Average Error: 29.5 → 4.4
Time: 28.4s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.75645805889384362 \cdot 10^{37} \lor \neg \left(z \le 2.4817666994432834 \cdot 10^{44}\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]
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 -1.75645805889384362 \cdot 10^{37} \lor \neg \left(z \le 2.4817666994432834 \cdot 10^{44}\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 + 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 r211659 = x;
        double r211660 = y;
        double r211661 = z;
        double r211662 = 3.13060547623;
        double r211663 = r211661 * r211662;
        double r211664 = 11.1667541262;
        double r211665 = r211663 + r211664;
        double r211666 = r211665 * r211661;
        double r211667 = t;
        double r211668 = r211666 + r211667;
        double r211669 = r211668 * r211661;
        double r211670 = a;
        double r211671 = r211669 + r211670;
        double r211672 = r211671 * r211661;
        double r211673 = b;
        double r211674 = r211672 + r211673;
        double r211675 = r211660 * r211674;
        double r211676 = 15.234687407;
        double r211677 = r211661 + r211676;
        double r211678 = r211677 * r211661;
        double r211679 = 31.4690115749;
        double r211680 = r211678 + r211679;
        double r211681 = r211680 * r211661;
        double r211682 = 11.9400905721;
        double r211683 = r211681 + r211682;
        double r211684 = r211683 * r211661;
        double r211685 = 0.607771387771;
        double r211686 = r211684 + r211685;
        double r211687 = r211675 / r211686;
        double r211688 = r211659 + r211687;
        return r211688;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r211689 = z;
        double r211690 = -1.7564580588938436e+37;
        bool r211691 = r211689 <= r211690;
        double r211692 = 2.4817666994432834e+44;
        bool r211693 = r211689 <= r211692;
        double r211694 = !r211693;
        bool r211695 = r211691 || r211694;
        double r211696 = x;
        double r211697 = 3.13060547623;
        double r211698 = y;
        double r211699 = r211697 * r211698;
        double r211700 = t;
        double r211701 = r211700 * r211698;
        double r211702 = 2.0;
        double r211703 = pow(r211689, r211702);
        double r211704 = r211701 / r211703;
        double r211705 = r211699 + r211704;
        double r211706 = 36.527041698806414;
        double r211707 = r211698 / r211689;
        double r211708 = r211706 * r211707;
        double r211709 = r211705 - r211708;
        double r211710 = r211696 + r211709;
        double r211711 = r211689 * r211697;
        double r211712 = 11.1667541262;
        double r211713 = r211711 + r211712;
        double r211714 = r211713 * r211689;
        double r211715 = r211714 + r211700;
        double r211716 = r211715 * r211689;
        double r211717 = a;
        double r211718 = r211716 + r211717;
        double r211719 = r211718 * r211689;
        double r211720 = b;
        double r211721 = r211719 + r211720;
        double r211722 = 15.234687407;
        double r211723 = r211689 + r211722;
        double r211724 = r211723 * r211689;
        double r211725 = 31.4690115749;
        double r211726 = r211724 + r211725;
        double r211727 = r211726 * r211689;
        double r211728 = 11.9400905721;
        double r211729 = r211727 + r211728;
        double r211730 = r211729 * r211689;
        double r211731 = 0.607771387771;
        double r211732 = r211730 + r211731;
        double r211733 = r211721 / r211732;
        double r211734 = r211698 * r211733;
        double r211735 = r211696 + r211734;
        double r211736 = r211695 ? r211710 : r211735;
        return r211736;
}

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

Original29.5
Target1.1
Herbie4.4
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.7564580588938436e+37 or 2.4817666994432834e+44 < z

    1. Initial program 59.8

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

    2. Taylor expanded around inf 8.4

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

    if -1.7564580588938436e+37 < z < 2.4817666994432834e+44

    1. Initial program 1.9

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

    3. Applied *-un-lft-identity1.9

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

    4. Applied times-frac0.7

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

    5. Simplified0.7

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

  4. Final simplification4.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.75645805889384362 \cdot 10^{37} \lor \neg \left(z \le 2.4817666994432834 \cdot 10^{44}\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 
(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 1.0))) (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 1.0)))))

  (+ 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))))