r429508 = r429479 ? r429488 : r429507;
        return r429508;
}

Original	29.0
Target	0.9
Herbie	1.2

Derivation

Split input into 2 regimes
if z < -3.9516838054894423e+18 or 2.929125147906606e+36 < z
1. Initial program 58.5
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified56.7
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Taylor expanded around inf 9.3
  \[\leadsto \color{blue}{x + \left(\frac{t \cdot y}{{z}^{2}} + 3.13060547622999996 \cdot y\right)}\]
4. Simplified1.8
  \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)}\]
if -3.9516838054894423e+18 < z < 2.929125147906606e+36
1. Initial program 1.1
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified0.5
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Using strategy rm
4. Applied div-inv0.6
  \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\]
Recombined 2 regimes into one program.
Final simplification1.2
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3951683805489442300 \lor \neg \left(z \le 2.9291251479066061 \cdot 10^{36}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020083 +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 < -3.9516838054894423e+18 or 2.929125147906606e+36 < z`

`if -3.9516838054894423e+18 < z < 2.929125147906606e+36`

Reproduce