\frac{\left(x - 2.0\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922228 + 78.6994924154\right) \cdot x + 137.519416416\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514\right) \cdot x + 263.505074721\right) \cdot x + 313.399215894\right) \cdot x + 47.066876606}\begin{array}{l}
\mathbf{if}\;x \le -6.460947809195672 \cdot 10^{+23}:\\
\;\;\;\;\mathsf{fma}\left(x, 4.16438922228, \frac{y}{x \cdot x} - 110.1139242984811\right)\\
\mathbf{elif}\;x \le 9.455030365015399 \cdot 10^{+42}:\\
\;\;\;\;\frac{x - 2.0}{\sqrt[3]{\sqrt{\sqrt{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \cdot \left(\sqrt{\sqrt{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \cdot \sqrt{\sqrt{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}\right)}} \cdot \left(\frac{1}{\sqrt{\sqrt{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}}} \cdot \left(\frac{1}{\sqrt{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(43.3400022514 + x, x, 263.505074721\right), x, 313.399215894\right), x, 47.066876606\right)}} \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, \mathsf{fma}\left(x, 4.16438922228, 78.6994924154\right), 137.519416416\right), y\right), z\right)\right)\right)\\
\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(x, 4.16438922228, \frac{y}{x \cdot x} - 110.1139242984811\right)\\
\end{array}double f(double x, double y, double z) {
double r18897848 = x;
double r18897849 = 2.0;
double r18897850 = r18897848 - r18897849;
double r18897851 = 4.16438922228;
double r18897852 = r18897848 * r18897851;
double r18897853 = 78.6994924154;
double r18897854 = r18897852 + r18897853;
double r18897855 = r18897854 * r18897848;
double r18897856 = 137.519416416;
double r18897857 = r18897855 + r18897856;
double r18897858 = r18897857 * r18897848;
double r18897859 = y;
double r18897860 = r18897858 + r18897859;
double r18897861 = r18897860 * r18897848;
double r18897862 = z;
double r18897863 = r18897861 + r18897862;
double r18897864 = r18897850 * r18897863;
double r18897865 = 43.3400022514;
double r18897866 = r18897848 + r18897865;
double r18897867 = r18897866 * r18897848;
double r18897868 = 263.505074721;
double r18897869 = r18897867 + r18897868;
double r18897870 = r18897869 * r18897848;
double r18897871 = 313.399215894;
double r18897872 = r18897870 + r18897871;
double r18897873 = r18897872 * r18897848;
double r18897874 = 47.066876606;
double r18897875 = r18897873 + r18897874;
double r18897876 = r18897864 / r18897875;
return r18897876;
}
double f(double x, double y, double z) {
double r18897877 = x;
double r18897878 = -6.460947809195672e+23;
bool r18897879 = r18897877 <= r18897878;
double r18897880 = 4.16438922228;
double r18897881 = y;
double r18897882 = r18897877 * r18897877;
double r18897883 = r18897881 / r18897882;
double r18897884 = 110.1139242984811;
double r18897885 = r18897883 - r18897884;
double r18897886 = fma(r18897877, r18897880, r18897885);
double r18897887 = 9.455030365015399e+42;
bool r18897888 = r18897877 <= r18897887;
double r18897889 = 2.0;
double r18897890 = r18897877 - r18897889;
double r18897891 = 43.3400022514;
double r18897892 = r18897891 + r18897877;
double r18897893 = 263.505074721;
double r18897894 = fma(r18897892, r18897877, r18897893);
double r18897895 = 313.399215894;
double r18897896 = fma(r18897894, r18897877, r18897895);
double r18897897 = 47.066876606;
double r18897898 = fma(r18897896, r18897877, r18897897);
double r18897899 = sqrt(r18897898);
double r18897900 = sqrt(r18897899);
double r18897901 = r18897900 * r18897900;
double r18897902 = r18897900 * r18897901;
double r18897903 = cbrt(r18897902);
double r18897904 = r18897890 / r18897903;
double r18897905 = 1.0;
double r18897906 = r18897905 / r18897900;
double r18897907 = r18897905 / r18897899;
double r18897908 = 78.6994924154;
double r18897909 = fma(r18897877, r18897880, r18897908);
double r18897910 = 137.519416416;
double r18897911 = fma(r18897877, r18897909, r18897910);
double r18897912 = fma(r18897877, r18897911, r18897881);
double r18897913 = z;
double r18897914 = fma(r18897877, r18897912, r18897913);
double r18897915 = r18897907 * r18897914;
double r18897916 = r18897906 * r18897915;
double r18897917 = r18897904 * r18897916;
double r18897918 = r18897888 ? r18897917 : r18897886;
double r18897919 = r18897879 ? r18897886 : r18897918;
return r18897919;
}




Bits error versus x




Bits error versus y




Bits error versus z
| Original | 25.4 |
|---|---|
| Target | 0.4 |
| Herbie | 0.9 |
if x < -6.460947809195672e+23 or 9.455030365015399e+42 < x Initial program 57.1
Simplified53.0
Taylor expanded around inf 1.2
Simplified1.2
if -6.460947809195672e+23 < x < 9.455030365015399e+42Initial program 0.6
Simplified0.6
rmApplied add-sqr-sqrt0.7
Applied *-un-lft-identity0.7
Applied times-frac0.8
Applied associate-*r*0.7
rmApplied add-sqr-sqrt0.7
Applied sqrt-prod1.0
Applied *-un-lft-identity1.0
Applied times-frac0.7
Applied associate-*r*0.7
rmApplied add-cbrt-cube0.7
Final simplification0.9
herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y z)
:name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
:herbie-target
(if (< x -3.326128725870005e+62) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811) (if (< x 9.429991714554673e+55) (* (/ (- x 2.0) 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 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))