Average Error: 29.0 → 1.1
Time: 6.4s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3951683805489442300 \lor \neg \left(z \le 3.95145515718158141 \cdot 10^{36}\right):\\ \;\;\;\;x + y \cdot \left(\left(\frac{t}{{z}^{2}} + 3.13060547622999996\right) - 36.527041698806414 \cdot \frac{1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]
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 -3951683805489442300 \lor \neg \left(z \le 3.95145515718158141 \cdot 10^{36}\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 r359990 = x;
        double r359991 = y;
        double r359992 = z;
        double r359993 = 3.13060547623;
        double r359994 = r359992 * r359993;
        double r359995 = 11.1667541262;
        double r359996 = r359994 + r359995;
        double r359997 = r359996 * r359992;
        double r359998 = t;
        double r359999 = r359997 + r359998;
        double r360000 = r359999 * r359992;
        double r360001 = a;
        double r360002 = r360000 + r360001;
        double r360003 = r360002 * r359992;
        double r360004 = b;
        double r360005 = r360003 + r360004;
        double r360006 = r359991 * r360005;
        double r360007 = 15.234687407;
        double r360008 = r359992 + r360007;
        double r360009 = r360008 * r359992;
        double r360010 = 31.4690115749;
        double r360011 = r360009 + r360010;
        double r360012 = r360011 * r359992;
        double r360013 = 11.9400905721;
        double r360014 = r360012 + r360013;
        double r360015 = r360014 * r359992;
        double r360016 = 0.607771387771;
        double r360017 = r360015 + r360016;
        double r360018 = r360006 / r360017;
        double r360019 = r359990 + r360018;
        return r360019;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r360020 = z;
        double r360021 = -3.9516838054894423e+18;
        bool r360022 = r360020 <= r360021;
        double r360023 = 3.9514551571815814e+36;
        bool r360024 = r360020 <= r360023;
        double r360025 = !r360024;
        bool r360026 = r360022 || r360025;
        double r360027 = x;
        double r360028 = y;
        double r360029 = t;
        double r360030 = 2.0;
        double r360031 = pow(r360020, r360030);
        double r360032 = r360029 / r360031;
        double r360033 = 3.13060547623;
        double r360034 = r360032 + r360033;
        double r360035 = 36.527041698806414;
        double r360036 = 1.0;
        double r360037 = r360036 / r360020;
        double r360038 = r360035 * r360037;
        double r360039 = r360034 - r360038;
        double r360040 = r360028 * r360039;
        double r360041 = r360027 + r360040;
        double r360042 = r360020 * r360033;
        double r360043 = 11.1667541262;
        double r360044 = r360042 + r360043;
        double r360045 = r360044 * r360020;
        double r360046 = r360045 + r360029;
        double r360047 = r360046 * r360020;
        double r360048 = a;
        double r360049 = r360047 + r360048;
        double r360050 = r360049 * r360020;
        double r360051 = b;
        double r360052 = r360050 + r360051;
        double r360053 = 15.234687407;
        double r360054 = r360020 + r360053;
        double r360055 = r360054 * r360020;
        double r360056 = 31.4690115749;
        double r360057 = r360055 + r360056;
        double r360058 = r360057 * r360020;
        double r360059 = 11.9400905721;
        double r360060 = r360058 + r360059;
        double r360061 = r360060 * r360020;
        double r360062 = 0.607771387771;
        double r360063 = r360061 + r360062;
        double r360064 = r360052 / r360063;
        double r360065 = r360028 * r360064;
        double r360066 = r360027 + r360065;
        double r360067 = r360026 ? r360041 : r360066;
        return r360067;
}

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

Derivation

  1. Split input into 2 regimes

  2. if z < -3.9516838054894423e+18 or 3.9514551571815814e+36 < z

    1. Initial program 58.5

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

    3. Applied *-un-lft-identity58.5

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

    4. Applied times-frac56.1

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

    5. Simplified56.1

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

    6. Taylor expanded around inf 1.8

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

    if -3.9516838054894423e+18 < z < 3.9514551571815814e+36

    1. Initial program 1.1

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

    3. Applied *-un-lft-identity1.1

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

    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 simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3951683805489442300 \lor \neg \left(z \le 3.95145515718158141 \cdot 10^{36}\right):\\ \;\;\;\;x + y \cdot \left(\left(\frac{t}{{z}^{2}} + 3.13060547622999996\right) - 36.527041698806414 \cdot \frac{1}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\\ \end{array}\]

Reproduce

herbie shell --seed 2020083 
(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))))