\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1.4705226423686669 \cdot 10^{23} \lor \neg \left(z \le 6.3289074280517147 \cdot 10^{31}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)} + x\\ \end{array}\]

x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}

↓

\begin{array}{l}
\mathbf{if}\;z \le -1.4705226423686669 \cdot 10^{23} \lor \neg \left(z \le 6.3289074280517147 \cdot 10^{31}\right):\\
\;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\

\mathbf{else}:\\
\;\;\;\;\frac{y \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)} + x\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r335889 = x;
        double r335890 = y;
        double r335891 = z;
        double r335892 = 3.13060547623;
        double r335893 = r335891 * r335892;
        double r335894 = 11.1667541262;
        double r335895 = r335893 + r335894;
        double r335896 = r335895 * r335891;
        double r335897 = t;
        double r335898 = r335896 + r335897;
        double r335899 = r335898 * r335891;
        double r335900 = a;
        double r335901 = r335899 + r335900;
        double r335902 = r335901 * r335891;
        double r335903 = b;
        double r335904 = r335902 + r335903;
        double r335905 = r335890 * r335904;
        double r335906 = 15.234687407;
        double r335907 = r335891 + r335906;
        double r335908 = r335907 * r335891;
        double r335909 = 31.4690115749;
        double r335910 = r335908 + r335909;
        double r335911 = r335910 * r335891;
        double r335912 = 11.9400905721;
        double r335913 = r335911 + r335912;
        double r335914 = r335913 * r335891;
        double r335915 = 0.607771387771;
        double r335916 = r335914 + r335915;
        double r335917 = r335905 / r335916;
        double r335918 = r335889 + r335917;
        return r335918;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r335919 = z;
        double r335920 = -1.470522642368667e+23;
        bool r335921 = r335919 <= r335920;
        double r335922 = 6.328907428051715e+31;
        bool r335923 = r335919 <= r335922;
        double r335924 = !r335923;
        bool r335925 = r335921 || r335924;
        double r335926 = y;
        double r335927 = 3.13060547623;
        double r335928 = t;
        double r335929 = 2.0;
        double r335930 = pow(r335919, r335929);
        double r335931 = r335928 / r335930;
        double r335932 = r335927 + r335931;
        double r335933 = x;
        double r335934 = fma(r335926, r335932, r335933);
        double r335935 = 11.1667541262;
        double r335936 = fma(r335919, r335927, r335935);
        double r335937 = fma(r335936, r335919, r335928);
        double r335938 = a;
        double r335939 = fma(r335937, r335919, r335938);
        double r335940 = b;
        double r335941 = fma(r335939, r335919, r335940);
        double r335942 = r335926 * r335941;
        double r335943 = 15.234687407;
        double r335944 = r335919 + r335943;
        double r335945 = 31.4690115749;
        double r335946 = fma(r335944, r335919, r335945);
        double r335947 = 11.9400905721;
        double r335948 = fma(r335946, r335919, r335947);
        double r335949 = 0.607771387771;
        double r335950 = fma(r335948, r335919, r335949);
        double r335951 = r335942 / r335950;
        double r335952 = r335951 + r335933;
        double r335953 = r335925 ? r335934 : r335952;
        return r335953;
}

Original	29.9
Target	0.9
Herbie	1.4

Derivation

Split input into 2 regimes
if z < -1.470522642368667e+23 or 6.328907428051715e+31 < z
1. Initial program 58.8
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified56.6
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Taylor expanded around inf 9.2
  \[\leadsto \color{blue}{x + \left(\frac{t \cdot y}{{z}^{2}} + 3.13060547622999996 \cdot y\right)}\]
4. Simplified1.8
  \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)}\]
if -1.470522642368667e+23 < z < 6.328907428051715e+31
1. Initial program 1.0
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified0.6
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Using strategy rm
4. Applied fma-udef0.6
  \[\leadsto \mathsf{fma}\left(\frac{y}{\color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right) \cdot z + 0.60777138777100004}}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\]
5. Using strategy rm
6. Applied fma-udef0.6
  \[\leadsto \color{blue}{\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right) \cdot z + 0.60777138777100004} \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right) + x}\]
7. Simplified1.0
  \[\leadsto \color{blue}{\frac{y \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}} + x\]
Recombined 2 regimes into one program.
Final simplification1.4
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.4705226423686669 \cdot 10^{23} \lor \neg \left(z \le 6.3289074280517147 \cdot 10^{31}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)} + x\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(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 -6.499344996252632e+53) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1))) (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)))))

  (+ 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))))

Error

Target

Derivation

`if z < -1.470522642368667e+23 or 6.328907428051715e+31 < z`

`if -1.470522642368667e+23 < z < 6.328907428051715e+31`

Reproduce