\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]

↓

\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -2.37460898105936542 \cdot 10^{120} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 2.15379248506655815 \cdot 10^{115}\right):\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + \sqrt{27} \cdot \left(\sqrt{27} \cdot \left(a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot x + 27 \cdot \left(a \cdot b\right)\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array}\]

\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b

↓

\begin{array}{l}
\mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -2.37460898105936542 \cdot 10^{120} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 2.15379248506655815 \cdot 10^{115}\right):\\
\;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + \sqrt{27} \cdot \left(\sqrt{27} \cdot \left(a \cdot b\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(2 \cdot x + 27 \cdot \left(a \cdot b\right)\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r752966 = x;
        double r752967 = 2.0;
        double r752968 = r752966 * r752967;
        double r752969 = y;
        double r752970 = 9.0;
        double r752971 = r752969 * r752970;
        double r752972 = z;
        double r752973 = r752971 * r752972;
        double r752974 = t;
        double r752975 = r752973 * r752974;
        double r752976 = r752968 - r752975;
        double r752977 = a;
        double r752978 = 27.0;
        double r752979 = r752977 * r752978;
        double r752980 = b;
        double r752981 = r752979 * r752980;
        double r752982 = r752976 + r752981;
        return r752982;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r752983 = y;
        double r752984 = 9.0;
        double r752985 = r752983 * r752984;
        double r752986 = z;
        double r752987 = r752985 * r752986;
        double r752988 = -2.3746089810593654e+120;
        bool r752989 = r752987 <= r752988;
        double r752990 = 2.153792485066558e+115;
        bool r752991 = r752987 <= r752990;
        double r752992 = !r752991;
        bool r752993 = r752989 || r752992;
        double r752994 = x;
        double r752995 = 2.0;
        double r752996 = r752994 * r752995;
        double r752997 = t;
        double r752998 = r752986 * r752997;
        double r752999 = r752984 * r752998;
        double r753000 = r752983 * r752999;
        double r753001 = r752996 - r753000;
        double r753002 = 27.0;
        double r753003 = sqrt(r753002);
        double r753004 = a;
        double r753005 = b;
        double r753006 = r753004 * r753005;
        double r753007 = r753003 * r753006;
        double r753008 = r753003 * r753007;
        double r753009 = r753001 + r753008;
        double r753010 = r752995 * r752994;
        double r753011 = r753002 * r753006;
        double r753012 = r753010 + r753011;
        double r753013 = r752986 * r752983;
        double r753014 = r752997 * r753013;
        double r753015 = r752984 * r753014;
        double r753016 = r753012 - r753015;
        double r753017 = r752993 ? r753009 : r753016;
        return r753017;
}

Original	4.0
Target	2.8
Herbie	0.9

Derivation

Split input into 2 regimes
if (* (* y 9.0) z) < -2.3746089810593654e+120 or 2.153792485066558e+115 < (* (* y 9.0) z)
1. Initial program 16.9
  \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
2. Taylor expanded around 0 16.8
  \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{27 \cdot \left(a \cdot b\right)}\]
3. Using strategy rm
4. Applied associate-*l*3.0
  \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + 27 \cdot \left(a \cdot b\right)\]
5. Using strategy rm
6. Applied associate-*l*2.6
  \[\leadsto \left(x \cdot 2 - \color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)}\right) + 27 \cdot \left(a \cdot b\right)\]
7. Using strategy rm
8. Applied add-sqr-sqrt2.6
  \[\leadsto \left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + \color{blue}{\left(\sqrt{27} \cdot \sqrt{27}\right)} \cdot \left(a \cdot b\right)\]
9. Applied associate-*l*2.7
  \[\leadsto \left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + \color{blue}{\sqrt{27} \cdot \left(\sqrt{27} \cdot \left(a \cdot b\right)\right)}\]
if -2.3746089810593654e+120 < (* (* y 9.0) z) < 2.153792485066558e+115
1. Initial program 0.4
  \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
2. Taylor expanded around 0 0.4
  \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{27 \cdot \left(a \cdot b\right)}\]
3. Taylor expanded around inf 0.4
  \[\leadsto \color{blue}{\left(2 \cdot x + 27 \cdot \left(a \cdot b\right)\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)}\]
Recombined 2 regimes into one program.
Final simplification0.9
\[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -2.37460898105936542 \cdot 10^{120} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 2.15379248506655815 \cdot 10^{115}\right):\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + \sqrt{27} \cdot \left(\sqrt{27} \cdot \left(a \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot x + 27 \cdot \left(a \cdot b\right)\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array}\]

Error

Try it out

Target

Derivation

`if (* (* y 9.0) z) < -2.3746089810593654e+120 or 2.153792485066558e+115 < (* (* y 9.0) z)`

`if -2.3746089810593654e+120 < (* (* y 9.0) z) < 2.153792485066558e+115`

Reproduce

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