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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -4110398356701687.5 \lor \neg \left(x \le 58699571.16996288\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(137.51941641600001 \cdot {x}^{2} + \left(78.6994924154000017 \cdot {x}^{3} + x \cdot y\right)\right) + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]

\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 -4110398356701687.5 \lor \neg \left(x \le 58699571.16996288\right):\\
\;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(137.51941641600001 \cdot {x}^{2} + \left(78.6994924154000017 \cdot {x}^{3} + x \cdot y\right)\right) + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\

\end{array}

double f(double x, double y, double z) {
        double r422910 = x;
        double r422911 = 2.0;
        double r422912 = r422910 - r422911;
        double r422913 = 4.16438922228;
        double r422914 = r422910 * r422913;
        double r422915 = 78.6994924154;
        double r422916 = r422914 + r422915;
        double r422917 = r422916 * r422910;
        double r422918 = 137.519416416;
        double r422919 = r422917 + r422918;
        double r422920 = r422919 * r422910;
        double r422921 = y;
        double r422922 = r422920 + r422921;
        double r422923 = r422922 * r422910;
        double r422924 = z;
        double r422925 = r422923 + r422924;
        double r422926 = r422912 * r422925;
        double r422927 = 43.3400022514;
        double r422928 = r422910 + r422927;
        double r422929 = r422928 * r422910;
        double r422930 = 263.505074721;
        double r422931 = r422929 + r422930;
        double r422932 = r422931 * r422910;
        double r422933 = 313.399215894;
        double r422934 = r422932 + r422933;
        double r422935 = r422934 * r422910;
        double r422936 = 47.066876606;
        double r422937 = r422935 + r422936;
        double r422938 = r422926 / r422937;
        return r422938;
}

↓

double f(double x, double y, double z) {
        double r422939 = x;
        double r422940 = -4110398356701687.5;
        bool r422941 = r422939 <= r422940;
        double r422942 = 58699571.16996288;
        bool r422943 = r422939 <= r422942;
        double r422944 = !r422943;
        bool r422945 = r422941 || r422944;
        double r422946 = y;
        double r422947 = 2.0;
        double r422948 = pow(r422939, r422947);
        double r422949 = r422946 / r422948;
        double r422950 = 4.16438922228;
        double r422951 = r422950 * r422939;
        double r422952 = r422949 + r422951;
        double r422953 = 110.1139242984811;
        double r422954 = r422952 - r422953;
        double r422955 = 2.0;
        double r422956 = r422939 - r422955;
        double r422957 = 137.519416416;
        double r422958 = r422957 * r422948;
        double r422959 = 78.6994924154;
        double r422960 = 3.0;
        double r422961 = pow(r422939, r422960);
        double r422962 = r422959 * r422961;
        double r422963 = r422939 * r422946;
        double r422964 = r422962 + r422963;
        double r422965 = r422958 + r422964;
        double r422966 = z;
        double r422967 = r422965 + r422966;
        double r422968 = r422956 * r422967;
        double r422969 = 43.3400022514;
        double r422970 = r422939 + r422969;
        double r422971 = r422970 * r422939;
        double r422972 = 263.505074721;
        double r422973 = r422971 + r422972;
        double r422974 = r422973 * r422939;
        double r422975 = 313.399215894;
        double r422976 = r422974 + r422975;
        double r422977 = r422976 * r422939;
        double r422978 = 47.066876606;
        double r422979 = r422977 + r422978;
        double r422980 = r422968 / r422979;
        double r422981 = r422945 ? r422954 : r422980;
        return r422981;
}

Original	26.6
Target	0.5
Herbie	1.8

Derivation

Split input into 2 regimes
if x < -4110398356701687.5 or 58699571.16996288 < x
1. Initial program 54.7
  \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
2. Taylor expanded around inf 2.6
  \[\leadsto \color{blue}{\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109}\]
if -4110398356701687.5 < x < 58699571.16996288
1. Initial program 0.2
  \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999964 + 78.6994924154000017\right) \cdot x + 137.51941641600001\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
2. Taylor expanded around 0 1.0
  \[\leadsto \frac{\left(x - 2\right) \cdot \left(\color{blue}{\left(137.51941641600001 \cdot {x}^{2} + \left(78.6994924154000017 \cdot {x}^{3} + x \cdot y\right)\right)} + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\]
Recombined 2 regimes into one program.
Final simplification1.8
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4110398356701687.5 \lor \neg \left(x \le 58699571.16996288\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999964 \cdot x\right) - 110.11392429848109\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(137.51941641600001 \cdot {x}^{2} + \left(78.6994924154000017 \cdot {x}^{3} + x \cdot y\right)\right) + z\right)}{\left(\left(\left(x + 43.3400022514000014\right) \cdot x + 263.50507472100003\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606000001}\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 
(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)))

Error

Try it out

Target

Derivation

`if x < -4110398356701687.5 or 58699571.16996288 < x`

`if -4110398356701687.5 < x < 58699571.16996288`

Reproduce

In
Out