Average Error: 29.0 → 4.9
Time: 17.3s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.74079175780789884 \cdot 10^{36} \lor \neg \left(z \le 10094.0500466464382\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]
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):\\
\;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r485453 = x;
        double r485454 = y;
        double r485455 = z;
        double r485456 = 3.13060547623;
        double r485457 = r485455 * r485456;
        double r485458 = 11.1667541262;
        double r485459 = r485457 + r485458;
        double r485460 = r485459 * r485455;
        double r485461 = t;
        double r485462 = r485460 + r485461;
        double r485463 = r485462 * r485455;
        double r485464 = a;
        double r485465 = r485463 + r485464;
        double r485466 = r485465 * r485455;
        double r485467 = b;
        double r485468 = r485466 + r485467;
        double r485469 = r485454 * r485468;
        double r485470 = 15.234687407;
        double r485471 = r485455 + r485470;
        double r485472 = r485471 * r485455;
        double r485473 = 31.4690115749;
        double r485474 = r485472 + r485473;
        double r485475 = r485474 * r485455;
        double r485476 = 11.9400905721;
        double r485477 = r485475 + r485476;
        double r485478 = r485477 * r485455;
        double r485479 = 0.607771387771;
        double r485480 = r485478 + r485479;
        double r485481 = r485469 / r485480;
        double r485482 = r485453 + r485481;
        return r485482;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r485483 = z;
        double r485484 = -1.7407917578078988e+36;
        bool r485485 = r485483 <= r485484;
        double r485486 = 10094.050046646438;
        bool r485487 = r485483 <= r485486;
        double r485488 = !r485487;
        bool r485489 = r485485 || r485488;
        double r485490 = x;
        double r485491 = 3.13060547623;
        double r485492 = y;
        double r485493 = r485491 * r485492;
        double r485494 = t;
        double r485495 = r485494 * r485492;
        double r485496 = 2.0;
        double r485497 = pow(r485483, r485496);
        double r485498 = r485495 / r485497;
        double r485499 = r485493 + r485498;
        double r485500 = 36.527041698806414;
        double r485501 = r485492 / r485483;
        double r485502 = r485500 * r485501;
        double r485503 = r485499 - r485502;
        double r485504 = r485490 + r485503;
        double r485505 = 15.234687407;
        double r485506 = r485483 + r485505;
        double r485507 = r485506 * r485483;
        double r485508 = 31.4690115749;
        double r485509 = r485507 + r485508;
        double r485510 = r485509 * r485483;
        double r485511 = 11.9400905721;
        double r485512 = r485510 + r485511;
        double r485513 = r485512 * r485483;
        double r485514 = 0.607771387771;
        double r485515 = r485513 + r485514;
        double r485516 = r485483 * r485491;
        double r485517 = 11.1667541262;
        double r485518 = r485516 + r485517;
        double r485519 = r485518 * r485483;
        double r485520 = r485519 + r485494;
        double r485521 = r485520 * r485483;
        double r485522 = a;
        double r485523 = r485521 + r485522;
        double r485524 = r485523 * r485483;
        double r485525 = b;
        double r485526 = r485524 + r485525;
        double r485527 = r485515 / r485526;
        double r485528 = r485492 / r485527;
        double r485529 = r485490 + r485528;
        double r485530 = r485489 ? r485504 : r485529;
        return r485530;
}

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

Original29.0
Target1.1
Herbie4.9
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. 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. Taylor expanded around inf 9.3

      \[\leadsto x + \color{blue}{\left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)}\]

    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. Using strategy rm

    3. Applied associate-/l*0.4

      \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification4.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.74079175780789884 \cdot 10^{36} \lor \neg \left(z \le 10094.0500466464382\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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))))