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

↓

\[\begin{array}{l} \mathbf{if}\;a \le -6.143232131925929682871142551410290774749 \cdot 10^{-28} \lor \neg \left(a \le 4.324311520218842582736217138705122405131 \cdot 10^{-174}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}, \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, t - \frac{t \cdot y}{z}\right)\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;a \le -6.143232131925929682871142551410290774749 \cdot 10^{-28} \lor \neg \left(a \le 4.324311520218842582736217138705122405131 \cdot 10^{-174}\right):\\
\;\;\;\;\mathsf{fma}\left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}, \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}, x\right)\\

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

\end{array}

double f(double x, double y, double z, double t, double a) {
        double r82238 = x;
        double r82239 = y;
        double r82240 = z;
        double r82241 = r82239 - r82240;
        double r82242 = t;
        double r82243 = r82242 - r82238;
        double r82244 = a;
        double r82245 = r82244 - r82240;
        double r82246 = r82243 / r82245;
        double r82247 = r82241 * r82246;
        double r82248 = r82238 + r82247;
        return r82248;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r82249 = a;
        double r82250 = -6.14323213192593e-28;
        bool r82251 = r82249 <= r82250;
        double r82252 = 4.324311520218843e-174;
        bool r82253 = r82249 <= r82252;
        double r82254 = !r82253;
        bool r82255 = r82251 || r82254;
        double r82256 = y;
        double r82257 = z;
        double r82258 = r82256 - r82257;
        double r82259 = t;
        double r82260 = x;
        double r82261 = r82259 - r82260;
        double r82262 = cbrt(r82261);
        double r82263 = r82262 * r82262;
        double r82264 = r82249 - r82257;
        double r82265 = cbrt(r82264);
        double r82266 = r82265 * r82265;
        double r82267 = r82263 / r82266;
        double r82268 = r82258 * r82267;
        double r82269 = r82262 / r82265;
        double r82270 = fma(r82268, r82269, r82260);
        double r82271 = r82260 / r82257;
        double r82272 = r82259 * r82256;
        double r82273 = r82272 / r82257;
        double r82274 = r82259 - r82273;
        double r82275 = fma(r82271, r82256, r82274);
        double r82276 = r82255 ? r82270 : r82275;
        return r82276;
}

Derivation

Split input into 2 regimes
if a < -6.14323213192593e-28 or 4.324311520218843e-174 < a
1. Initial program 10.9
  \[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
2. Simplified10.9
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, y - z, x\right)}\]
3. Using strategy rm
4. Applied clear-num11.1
  \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - z}{t - x}}}, y - z, x\right)\]
5. Using strategy rm
6. Applied fma-udef11.2
  \[\leadsto \color{blue}{\frac{1}{\frac{a - z}{t - x}} \cdot \left(y - z\right) + x}\]
7. Simplified10.9
  \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} + x\]
8. Using strategy rm
9. Applied add-cube-cbrt11.4
  \[\leadsto \left(y - z\right) \cdot \frac{t - x}{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}} + x\]
10. Applied add-cube-cbrt11.6
  \[\leadsto \left(y - z\right) \cdot \frac{\color{blue}{\left(\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}\right) \cdot \sqrt[3]{t - x}}}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}} + x\]
11. Applied times-frac11.6
  \[\leadsto \left(y - z\right) \cdot \color{blue}{\left(\frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}\right)} + x\]
12. Applied associate-*r*9.1
  \[\leadsto \color{blue}{\left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}} + x\]
13. Using strategy rm
14. Applied fma-def9.1
  \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}, \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}, x\right)}\]
if -6.14323213192593e-28 < a < 4.324311520218843e-174
1. Initial program 24.3
  \[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
2. Simplified24.3
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - x}{a - z}, y - z, x\right)}\]
3. Using strategy rm
4. Applied clear-num24.5
  \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - z}{t - x}}}, y - z, x\right)\]
5. Using strategy rm
6. Applied fma-udef24.5
  \[\leadsto \color{blue}{\frac{1}{\frac{a - z}{t - x}} \cdot \left(y - z\right) + x}\]
7. Simplified24.3
  \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{t - x}{a - z}} + x\]
8. Taylor expanded around inf 16.4
  \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}}\]
9. Simplified16.1
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{z}, y, t - \frac{t \cdot y}{z}\right)}\]
Recombined 2 regimes into one program.
Final simplification11.2
\[\leadsto \begin{array}{l} \mathbf{if}\;a \le -6.143232131925929682871142551410290774749 \cdot 10^{-28} \lor \neg \left(a \le 4.324311520218842582736217138705122405131 \cdot 10^{-174}\right):\\ \;\;\;\;\mathsf{fma}\left(\left(y - z\right) \cdot \frac{\sqrt[3]{t - x} \cdot \sqrt[3]{t - x}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}, \frac{\sqrt[3]{t - x}}{\sqrt[3]{a - z}}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, t - \frac{t \cdot y}{z}\right)\\ \end{array}\]

Error

Derivation

`if a < -6.14323213192593e-28 or 4.324311520218843e-174 < a`

`if -6.14323213192593e-28 < a < 4.324311520218843e-174`

Reproduce