\[x \cdot \left(1 - y \cdot z\right)\]

↓

\[\begin{array}{l} \mathbf{if}\;y \cdot z = -\infty \lor \neg \left(y \cdot z \le 1.2079824086365364 \cdot 10^{227}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot y\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right) + x \cdot \mathsf{fma}\left(-z, y, z \cdot y\right)\\ \end{array}\]

x \cdot \left(1 - y \cdot z\right)

↓

\begin{array}{l}
\mathbf{if}\;y \cdot z = -\infty \lor \neg \left(y \cdot z \le 1.2079824086365364 \cdot 10^{227}\right):\\
\;\;\;\;x \cdot 1 + \left(x \cdot y\right) \cdot \left(-z\right)\\

\mathbf{else}:\\
\;\;\;\;x \cdot \left(1 - y \cdot z\right) + x \cdot \mathsf{fma}\left(-z, y, z \cdot y\right)\\

\end{array}

double f(double x, double y, double z) {
        double r260107 = x;
        double r260108 = 1.0;
        double r260109 = y;
        double r260110 = z;
        double r260111 = r260109 * r260110;
        double r260112 = r260108 - r260111;
        double r260113 = r260107 * r260112;
        return r260113;
}

↓

double f(double x, double y, double z) {
        double r260114 = y;
        double r260115 = z;
        double r260116 = r260114 * r260115;
        double r260117 = -inf.0;
        bool r260118 = r260116 <= r260117;
        double r260119 = 1.2079824086365364e+227;
        bool r260120 = r260116 <= r260119;
        double r260121 = !r260120;
        bool r260122 = r260118 || r260121;
        double r260123 = x;
        double r260124 = 1.0;
        double r260125 = r260123 * r260124;
        double r260126 = r260123 * r260114;
        double r260127 = -r260115;
        double r260128 = r260126 * r260127;
        double r260129 = r260125 + r260128;
        double r260130 = r260124 - r260116;
        double r260131 = r260123 * r260130;
        double r260132 = r260115 * r260114;
        double r260133 = fma(r260127, r260114, r260132);
        double r260134 = r260123 * r260133;
        double r260135 = r260131 + r260134;
        double r260136 = r260122 ? r260129 : r260135;
        return r260136;
}

Derivation

Split input into 2 regimes
if (* y z) < -inf.0 or 1.2079824086365364e+227 < (* y z)
1. Initial program 42.8
  \[x \cdot \left(1 - y \cdot z\right)\]
2. Using strategy rm
3. Applied sub-neg42.8
  \[\leadsto x \cdot \color{blue}{\left(1 + \left(-y \cdot z\right)\right)}\]
4. Applied distribute-lft-in42.8
  \[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(-y \cdot z\right)}\]
5. Using strategy rm
6. Applied distribute-rgt-neg-in42.8
  \[\leadsto x \cdot 1 + x \cdot \color{blue}{\left(y \cdot \left(-z\right)\right)}\]
7. Applied associate-*r*0.4
  \[\leadsto x \cdot 1 + \color{blue}{\left(x \cdot y\right) \cdot \left(-z\right)}\]
if -inf.0 < (* y z) < 1.2079824086365364e+227
1. Initial program 0.1
  \[x \cdot \left(1 - y \cdot z\right)\]
2. Using strategy rm
3. Applied add-cube-cbrt0.1
  \[\leadsto x \cdot \left(\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}} - y \cdot z\right)\]
4. Applied prod-diff0.1
  \[\leadsto x \cdot \color{blue}{\left(\mathsf{fma}\left(\sqrt[3]{1} \cdot \sqrt[3]{1}, \sqrt[3]{1}, -z \cdot y\right) + \mathsf{fma}\left(-z, y, z \cdot y\right)\right)}\]
5. Applied distribute-lft-in0.1
  \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(\sqrt[3]{1} \cdot \sqrt[3]{1}, \sqrt[3]{1}, -z \cdot y\right) + x \cdot \mathsf{fma}\left(-z, y, z \cdot y\right)}\]
6. Simplified0.1
  \[\leadsto \color{blue}{x \cdot \left(1 - y \cdot z\right)} + x \cdot \mathsf{fma}\left(-z, y, z \cdot y\right)\]
Recombined 2 regimes into one program.
Final simplification0.1
\[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot z = -\infty \lor \neg \left(y \cdot z \le 1.2079824086365364 \cdot 10^{227}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot y\right) \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y \cdot z\right) + x \cdot \mathsf{fma}\left(-z, y, z \cdot y\right)\\ \end{array}\]

Error

Derivation

`if (* y z) < -inf.0 or 1.2079824086365364e+227 < (* y z)`

`if -inf.0 < (* y z) < 1.2079824086365364e+227`

Reproduce