\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]

↓

\[\begin{array}{l} \mathbf{if}\;a \le -4.016598119805832112067423593203436782632 \cdot 10^{-193} \lor \neg \left(a \le 1.378728743140737444719887307656154525911 \cdot 10^{-126}\right):\\ \;\;\;\;\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, t\right) - \frac{t}{\frac{z}{y}}\\ \end{array}\]

x + \left(y - z\right) \cdot \frac{t - x}{a - z}

↓

\begin{array}{l}
\mathbf{if}\;a \le -4.016598119805832112067423593203436782632 \cdot 10^{-193} \lor \neg \left(a \le 1.378728743140737444719887307656154525911 \cdot 10^{-126}\right):\\
\;\;\;\;\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}} + x\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, t\right) - \frac{t}{\frac{z}{y}}\\

\end{array}

double f(double x, double y, double z, double t, double a) {
        double r104049 = x;
        double r104050 = y;
        double r104051 = z;
        double r104052 = r104050 - r104051;
        double r104053 = t;
        double r104054 = r104053 - r104049;
        double r104055 = a;
        double r104056 = r104055 - r104051;
        double r104057 = r104054 / r104056;
        double r104058 = r104052 * r104057;
        double r104059 = r104049 + r104058;
        return r104059;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r104060 = a;
        double r104061 = -4.016598119805832e-193;
        bool r104062 = r104060 <= r104061;
        double r104063 = 1.3787287431407374e-126;
        bool r104064 = r104060 <= r104063;
        double r104065 = !r104064;
        bool r104066 = r104062 || r104065;
        double r104067 = y;
        double r104068 = z;
        double r104069 = r104067 - r104068;
        double r104070 = r104060 - r104068;
        double r104071 = cbrt(r104070);
        double r104072 = r104071 * r104071;
        double r104073 = r104069 / r104072;
        double r104074 = t;
        double r104075 = x;
        double r104076 = r104074 - r104075;
        double r104077 = r104076 / r104071;
        double r104078 = r104073 * r104077;
        double r104079 = r104078 + r104075;
        double r104080 = r104075 / r104068;
        double r104081 = fma(r104080, r104067, r104074);
        double r104082 = r104068 / r104067;
        double r104083 = r104074 / r104082;
        double r104084 = r104081 - r104083;
        double r104085 = r104066 ? r104079 : r104084;
        return r104085;
}

Derivation

Split input into 2 regimes
if a < -4.016598119805832e-193 or 1.3787287431407374e-126 < a
1. Initial program 11.7
  \[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
2. Using strategy rm
3. Applied add-cube-cbrt12.2
  \[\leadsto x + \left(y - z\right) \cdot \frac{t - x}{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}}\]
4. Applied *-un-lft-identity12.2
  \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{1 \cdot \left(t - x\right)}}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}\]
5. Applied times-frac12.2
  \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)}\]
6. Applied associate-*r*10.1
  \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \frac{1}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{t - x}{\sqrt[3]{a - z}}}\]
7. Simplified10.1
  \[\leadsto x + \color{blue}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\]
if -4.016598119805832e-193 < a < 1.3787287431407374e-126
1. Initial program 24.8
  \[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
2. Using strategy rm
3. Applied add-cube-cbrt25.5
  \[\leadsto x + \left(y - z\right) \cdot \frac{t - x}{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}}\]
4. Applied *-un-lft-identity25.5
  \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{1 \cdot \left(t - x\right)}}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}\]
5. Applied times-frac25.5
  \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)}\]
6. Applied associate-*r*21.7
  \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \frac{1}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{t - x}{\sqrt[3]{a - z}}}\]
7. Simplified21.6
  \[\leadsto x + \color{blue}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\]
8. Taylor expanded around inf 13.5
  \[\leadsto \color{blue}{\left(t + \frac{x \cdot y}{z}\right) - \frac{t \cdot y}{z}}\]
9. Simplified10.2
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{z}, y, t\right) - \frac{t}{\frac{z}{y}}}\]
Recombined 2 regimes into one program.
Final simplification10.1
\[\leadsto \begin{array}{l} \mathbf{if}\;a \le -4.016598119805832112067423593203436782632 \cdot 10^{-193} \lor \neg \left(a \le 1.378728743140737444719887307656154525911 \cdot 10^{-126}\right):\\ \;\;\;\;\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, t\right) - \frac{t}{\frac{z}{y}}\\ \end{array}\]

Error

Derivation

`if a < -4.016598119805832e-193 or 1.3787287431407374e-126 < a`

`if -4.016598119805832e-193 < a < 1.3787287431407374e-126`

Reproduce