Average Error: 30.0 → 4.9
Time: 11.4s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.983991909224869626959693820538238066719 \cdot 10^{68} \lor \neg \left(z \le 26781923308.5818939208984375\right):\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.52704169880641416057187598198652267456 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\left(\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227\right) \cdot \frac{1}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]
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 -6.983991909224869626959693820538238066719 \cdot 10^{68} \lor \neg \left(z \le 26781923308.5818939208984375\right):\\
\;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.52704169880641416057187598198652267456 \cdot \frac{y}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{\left(\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227\right) \cdot \frac{1}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r320938 = x;
        double r320939 = y;
        double r320940 = z;
        double r320941 = 3.13060547623;
        double r320942 = r320940 * r320941;
        double r320943 = 11.1667541262;
        double r320944 = r320942 + r320943;
        double r320945 = r320944 * r320940;
        double r320946 = t;
        double r320947 = r320945 + r320946;
        double r320948 = r320947 * r320940;
        double r320949 = a;
        double r320950 = r320948 + r320949;
        double r320951 = r320950 * r320940;
        double r320952 = b;
        double r320953 = r320951 + r320952;
        double r320954 = r320939 * r320953;
        double r320955 = 15.234687407;
        double r320956 = r320940 + r320955;
        double r320957 = r320956 * r320940;
        double r320958 = 31.4690115749;
        double r320959 = r320957 + r320958;
        double r320960 = r320959 * r320940;
        double r320961 = 11.9400905721;
        double r320962 = r320960 + r320961;
        double r320963 = r320962 * r320940;
        double r320964 = 0.607771387771;
        double r320965 = r320963 + r320964;
        double r320966 = r320954 / r320965;
        double r320967 = r320938 + r320966;
        return r320967;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r320968 = z;
        double r320969 = -6.98399190922487e+68;
        bool r320970 = r320968 <= r320969;
        double r320971 = 26781923308.581894;
        bool r320972 = r320968 <= r320971;
        double r320973 = !r320972;
        bool r320974 = r320970 || r320973;
        double r320975 = x;
        double r320976 = 3.13060547623;
        double r320977 = y;
        double r320978 = r320976 * r320977;
        double r320979 = t;
        double r320980 = r320979 * r320977;
        double r320981 = 2.0;
        double r320982 = pow(r320968, r320981);
        double r320983 = r320980 / r320982;
        double r320984 = r320978 + r320983;
        double r320985 = 36.527041698806414;
        double r320986 = r320977 / r320968;
        double r320987 = r320985 * r320986;
        double r320988 = r320984 - r320987;
        double r320989 = r320975 + r320988;
        double r320990 = 15.234687407;
        double r320991 = r320968 + r320990;
        double r320992 = r320991 * r320968;
        double r320993 = 31.4690115749;
        double r320994 = r320992 + r320993;
        double r320995 = r320994 * r320968;
        double r320996 = 11.9400905721;
        double r320997 = r320995 + r320996;
        double r320998 = r320997 * r320968;
        double r320999 = 0.607771387771;
        double r321000 = r320998 + r320999;
        double r321001 = 1.0;
        double r321002 = r320968 * r320976;
        double r321003 = 11.1667541262;
        double r321004 = r321002 + r321003;
        double r321005 = r321004 * r320968;
        double r321006 = r321005 + r320979;
        double r321007 = r321006 * r320968;
        double r321008 = a;
        double r321009 = r321007 + r321008;
        double r321010 = r321009 * r320968;
        double r321011 = b;
        double r321012 = r321010 + r321011;
        double r321013 = r321001 / r321012;
        double r321014 = r321000 * r321013;
        double r321015 = r320977 / r321014;
        double r321016 = r320975 + r321015;
        double r321017 = r320974 ? r320989 : r321016;
        return r321017;
}

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

Original30.0
Target1.0
Herbie4.9
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252631754123144978817242590467 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914286795694558389038333165002 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 - \frac{36.52704169880641416057187598198652267456}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -6.98399190922487e+68 or 26781923308.581894 < z

    1. Initial program 59.7

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

    2. Taylor expanded around inf 9.0

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

    if -6.98399190922487e+68 < z < 26781923308.581894

    1. Initial program 2.3

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

    3. Applied associate-/l*1.0

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

    5. Applied div-inv1.0

      \[\leadsto x + \frac{y}{\color{blue}{\left(\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227\right) \cdot \frac{1}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification4.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.983991909224869626959693820538238066719 \cdot 10^{68} \lor \neg \left(z \le 26781923308.5818939208984375\right):\\ \;\;\;\;x + \left(\left(3.130605476229999961645944495103321969509 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.52704169880641416057187598198652267456 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\left(\left(\left(\left(z + 15.2346874069999991263557603815570473671\right) \cdot z + 31.46901157490000144889563671313226222992\right) \cdot z + 11.94009057210000079862766142468899488449\right) \cdot z + 0.6077713877710000378584709324059076607227\right) \cdot \frac{1}{\left(\left(\left(z \cdot 3.130605476229999961645944495103321969509 + 11.16675412620000074070958362426608800888\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 
(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 -6.4993449962526318e53) (+ x (* (+ (- 3.13060547622999996 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1))) (if (< z 7.0669654369142868e59) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15.234687406999999) z) 31.469011574900001) z) 11.940090572100001) z) 0.60777138777100004) (+ (* (+ (* (+ (* (+ (* z 3.13060547622999996) 11.166754126200001) z) t) z) a) z) b)))) (+ x (* (+ (- 3.13060547622999996 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1)))))

  (+ x (/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547622999996) 11.166754126200001) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687406999999) z) 31.469011574900001) z) 11.940090572100001) z) 0.60777138777100004))))