\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

↓

\[\begin{array}{l} \mathbf{if}\;b \le 4.281799399469648 \cdot 10^{-78}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(\sqrt[3]{b} \cdot \left(z \cdot c\right)\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) + a \cdot \left(-b \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \sqrt{b} \cdot \left(\left(z \cdot c - a \cdot i\right) \cdot \sqrt{b}\right)\right)\\ \end{array}\]

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r13651173 = x;
        double r13651174 = y;
        double r13651175 = z;
        double r13651176 = r13651174 * r13651175;
        double r13651177 = t;
        double r13651178 = a;
        double r13651179 = r13651177 * r13651178;
        double r13651180 = r13651176 - r13651179;
        double r13651181 = r13651173 * r13651180;
        double r13651182 = b;
        double r13651183 = c;
        double r13651184 = r13651183 * r13651175;
        double r13651185 = i;
        double r13651186 = r13651185 * r13651178;
        double r13651187 = r13651184 - r13651186;
        double r13651188 = r13651182 * r13651187;
        double r13651189 = r13651181 - r13651188;
        double r13651190 = j;
        double r13651191 = r13651183 * r13651177;
        double r13651192 = r13651185 * r13651174;
        double r13651193 = r13651191 - r13651192;
        double r13651194 = r13651190 * r13651193;
        double r13651195 = r13651189 + r13651194;
        return r13651195;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r13651196 = b;
        double r13651197 = 4.281799399469648e-78;
        bool r13651198 = r13651196 <= r13651197;
        double r13651199 = j;
        double r13651200 = t;
        double r13651201 = c;
        double r13651202 = r13651200 * r13651201;
        double r13651203 = y;
        double r13651204 = i;
        double r13651205 = r13651203 * r13651204;
        double r13651206 = r13651202 - r13651205;
        double r13651207 = r13651199 * r13651206;
        double r13651208 = z;
        double r13651209 = r13651203 * r13651208;
        double r13651210 = a;
        double r13651211 = r13651200 * r13651210;
        double r13651212 = r13651209 - r13651211;
        double r13651213 = x;
        double r13651214 = r13651212 * r13651213;
        double r13651215 = cbrt(r13651196);
        double r13651216 = r13651208 * r13651201;
        double r13651217 = r13651215 * r13651216;
        double r13651218 = r13651215 * r13651215;
        double r13651219 = r13651217 * r13651218;
        double r13651220 = r13651196 * r13651204;
        double r13651221 = -r13651220;
        double r13651222 = r13651210 * r13651221;
        double r13651223 = r13651219 + r13651222;
        double r13651224 = r13651214 - r13651223;
        double r13651225 = r13651207 + r13651224;
        double r13651226 = sqrt(r13651196);
        double r13651227 = r13651210 * r13651204;
        double r13651228 = r13651216 - r13651227;
        double r13651229 = r13651228 * r13651226;
        double r13651230 = r13651226 * r13651229;
        double r13651231 = r13651214 - r13651230;
        double r13651232 = r13651207 + r13651231;
        double r13651233 = r13651198 ? r13651225 : r13651232;
        return r13651233;
}

\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)

↓

\begin{array}{l}
\mathbf{if}\;b \le 4.281799399469648 \cdot 10^{-78}:\\
\;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(\sqrt[3]{b} \cdot \left(z \cdot c\right)\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) + a \cdot \left(-b \cdot i\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \sqrt{b} \cdot \left(\left(z \cdot c - a \cdot i\right) \cdot \sqrt{b}\right)\right)\\

\end{array}

Derivation

Split input into 2 regimes
if b < 4.281799399469648e-78
1. Initial program 12.6
  \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
2. Using strategy rm
3. Applied add-cube-cbrt12.9
  \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \sqrt[3]{b}\right)} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
4. Applied associate-*l*12.9
  \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\sqrt[3]{b} \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
5. Using strategy rm
6. Applied sub-neg12.9
  \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\sqrt[3]{b} \cdot \color{blue}{\left(c \cdot z + \left(-i \cdot a\right)\right)}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
7. Applied distribute-lft-in12.9
  \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \color{blue}{\left(\sqrt[3]{b} \cdot \left(c \cdot z\right) + \sqrt[3]{b} \cdot \left(-i \cdot a\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
8. Applied distribute-rgt-in12.9
  \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\left(\sqrt[3]{b} \cdot \left(c \cdot z\right)\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) + \left(\sqrt[3]{b} \cdot \left(-i \cdot a\right)\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
9. Simplified12.1
  \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(\sqrt[3]{b} \cdot \left(c \cdot z\right)\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) + \color{blue}{\left(-a\right) \cdot \left(b \cdot i\right)}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
if 4.281799399469648e-78 < b
1. Initial program 8.1
  \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
2. Using strategy rm
3. Applied add-sqr-sqrt8.2
  \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\sqrt{b} \cdot \sqrt{b}\right)} \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
4. Applied associate-*l*8.3
  \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\sqrt{b} \cdot \left(\sqrt{b} \cdot \left(c \cdot z - i \cdot a\right)\right)}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
Recombined 2 regimes into one program.
Final simplification11.1
\[\leadsto \begin{array}{l} \mathbf{if}\;b \le 4.281799399469648 \cdot 10^{-78}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(\sqrt[3]{b} \cdot \left(z \cdot c\right)\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) + a \cdot \left(-b \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \sqrt{b} \cdot \left(\left(z \cdot c - a \cdot i\right) \cdot \sqrt{b}\right)\right)\\ \end{array}\]

Error

Derivation

`if b < 4.281799399469648e-78`

`if 4.281799399469648e-78 < b`

Reproduce