Average Error: 28.8 → 1.1
Time: 31.3s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.9856954798303585 \cdot 10^{+39}:\\ \;\;\;\;\left(\left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.527041698806414\right) + y \cdot \frac{t}{z \cdot z}\right) + x\\ \mathbf{elif}\;z \le 4.8590408174333496 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{y}{\frac{z \cdot \left(11.9400905721 + \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right) \cdot z\right) + 0.607771387771}{b + \left(z \cdot \left(\left(3.13060547623 \cdot z + 11.1667541262\right) \cdot z + t\right) + a\right) \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.527041698806414\right) + y \cdot \frac{t}{z \cdot z}\right) + x\\ \end{array}\]
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}
↓
\begin{array}{l}
\mathbf{if}\;z \le -3.9856954798303585 \cdot 10^{+39}:\\
\;\;\;\;\left(\left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.527041698806414\right) + y \cdot \frac{t}{z \cdot z}\right) + x\\

\mathbf{elif}\;z \le 4.8590408174333496 \cdot 10^{+55}:\\
\;\;\;\;x + \frac{y}{\frac{z \cdot \left(11.9400905721 + \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right) \cdot z\right) + 0.607771387771}{b + \left(z \cdot \left(\left(3.13060547623 \cdot z + 11.1667541262\right) \cdot z + t\right) + a\right) \cdot z}}\\

\mathbf{else}:\\
\;\;\;\;\left(\left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.527041698806414\right) + y \cdot \frac{t}{z \cdot z}\right) + x\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r21421504 = x;
        double r21421505 = y;
        double r21421506 = z;
        double r21421507 = 3.13060547623;
        double r21421508 = r21421506 * r21421507;
        double r21421509 = 11.1667541262;
        double r21421510 = r21421508 + r21421509;
        double r21421511 = r21421510 * r21421506;
        double r21421512 = t;
        double r21421513 = r21421511 + r21421512;
        double r21421514 = r21421513 * r21421506;
        double r21421515 = a;
        double r21421516 = r21421514 + r21421515;
        double r21421517 = r21421516 * r21421506;
        double r21421518 = b;
        double r21421519 = r21421517 + r21421518;
        double r21421520 = r21421505 * r21421519;
        double r21421521 = 15.234687407;
        double r21421522 = r21421506 + r21421521;
        double r21421523 = r21421522 * r21421506;
        double r21421524 = 31.4690115749;
        double r21421525 = r21421523 + r21421524;
        double r21421526 = r21421525 * r21421506;
        double r21421527 = 11.9400905721;
        double r21421528 = r21421526 + r21421527;
        double r21421529 = r21421528 * r21421506;
        double r21421530 = 0.607771387771;
        double r21421531 = r21421529 + r21421530;
        double r21421532 = r21421520 / r21421531;
        double r21421533 = r21421504 + r21421532;
        return r21421533;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r21421534 = z;
        double r21421535 = -3.9856954798303585e+39;
        bool r21421536 = r21421534 <= r21421535;
        double r21421537 = y;
        double r21421538 = 3.13060547623;
        double r21421539 = r21421537 * r21421538;
        double r21421540 = r21421537 / r21421534;
        double r21421541 = 36.527041698806414;
        double r21421542 = r21421540 * r21421541;
        double r21421543 = r21421539 - r21421542;
        double r21421544 = t;
        double r21421545 = r21421534 * r21421534;
        double r21421546 = r21421544 / r21421545;
        double r21421547 = r21421537 * r21421546;
        double r21421548 = r21421543 + r21421547;
        double r21421549 = x;
        double r21421550 = r21421548 + r21421549;
        double r21421551 = 4.8590408174333496e+55;
        bool r21421552 = r21421534 <= r21421551;
        double r21421553 = 11.9400905721;
        double r21421554 = 31.4690115749;
        double r21421555 = 15.234687407;
        double r21421556 = r21421534 + r21421555;
        double r21421557 = r21421534 * r21421556;
        double r21421558 = r21421554 + r21421557;
        double r21421559 = r21421558 * r21421534;
        double r21421560 = r21421553 + r21421559;
        double r21421561 = r21421534 * r21421560;
        double r21421562 = 0.607771387771;
        double r21421563 = r21421561 + r21421562;
        double r21421564 = b;
        double r21421565 = r21421538 * r21421534;
        double r21421566 = 11.1667541262;
        double r21421567 = r21421565 + r21421566;
        double r21421568 = r21421567 * r21421534;
        double r21421569 = r21421568 + r21421544;
        double r21421570 = r21421534 * r21421569;
        double r21421571 = a;
        double r21421572 = r21421570 + r21421571;
        double r21421573 = r21421572 * r21421534;
        double r21421574 = r21421564 + r21421573;
        double r21421575 = r21421563 / r21421574;
        double r21421576 = r21421537 / r21421575;
        double r21421577 = r21421549 + r21421576;
        double r21421578 = r21421552 ? r21421577 : r21421550;
        double r21421579 = r21421536 ? r21421550 : r21421578;
        return r21421579;
}

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

Original28.8
Target1.0
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.9856954798303585e+39 or 4.8590408174333496e+55 < z

    1. Initial program 58.9

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
    2. Using strategy rm

    3. Applied associate-/l*56.8

      \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\]

    4. Taylor expanded around inf 8.3

      \[\leadsto x + \color{blue}{\left(\left(\frac{t \cdot y}{{z}^{2}} + 3.13060547623 \cdot y\right) - 36.527041698806414 \cdot \frac{y}{z}\right)}\]

    5. Simplified1.3

      \[\leadsto x + \color{blue}{\left(\left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.527041698806414\right) + \frac{t}{z \cdot z} \cdot y\right)}\]

    if -3.9856954798303585e+39 < z < 4.8590408174333496e+55

    1. Initial program 2.2

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
    2. Using strategy rm

    3. Applied associate-/l*0.9

      \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.9856954798303585 \cdot 10^{+39}:\\ \;\;\;\;\left(\left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.527041698806414\right) + y \cdot \frac{t}{z \cdot z}\right) + x\\ \mathbf{elif}\;z \le 4.8590408174333496 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{y}{\frac{z \cdot \left(11.9400905721 + \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right) \cdot z\right) + 0.607771387771}{b + \left(z \cdot \left(\left(3.13060547623 \cdot z + 11.1667541262\right) \cdot z + t\right) + a\right) \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot 3.13060547623 - \frac{y}{z} \cdot 36.527041698806414\right) + y \cdot \frac{t}{z \cdot z}\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"

  :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))))