Average Error: 29.4 → 1.0
Time: 25.3s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.0909237088750185749096961166589856352 \cdot 10^{50} \lor \neg \left(z \le 31413547445392871784448\right):\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 + \frac{t}{z \cdot z}\right) - \frac{36.52704169880641416057187598198652267456}{z}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(3.130605476229999961645944495103321969509 \cdot z + 11.16675412620000074070958362426608800888\right)\right)\right) + b}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227} \cdot y\\ \end{array}\]
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.0909237088750185749096961166589856352 \cdot 10^{50} \lor \neg \left(z \le 31413547445392871784448\right):\\
\;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 + \frac{t}{z \cdot z}\right) - \frac{36.52704169880641416057187598198652267456}{z}\right) \cdot y\\

\mathbf{else}:\\
\;\;\;\;x + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(3.130605476229999961645944495103321969509 \cdot z + 11.16675412620000074070958362426608800888\right)\right)\right) + b}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227} \cdot y\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r277973 = x;
        double r277974 = y;
        double r277975 = z;
        double r277976 = 3.13060547623;
        double r277977 = r277975 * r277976;
        double r277978 = 11.1667541262;
        double r277979 = r277977 + r277978;
        double r277980 = r277979 * r277975;
        double r277981 = t;
        double r277982 = r277980 + r277981;
        double r277983 = r277982 * r277975;
        double r277984 = a;
        double r277985 = r277983 + r277984;
        double r277986 = r277985 * r277975;
        double r277987 = b;
        double r277988 = r277986 + r277987;
        double r277989 = r277974 * r277988;
        double r277990 = 15.234687407;
        double r277991 = r277975 + r277990;
        double r277992 = r277991 * r277975;
        double r277993 = 31.4690115749;
        double r277994 = r277992 + r277993;
        double r277995 = r277994 * r277975;
        double r277996 = 11.9400905721;
        double r277997 = r277995 + r277996;
        double r277998 = r277997 * r277975;
        double r277999 = 0.607771387771;
        double r278000 = r277998 + r277999;
        double r278001 = r277989 / r278000;
        double r278002 = r277973 + r278001;
        return r278002;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r278003 = z;
        double r278004 = -1.0909237088750186e+50;
        bool r278005 = r278003 <= r278004;
        double r278006 = 3.141354744539287e+22;
        bool r278007 = r278003 <= r278006;
        double r278008 = !r278007;
        bool r278009 = r278005 || r278008;
        double r278010 = x;
        double r278011 = 3.13060547623;
        double r278012 = t;
        double r278013 = r278003 * r278003;
        double r278014 = r278012 / r278013;
        double r278015 = r278011 + r278014;
        double r278016 = 36.527041698806414;
        double r278017 = r278016 / r278003;
        double r278018 = r278015 - r278017;
        double r278019 = y;
        double r278020 = r278018 * r278019;
        double r278021 = r278010 + r278020;
        double r278022 = a;
        double r278023 = r278011 * r278003;
        double r278024 = 11.1667541262;
        double r278025 = r278023 + r278024;
        double r278026 = r278003 * r278025;
        double r278027 = r278012 + r278026;
        double r278028 = r278003 * r278027;
        double r278029 = r278022 + r278028;
        double r278030 = r278003 * r278029;
        double r278031 = b;
        double r278032 = r278030 + r278031;
        double r278033 = 15.234687407;
        double r278034 = r278003 + r278033;
        double r278035 = r278034 * r278003;
        double r278036 = 31.4690115749;
        double r278037 = r278035 + r278036;
        double r278038 = r278037 * r278003;
        double r278039 = 11.9400905721;
        double r278040 = r278038 + r278039;
        double r278041 = r278040 * r278003;
        double r278042 = 0.607771387771;
        double r278043 = r278041 + r278042;
        double r278044 = r278032 / r278043;
        double r278045 = r278044 * r278019;
        double r278046 = r278010 + r278045;
        double r278047 = r278009 ? r278021 : r278046;
        return r278047;
}

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
Target1.0
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252631754123144978817242590467 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914286795694558389038333165002 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.0909237088750186e+50 or 3.141354744539287e+22 < z

    1. Initial program 59.8

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]

    2. Simplified57.5

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(a + z \cdot \left(t + \left(11.16675412620000074070958362426608800888 + z \cdot 3.130605476229999961645944495103321969509\right) \cdot z\right)\right) + b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.2346874069999991263557603815570473671\right) + 31.46901157490000144889563671313226222992\right) + 11.94009057210000079862766142468899488449\right) + 0.6077713877710000378584709324059076607227} \cdot y}\]

    3. Taylor expanded around inf 1.3

      \[\leadsto x + \color{blue}{\left(\left(\frac{t}{{z}^{2}} + 3.130605476229999961645944495103321969509\right) - 36.52704169880641416057187598198652267456 \cdot \frac{1}{z}\right)} \cdot y\]

    4. Simplified1.3

      \[\leadsto x + \color{blue}{\left(\left(\frac{t}{z \cdot z} + 3.130605476229999961645944495103321969509\right) - \frac{36.52704169880641416057187598198652267456}{z}\right)} \cdot y\]

    if -1.0909237088750186e+50 < z < 3.141354744539287e+22

    1. Initial program 1.5

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]

    2. Simplified0.8

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(a + z \cdot \left(t + \left(11.16675412620000074070958362426608800888 + z \cdot 3.130605476229999961645944495103321969509\right) \cdot z\right)\right) + b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.2346874069999991263557603815570473671\right) + 31.46901157490000144889563671313226222992\right) + 11.94009057210000079862766142468899488449\right) + 0.6077713877710000378584709324059076607227} \cdot y}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.0909237088750185749096961166589856352 \cdot 10^{50} \lor \neg \left(z \le 31413547445392871784448\right):\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 + \frac{t}{z \cdot z}\right) - \frac{36.52704169880641416057187598198652267456}{z}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(a + z \cdot \left(t + z \cdot \left(3.130605476229999961645944495103321969509 \cdot z + 11.16675412620000074070958362426608800888\right)\right)\right) + b}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019196 
(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))))