Average Error: 26.5 → 0.9
Time: 8.7s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -1.36934200842090372 \cdot 10^{41}:\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{elif}\;x \le 5.12463244014639382 \cdot 10^{25}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\frac{\left(\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x\right) \cdot \left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x\right) - 313.399215894 \cdot 313.399215894\right) \cdot x}{\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x - 313.399215894} + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)\\ \end{array}\]
\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}
↓
\begin{array}{l}
\mathbf{if}\;x \le -1.36934200842090372 \cdot 10^{41}:\\
\;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\

\mathbf{elif}\;x \le 5.12463244014639382 \cdot 10^{25}:\\
\;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\frac{\left(\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x\right) \cdot \left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x\right) - 313.399215894 \cdot 313.399215894\right) \cdot x}{\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x - 313.399215894} + 47.066876606000001}\\

\mathbf{else}:\\
\;\;\;\;\left(x - 2\right) \cdot \left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)\\

\end{array}
double f(double x, double y, double z) {
        double r474864 = x;
        double r474865 = 2.0;
        double r474866 = r474864 - r474865;
        double r474867 = 4.16438922228;
        double r474868 = r474864 * r474867;
        double r474869 = 78.6994924154;
        double r474870 = r474868 + r474869;
        double r474871 = r474870 * r474864;
        double r474872 = 137.519416416;
        double r474873 = r474871 + r474872;
        double r474874 = r474873 * r474864;
        double r474875 = y;
        double r474876 = r474874 + r474875;
        double r474877 = r474876 * r474864;
        double r474878 = z;
        double r474879 = r474877 + r474878;
        double r474880 = r474866 * r474879;
        double r474881 = 43.3400022514;
        double r474882 = r474864 + r474881;
        double r474883 = r474882 * r474864;
        double r474884 = 263.505074721;
        double r474885 = r474883 + r474884;
        double r474886 = r474885 * r474864;
        double r474887 = 313.399215894;
        double r474888 = r474886 + r474887;
        double r474889 = r474888 * r474864;
        double r474890 = 47.066876606;
        double r474891 = r474889 + r474890;
        double r474892 = r474880 / r474891;
        return r474892;
}
↓
double f(double x, double y, double z) {
        double r474893 = x;
        double r474894 = -1.3693420084209037e+41;
        bool r474895 = r474893 <= r474894;
        double r474896 = y;
        double r474897 = 2.0;
        double r474898 = pow(r474893, r474897);
        double r474899 = r474896 / r474898;
        double r474900 = 4.16438922228;
        double r474901 = r474900 * r474893;
        double r474902 = r474899 + r474901;
        double r474903 = 110.1139242984811;
        double r474904 = r474902 - r474903;
        double r474905 = 5.124632440146394e+25;
        bool r474906 = r474893 <= r474905;
        double r474907 = 2.0;
        double r474908 = r474893 - r474907;
        double r474909 = r474893 * r474900;
        double r474910 = 78.6994924154;
        double r474911 = r474909 + r474910;
        double r474912 = r474911 * r474893;
        double r474913 = 137.519416416;
        double r474914 = r474912 + r474913;
        double r474915 = r474914 * r474893;
        double r474916 = r474915 + r474896;
        double r474917 = r474916 * r474893;
        double r474918 = z;
        double r474919 = r474917 + r474918;
        double r474920 = r474908 * r474919;
        double r474921 = 43.3400022514;
        double r474922 = r474893 + r474921;
        double r474923 = r474922 * r474893;
        double r474924 = 263.505074721;
        double r474925 = r474923 + r474924;
        double r474926 = r474925 * r474893;
        double r474927 = r474926 * r474926;
        double r474928 = 313.399215894;
        double r474929 = r474928 * r474928;
        double r474930 = r474927 - r474929;
        double r474931 = r474930 * r474893;
        double r474932 = r474926 - r474928;
        double r474933 = r474931 / r474932;
        double r474934 = 47.066876606;
        double r474935 = r474933 + r474934;
        double r474936 = r474920 / r474935;
        double r474937 = 3.0;
        double r474938 = pow(r474893, r474937);
        double r474939 = r474896 / r474938;
        double r474940 = r474939 + r474900;
        double r474941 = 101.7851458539211;
        double r474942 = 1.0;
        double r474943 = r474942 / r474893;
        double r474944 = r474941 * r474943;
        double r474945 = r474940 - r474944;
        double r474946 = r474908 * r474945;
        double r474947 = r474906 ? r474936 : r474946;
        double r474948 = r474895 ? r474904 : r474947;
        return r474948;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original26.5
Target0.5
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;x \lt -3.3261287258700048 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{elif}\;x \lt 9.4299917145546727 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.50507472100003 \cdot x + \left(43.3400022514000014 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.399215894\right) \cdot x + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -1.3693420084209037e+41

    1. Initial program 60.7

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

    2. Taylor expanded around inf 0.7

      \[\leadsto \color{blue}{\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109}\]

    if -1.3693420084209037e+41 < x < 5.124632440146394e+25

    1. Initial program 0.7

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
    2. Using strategy rm

    3. Applied flip-+0.7

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{\frac{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x\right) \cdot \left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x\right) - 313.399215894 \cdot 313.399215894}{\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x - 313.399215894}} \cdot x + 47.066876606000001}\]

    4. Applied associate-*l/0.7

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{\frac{\left(\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x\right) \cdot \left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x\right) - 313.399215894 \cdot 313.399215894\right) \cdot x}{\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x - 313.399215894}} + 47.066876606000001}\]

    if 5.124632440146394e+25 < x

    1. Initial program 57.7

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity57.7

      \[\leadsto \frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001\right)}}\]

    4. Applied times-frac53.9

      \[\leadsto \color{blue}{\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}}\]

    5. Simplified53.9

      \[\leadsto \color{blue}{\left(x - 2\right)} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]

    6. Taylor expanded around inf 1.5

      \[\leadsto \left(x - 2\right) \cdot \color{blue}{\left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.36934200842090372 \cdot 10^{41}:\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{elif}\;x \le 5.12463244014639382 \cdot 10^{25}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\frac{\left(\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x\right) \cdot \left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x\right) - 313.399215894 \cdot 313.399215894\right) \cdot x}{\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x - 313.399215894} + 47.066876606000001}\\ \mathbf{else}:\\ \;\;\;\;\left(x - 2\right) \cdot \left(\left(\frac{y}{{x}^{3}} + 4.16438922227999964\right) - 101.785145853921094 \cdot \frac{1}{x}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020056 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< x -3.326128725870005e+62) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811) (if (< x 9.429991714554673e+55) (* (/ (- x 2) 1) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x)))) 313.399215894) x) 47.066876606))) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))

  (/ (* (- x 2) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))