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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -4.78832916976804162 \cdot 10^{29} \lor \neg \left(z \le 2.17040498130427483 \cdot 10^{24}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}} \cdot \frac{1}{\sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

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 -4.78832916976804162 \cdot 10^{29} \lor \neg \left(z \le 2.17040498130427483 \cdot 10^{24}\right):\\
\;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(\frac{y}{\sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}} \cdot \frac{1}{\sqrt[3]{\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)\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r317865 = x;
        double r317866 = y;
        double r317867 = z;
        double r317868 = 3.13060547623;
        double r317869 = r317867 * r317868;
        double r317870 = 11.1667541262;
        double r317871 = r317869 + r317870;
        double r317872 = r317871 * r317867;
        double r317873 = t;
        double r317874 = r317872 + r317873;
        double r317875 = r317874 * r317867;
        double r317876 = a;
        double r317877 = r317875 + r317876;
        double r317878 = r317877 * r317867;
        double r317879 = b;
        double r317880 = r317878 + r317879;
        double r317881 = r317866 * r317880;
        double r317882 = 15.234687407;
        double r317883 = r317867 + r317882;
        double r317884 = r317883 * r317867;
        double r317885 = 31.4690115749;
        double r317886 = r317884 + r317885;
        double r317887 = r317886 * r317867;
        double r317888 = 11.9400905721;
        double r317889 = r317887 + r317888;
        double r317890 = r317889 * r317867;
        double r317891 = 0.607771387771;
        double r317892 = r317890 + r317891;
        double r317893 = r317881 / r317892;
        double r317894 = r317865 + r317893;
        return r317894;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r317895 = z;
        double r317896 = -4.7883291697680416e+29;
        bool r317897 = r317895 <= r317896;
        double r317898 = 2.1704049813042748e+24;
        bool r317899 = r317895 <= r317898;
        double r317900 = !r317899;
        bool r317901 = r317897 || r317900;
        double r317902 = y;
        double r317903 = 3.13060547623;
        double r317904 = t;
        double r317905 = 2.0;
        double r317906 = pow(r317895, r317905);
        double r317907 = r317904 / r317906;
        double r317908 = r317903 + r317907;
        double r317909 = x;
        double r317910 = fma(r317902, r317908, r317909);
        double r317911 = 15.234687407;
        double r317912 = r317895 + r317911;
        double r317913 = 31.4690115749;
        double r317914 = fma(r317912, r317895, r317913);
        double r317915 = 11.9400905721;
        double r317916 = fma(r317914, r317895, r317915);
        double r317917 = 0.607771387771;
        double r317918 = fma(r317916, r317895, r317917);
        double r317919 = cbrt(r317918);
        double r317920 = r317919 * r317919;
        double r317921 = r317902 / r317920;
        double r317922 = 1.0;
        double r317923 = r317922 / r317919;
        double r317924 = r317921 * r317923;
        double r317925 = 11.1667541262;
        double r317926 = fma(r317895, r317903, r317925);
        double r317927 = fma(r317926, r317895, r317904);
        double r317928 = a;
        double r317929 = fma(r317927, r317895, r317928);
        double r317930 = b;
        double r317931 = fma(r317929, r317895, r317930);
        double r317932 = fma(r317924, r317931, r317909);
        double r317933 = r317901 ? r317910 : r317932;
        return r317933;
}

Original	29.1
Target	1.0
Herbie	1.1

Derivation

Split input into 2 regimes
if z < -4.7883291697680416e+29 or 2.1704049813042748e+24 < z
1. Initial program 58.4
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. Simplified56.3
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)}\]
3. Taylor expanded around inf 8.5
  \[\leadsto \color{blue}{x + \left(\frac{t \cdot y}{{z}^{2}} + 3.13060547622999996 \cdot y\right)}\]
4. Simplified1.6
  \[\leadsto \color{blue}{\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)}\]
if -4.7883291697680416e+29 < z < 2.1704049813042748e+24
1. Initial program 0.8
  \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
2. 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 div-inv0.7
  \[\leadsto \mathsf{fma}\left(\color{blue}{y \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\]
5. Using strategy rm
6. Applied add-cube-cbrt0.7
  \[\leadsto \mathsf{fma}\left(y \cdot \frac{1}{\color{blue}{\left(\sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}}}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\]
7. Applied *-un-lft-identity0.7
  \[\leadsto \mathsf{fma}\left(y \cdot \frac{\color{blue}{1 \cdot 1}}{\left(\sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\]
8. Applied times-frac0.7
  \[\leadsto \mathsf{fma}\left(y \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}} \cdot \frac{1}{\sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}}\right)}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\]
9. Applied associate-*r*0.7
  \[\leadsto \mathsf{fma}\left(\color{blue}{\left(y \cdot \frac{1}{\sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}}\right) \cdot \frac{1}{\sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}}}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\]
10. Simplified0.7
  \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{\sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}}} \cdot \frac{1}{\sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\]
Recombined 2 regimes into one program.
Final simplification1.1
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4.78832916976804162 \cdot 10^{29} \lor \neg \left(z \le 2.17040498130427483 \cdot 10^{24}\right):\\ \;\;\;\;\mathsf{fma}\left(y, 3.13060547622999996 + \frac{t}{{z}^{2}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)} \cdot \sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}} \cdot \frac{1}{\sqrt[3]{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z + 15.234687406999999, z, 31.469011574900001\right), z, 11.940090572100001\right), z, 0.60777138777100004\right)}}, \mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(z, 3.13060547622999996, 11.166754126200001\right), z, t\right), z, a\right), z, b\right), x\right)\\ \end{array}\]

Error

Target

Derivation

`if z < -4.7883291697680416e+29 or 2.1704049813042748e+24 < z`

`if -4.7883291697680416e+29 < z < 2.1704049813042748e+24`

Reproduce