Average Error: 29.4 → 4.9
Time: 12.2s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -441648319598393860 \lor \neg \left(z \le 706881567136002.375\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]
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 -441648319598393860 \lor \neg \left(z \le 706881567136002.375\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 r102488 = x;
        double r102489 = y;
        double r102490 = z;
        double r102491 = 3.13060547623;
        double r102492 = r102490 * r102491;
        double r102493 = 11.1667541262;
        double r102494 = r102492 + r102493;
        double r102495 = r102494 * r102490;
        double r102496 = t;
        double r102497 = r102495 + r102496;
        double r102498 = r102497 * r102490;
        double r102499 = a;
        double r102500 = r102498 + r102499;
        double r102501 = r102500 * r102490;
        double r102502 = b;
        double r102503 = r102501 + r102502;
        double r102504 = r102489 * r102503;
        double r102505 = 15.234687407;
        double r102506 = r102490 + r102505;
        double r102507 = r102506 * r102490;
        double r102508 = 31.4690115749;
        double r102509 = r102507 + r102508;
        double r102510 = r102509 * r102490;
        double r102511 = 11.9400905721;
        double r102512 = r102510 + r102511;
        double r102513 = r102512 * r102490;
        double r102514 = 0.607771387771;
        double r102515 = r102513 + r102514;
        double r102516 = r102504 / r102515;
        double r102517 = r102488 + r102516;
        return r102517;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r102518 = z;
        double r102519 = -4.4164831959839386e+17;
        bool r102520 = r102518 <= r102519;
        double r102521 = 706881567136002.4;
        bool r102522 = r102518 <= r102521;
        double r102523 = !r102522;
        bool r102524 = r102520 || r102523;
        double r102525 = x;
        double r102526 = 3.13060547623;
        double r102527 = y;
        double r102528 = r102526 * r102527;
        double r102529 = t;
        double r102530 = r102529 * r102527;
        double r102531 = 2.0;
        double r102532 = pow(r102518, r102531);
        double r102533 = r102530 / r102532;
        double r102534 = r102528 + r102533;
        double r102535 = 36.527041698806414;
        double r102536 = r102527 / r102518;
        double r102537 = r102535 * r102536;
        double r102538 = r102534 - r102537;
        double r102539 = r102525 + r102538;
        double r102540 = 15.234687407;
        double r102541 = r102518 + r102540;
        double r102542 = r102541 * r102518;
        double r102543 = 31.4690115749;
        double r102544 = r102542 + r102543;
        double r102545 = r102544 * r102518;
        double r102546 = 11.9400905721;
        double r102547 = r102545 + r102546;
        double r102548 = r102547 * r102518;
        double r102549 = 0.607771387771;
        double r102550 = r102548 + r102549;
        double r102551 = r102518 * r102526;
        double r102552 = 11.1667541262;
        double r102553 = r102551 + r102552;
        double r102554 = r102553 * r102518;
        double r102555 = r102554 + r102529;
        double r102556 = r102555 * r102518;
        double r102557 = a;
        double r102558 = r102556 + r102557;
        double r102559 = r102558 * r102518;
        double r102560 = b;
        double r102561 = r102559 + r102560;
        double r102562 = r102550 / r102561;
        double r102563 = r102527 / r102562;
        double r102564 = r102525 + r102563;
        double r102565 = r102524 ? r102539 : r102564;
        return r102565;
}

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

Original29.4
Target1.2
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 < -4.4164831959839386e+17 or 706881567136002.4 < z

    1. Initial program 56.9

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

    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 -4.4164831959839386e+17 < z < 706881567136002.4

    1. Initial program 0.5

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

    3. Applied associate-/l*0.2

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

  4. Final simplification4.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -441648319598393860 \lor \neg \left(z \le 706881567136002.375\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(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))))