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

↓

\[\begin{array}{l} \mathbf{if}\;y \le -7.2999266771936822 \cdot 10^{-146} \lor \neg \left(y \le 1.5849138783300118 \cdot 10^{35}\right):\\ \;\;\;\;\mathsf{fma}\left(1, z, -\sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{x}{y} + \mathsf{fma}\left(\mathsf{fma}\left(-t, 1, t\right), \frac{x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\left(z - t\right) \cdot x}{y}\right)}^{1} + t\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;y \le -7.2999266771936822 \cdot 10^{-146} \lor \neg \left(y \le 1.5849138783300118 \cdot 10^{35}\right):\\
\;\;\;\;\mathsf{fma}\left(1, z, -\sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{x}{y} + \mathsf{fma}\left(\mathsf{fma}\left(-t, 1, t\right), \frac{x}{y}, t\right)\\

\mathbf{else}:\\
\;\;\;\;{\left(\frac{\left(z - t\right) \cdot x}{y}\right)}^{1} + t\\

\end{array}

double f(double x, double y, double z, double t) {
        double r450289 = x;
        double r450290 = y;
        double r450291 = r450289 / r450290;
        double r450292 = z;
        double r450293 = t;
        double r450294 = r450292 - r450293;
        double r450295 = r450291 * r450294;
        double r450296 = r450295 + r450293;
        return r450296;
}

↓

double f(double x, double y, double z, double t) {
        double r450297 = y;
        double r450298 = -7.299926677193682e-146;
        bool r450299 = r450297 <= r450298;
        double r450300 = 1.5849138783300118e+35;
        bool r450301 = r450297 <= r450300;
        double r450302 = !r450301;
        bool r450303 = r450299 || r450302;
        double r450304 = 1.0;
        double r450305 = z;
        double r450306 = t;
        double r450307 = cbrt(r450306);
        double r450308 = r450307 * r450307;
        double r450309 = r450307 * r450308;
        double r450310 = -r450309;
        double r450311 = fma(r450304, r450305, r450310);
        double r450312 = x;
        double r450313 = r450312 / r450297;
        double r450314 = r450311 * r450313;
        double r450315 = -r450306;
        double r450316 = fma(r450315, r450304, r450306);
        double r450317 = fma(r450316, r450313, r450306);
        double r450318 = r450314 + r450317;
        double r450319 = r450305 - r450306;
        double r450320 = r450319 * r450312;
        double r450321 = r450320 / r450297;
        double r450322 = pow(r450321, r450304);
        double r450323 = r450322 + r450306;
        double r450324 = r450303 ? r450318 : r450323;
        return r450324;
}

Original	2.2
Target	2.4
Herbie	1.6

Derivation

Split input into 2 regimes
if y < -7.299926677193682e-146 or 1.5849138783300118e+35 < y
1. Initial program 1.3
  \[\frac{x}{y} \cdot \left(z - t\right) + t\]
2. Using strategy rm
3. Applied add-cube-cbrt1.4
  \[\leadsto \frac{x}{y} \cdot \left(z - \color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}\right) + t\]
4. Applied *-un-lft-identity1.4
  \[\leadsto \frac{x}{y} \cdot \left(\color{blue}{1 \cdot z} - \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right) + t\]
5. Applied prod-diff1.4
  \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(\mathsf{fma}\left(1, z, -\sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) + \mathsf{fma}\left(-\sqrt[3]{t}, \sqrt[3]{t} \cdot \sqrt[3]{t}, \sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right)\right)} + t\]
6. Applied distribute-rgt-in1.4
  \[\leadsto \color{blue}{\left(\mathsf{fma}\left(1, z, -\sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{x}{y} + \mathsf{fma}\left(-\sqrt[3]{t}, \sqrt[3]{t} \cdot \sqrt[3]{t}, \sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{x}{y}\right)} + t\]
7. Applied associate-+l+1.4
  \[\leadsto \color{blue}{\mathsf{fma}\left(1, z, -\sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{x}{y} + \left(\mathsf{fma}\left(-\sqrt[3]{t}, \sqrt[3]{t} \cdot \sqrt[3]{t}, \sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{x}{y} + t\right)}\]
8. Simplified1.4
  \[\leadsto \mathsf{fma}\left(1, z, -\sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{x}{y} + \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(-t, 1, t\right), \frac{x}{y}, t\right)}\]
if -7.299926677193682e-146 < y < 1.5849138783300118e+35
1. Initial program 4.3
  \[\frac{x}{y} \cdot \left(z - t\right) + t\]
2. Using strategy rm
3. Applied pow14.3
  \[\leadsto \frac{x}{y} \cdot \color{blue}{{\left(z - t\right)}^{1}} + t\]
4. Applied pow14.3
  \[\leadsto \color{blue}{{\left(\frac{x}{y}\right)}^{1}} \cdot {\left(z - t\right)}^{1} + t\]
5. Applied pow-prod-down4.3
  \[\leadsto \color{blue}{{\left(\frac{x}{y} \cdot \left(z - t\right)\right)}^{1}} + t\]
6. Simplified2.2
  \[\leadsto {\color{blue}{\left(\frac{\left(z - t\right) \cdot x}{y}\right)}}^{1} + t\]
Recombined 2 regimes into one program.
Final simplification1.6
\[\leadsto \begin{array}{l} \mathbf{if}\;y \le -7.2999266771936822 \cdot 10^{-146} \lor \neg \left(y \le 1.5849138783300118 \cdot 10^{35}\right):\\ \;\;\;\;\mathsf{fma}\left(1, z, -\sqrt[3]{t} \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \frac{x}{y} + \mathsf{fma}\left(\mathsf{fma}\left(-t, 1, t\right), \frac{x}{y}, t\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{\left(z - t\right) \cdot x}{y}\right)}^{1} + t\\ \end{array}\]

Error

Target

Derivation

`if y < -7.299926677193682e-146 or 1.5849138783300118e+35 < y`

`if -7.299926677193682e-146 < y < 1.5849138783300118e+35`

Reproduce