Average Error: 29.9 → 1.0
Time: 9.0s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -9.4391244631836989 \cdot 10^{36} \lor \neg \left(z \le 1.5383193237246159 \cdot 10^{32}\right):\\ \;\;\;\;x + y \cdot \left(\left(\frac{t}{{z}^{2}} + 3.13060547622999996\right) - 36.527041698806414 \cdot \frac{1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]
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 -9.4391244631836989 \cdot 10^{36} \lor \neg \left(z \le 1.5383193237246159 \cdot 10^{32}\right):\\
\;\;\;\;x + y \cdot \left(\left(\frac{t}{{z}^{2}} + 3.13060547622999996\right) - 36.527041698806414 \cdot \frac{1}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\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 r329407 = x;
        double r329408 = y;
        double r329409 = z;
        double r329410 = 3.13060547623;
        double r329411 = r329409 * r329410;
        double r329412 = 11.1667541262;
        double r329413 = r329411 + r329412;
        double r329414 = r329413 * r329409;
        double r329415 = t;
        double r329416 = r329414 + r329415;
        double r329417 = r329416 * r329409;
        double r329418 = a;
        double r329419 = r329417 + r329418;
        double r329420 = r329419 * r329409;
        double r329421 = b;
        double r329422 = r329420 + r329421;
        double r329423 = r329408 * r329422;
        double r329424 = 15.234687407;
        double r329425 = r329409 + r329424;
        double r329426 = r329425 * r329409;
        double r329427 = 31.4690115749;
        double r329428 = r329426 + r329427;
        double r329429 = r329428 * r329409;
        double r329430 = 11.9400905721;
        double r329431 = r329429 + r329430;
        double r329432 = r329431 * r329409;
        double r329433 = 0.607771387771;
        double r329434 = r329432 + r329433;
        double r329435 = r329423 / r329434;
        double r329436 = r329407 + r329435;
        return r329436;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r329437 = z;
        double r329438 = -9.439124463183699e+36;
        bool r329439 = r329437 <= r329438;
        double r329440 = 1.5383193237246159e+32;
        bool r329441 = r329437 <= r329440;
        double r329442 = !r329441;
        bool r329443 = r329439 || r329442;
        double r329444 = x;
        double r329445 = y;
        double r329446 = t;
        double r329447 = 2.0;
        double r329448 = pow(r329437, r329447);
        double r329449 = r329446 / r329448;
        double r329450 = 3.13060547623;
        double r329451 = r329449 + r329450;
        double r329452 = 36.527041698806414;
        double r329453 = 1.0;
        double r329454 = r329453 / r329437;
        double r329455 = r329452 * r329454;
        double r329456 = r329451 - r329455;
        double r329457 = r329445 * r329456;
        double r329458 = r329444 + r329457;
        double r329459 = r329437 * r329450;
        double r329460 = 11.1667541262;
        double r329461 = r329459 + r329460;
        double r329462 = r329461 * r329437;
        double r329463 = r329462 + r329446;
        double r329464 = r329463 * r329437;
        double r329465 = a;
        double r329466 = r329464 + r329465;
        double r329467 = r329466 * r329437;
        double r329468 = b;
        double r329469 = r329467 + r329468;
        double r329470 = 15.234687407;
        double r329471 = r329437 + r329470;
        double r329472 = r329471 * r329437;
        double r329473 = 31.4690115749;
        double r329474 = r329472 + r329473;
        double r329475 = r329474 * r329437;
        double r329476 = 11.9400905721;
        double r329477 = r329475 + r329476;
        double r329478 = r329477 * r329437;
        double r329479 = 0.607771387771;
        double r329480 = r329478 + r329479;
        double r329481 = r329469 / r329480;
        double r329482 = r329445 * r329481;
        double r329483 = r329444 + r329482;
        double r329484 = r329443 ? r329458 : r329483;
        return r329484;
}

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

Original29.9
Target0.9
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -9.439124463183699e+36 or 1.5383193237246159e+32 < z

    1. Initial program 59.9

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

    3. Applied *-un-lft-identity59.9

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004\right)}}\]

    4. Applied times-frac57.3

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}}\]

    5. Simplified57.3

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

    6. Taylor expanded around inf 1.5

      \[\leadsto x + y \cdot \color{blue}{\left(\left(\frac{t}{{z}^{2}} + 3.13060547622999996\right) - 36.527041698806414 \cdot \frac{1}{z}\right)}\]

    if -9.439124463183699e+36 < z < 1.5383193237246159e+32

    1. Initial program 1.4

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

    3. Applied *-un-lft-identity1.4

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004\right)}}\]

    4. Applied times-frac0.5

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}}\]

    5. Simplified0.5

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -9.4391244631836989 \cdot 10^{36} \lor \neg \left(z \le 1.5383193237246159 \cdot 10^{32}\right):\\ \;\;\;\;x + y \cdot \left(\left(\frac{t}{{z}^{2}} + 3.13060547622999996\right) - 36.527041698806414 \cdot \frac{1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 
(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))))