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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1.74079175780789884 \cdot 10^{36} \lor \neg \left(z \le 10094.0500466464382\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547622999996, y, \mathsf{fma}\left(\frac{t}{{z}^{2}}, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

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 -1.74079175780789884 \cdot 10^{36} \lor \neg \left(z \le 10094.0500466464382\right):\\
\;\;\;\;\mathsf{fma}\left(3.13060547622999996, y, \mathsf{fma}\left(\frac{t}{{z}^{2}}, y, x\right)\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 r328507 = x;
        double r328508 = y;
        double r328509 = z;
        double r328510 = 3.13060547623;
        double r328511 = r328509 * r328510;
        double r328512 = 11.1667541262;
        double r328513 = r328511 + r328512;
        double r328514 = r328513 * r328509;
        double r328515 = t;
        double r328516 = r328514 + r328515;
        double r328517 = r328516 * r328509;
        double r328518 = a;
        double r328519 = r328517 + r328518;
        double r328520 = r328519 * r328509;
        double r328521 = b;
        double r328522 = r328520 + r328521;
        double r328523 = r328508 * r328522;
        double r328524 = 15.234687407;
        double r328525 = r328509 + r328524;
        double r328526 = r328525 * r328509;
        double r328527 = 31.4690115749;
        double r328528 = r328526 + r328527;
        double r328529 = r328528 * r328509;
        double r328530 = 11.9400905721;
        double r328531 = r328529 + r328530;
        double r328532 = r328531 * r328509;
        double r328533 = 0.607771387771;
        double r328534 = r328532 + r328533;
        double r328535 = r328523 / r328534;
        double r328536 = r328507 + r328535;
        return r328536;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r328537 = z;
        double r328538 = -1.7407917578078988e+36;
        bool r328539 = r328537 <= r328538;
        double r328540 = 10094.050046646438;
        bool r328541 = r328537 <= r328540;
        double r328542 = !r328541;
        bool r328543 = r328539 || r328542;
        double r328544 = 3.13060547623;
        double r328545 = y;
        double r328546 = t;
        double r328547 = 2.0;
        double r328548 = pow(r328537, r328547);
        double r328549 = r328546 / r328548;
        double r328550 = x;
        double r328551 = fma(r328549, r328545, r328550);
        double r328552 = fma(r328544, r328545, r328551);
        double r328553 = 1.0;
        double r328554 = 15.234687407;
        double r328555 = r328537 + r328554;
        double r328556 = 31.4690115749;
        double r328557 = fma(r328555, r328537, r328556);
        double r328558 = 11.9400905721;
        double r328559 = fma(r328557, r328537, r328558);
        double r328560 = 0.607771387771;
        double r328561 = fma(r328559, r328537, r328560);
        double r328562 = r328553 / r328561;
        double r328563 = r328545 * r328562;
        double r328564 = 11.1667541262;
        double r328565 = fma(r328537, r328544, r328564);
        double r328566 = fma(r328565, r328537, r328546);
        double r328567 = a;
        double r328568 = fma(r328566, r328537, r328567);
        double r328569 = b;
        double r328570 = fma(r328568, r328537, r328569);
        double r328571 = fma(r328563, r328570, r328550);
        double r328572 = r328543 ? r328552 : r328571;
        return r328572;
}

Original	29.0
Target	1.1
Herbie	1.4

Derivation

Split input into 2 regimes
if z < -1.7407917578078988e+36 or 10094.050046646438 < z
1. Initial program 57.3
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified55.4
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Using strategy rm
4. Applied div-inv55.4
  \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\]
5. Taylor expanded around inf 9.3
  \[\leadsto \color{blue}{x + \left(\frac{t \cdot y}{{z}^{2}} + 3.13060547622999996 \cdot y\right)}\]
6. Simplified2.2
  \[\leadsto \color{blue}{\mathsf{fma}\left(3.13060547622999996, y, \mathsf{fma}\left(\frac{t}{{z}^{2}}, y, x\right)\right)}\]
if -1.7407917578078988e+36 < z < 10094.050046646438
1. Initial program 0.7
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
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 simplification1.4
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.74079175780789884 \cdot 10^{36} \lor \neg \left(z \le 10094.0500466464382\right):\\ \;\;\;\;\mathsf{fma}\left(3.13060547622999996, y, \mathsf{fma}\left(\frac{t}{{z}^{2}}, y, x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 +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 < -1.7407917578078988e+36 or 10094.050046646438 < z`

`if -1.7407917578078988e+36 < z < 10094.050046646438`

Reproduce