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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -2.1890101961612443 \cdot 10^{88}:\\ \;\;\;\;-1 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \le 4.5181325422403336 \cdot 10^{112}:\\ \;\;\;\;\frac{x \cdot y}{\left|\sqrt[3]{z \cdot z - t \cdot a}\right|} \cdot \frac{z}{\sqrt{\sqrt[3]{z \cdot z - t \cdot a}}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;z \le -2.1890101961612443 \cdot 10^{88}:\\
\;\;\;\;-1 \cdot \left(x \cdot y\right)\\

\mathbf{elif}\;z \le 4.5181325422403336 \cdot 10^{112}:\\
\;\;\;\;\frac{x \cdot y}{\left|\sqrt[3]{z \cdot z - t \cdot a}\right|} \cdot \frac{z}{\sqrt{\sqrt[3]{z \cdot z - t \cdot a}}}\\

\mathbf{else}:\\
\;\;\;\;x \cdot y\\

\end{array}

double f(double x, double y, double z, double t, double a) {
        double r274267 = x;
        double r274268 = y;
        double r274269 = r274267 * r274268;
        double r274270 = z;
        double r274271 = r274269 * r274270;
        double r274272 = r274270 * r274270;
        double r274273 = t;
        double r274274 = a;
        double r274275 = r274273 * r274274;
        double r274276 = r274272 - r274275;
        double r274277 = sqrt(r274276);
        double r274278 = r274271 / r274277;
        return r274278;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r274279 = z;
        double r274280 = -2.1890101961612443e+88;
        bool r274281 = r274279 <= r274280;
        double r274282 = -1.0;
        double r274283 = x;
        double r274284 = y;
        double r274285 = r274283 * r274284;
        double r274286 = r274282 * r274285;
        double r274287 = 4.518132542240334e+112;
        bool r274288 = r274279 <= r274287;
        double r274289 = r274279 * r274279;
        double r274290 = t;
        double r274291 = a;
        double r274292 = r274290 * r274291;
        double r274293 = r274289 - r274292;
        double r274294 = cbrt(r274293);
        double r274295 = fabs(r274294);
        double r274296 = r274285 / r274295;
        double r274297 = sqrt(r274294);
        double r274298 = r274279 / r274297;
        double r274299 = r274296 * r274298;
        double r274300 = r274288 ? r274299 : r274285;
        double r274301 = r274281 ? r274286 : r274300;
        return r274301;
}

Original	24.6
Target	7.9
Herbie	7.1

Derivation

Split input into 3 regimes
if z < -2.1890101961612443e+88
1. Initial program 41.5
  \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}}\]
2. Taylor expanded around -inf 2.4
  \[\leadsto \color{blue}{-1 \cdot \left(x \cdot y\right)}\]
if -2.1890101961612443e+88 < z < 4.518132542240334e+112
1. Initial program 11.0
  \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}}\]
2. Using strategy rm
3. Applied *-un-lft-identity11.0
  \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\sqrt{\color{blue}{1 \cdot \left(z \cdot z - t \cdot a\right)}}}\]
4. Applied sqrt-prod11.0
  \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\color{blue}{\sqrt{1} \cdot \sqrt{z \cdot z - t \cdot a}}}\]
5. Applied times-frac9.4
  \[\leadsto \color{blue}{\frac{x \cdot y}{\sqrt{1}} \cdot \frac{z}{\sqrt{z \cdot z - t \cdot a}}}\]
6. Simplified9.4
  \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot \frac{z}{\sqrt{z \cdot z - t \cdot a}}\]
7. Using strategy rm
8. Applied add-cube-cbrt9.8
  \[\leadsto \left(x \cdot y\right) \cdot \frac{z}{\sqrt{\color{blue}{\left(\sqrt[3]{z \cdot z - t \cdot a} \cdot \sqrt[3]{z \cdot z - t \cdot a}\right) \cdot \sqrt[3]{z \cdot z - t \cdot a}}}}\]
9. Applied sqrt-prod9.8
  \[\leadsto \left(x \cdot y\right) \cdot \frac{z}{\color{blue}{\sqrt{\sqrt[3]{z \cdot z - t \cdot a} \cdot \sqrt[3]{z \cdot z - t \cdot a}} \cdot \sqrt{\sqrt[3]{z \cdot z - t \cdot a}}}}\]
10. Applied *-un-lft-identity9.8
  \[\leadsto \left(x \cdot y\right) \cdot \frac{\color{blue}{1 \cdot z}}{\sqrt{\sqrt[3]{z \cdot z - t \cdot a} \cdot \sqrt[3]{z \cdot z - t \cdot a}} \cdot \sqrt{\sqrt[3]{z \cdot z - t \cdot a}}}\]
11. Applied times-frac9.8
  \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{\left(\frac{1}{\sqrt{\sqrt[3]{z \cdot z - t \cdot a} \cdot \sqrt[3]{z \cdot z - t \cdot a}}} \cdot \frac{z}{\sqrt{\sqrt[3]{z \cdot z - t \cdot a}}}\right)}\]
12. Applied associate-*r*10.6
  \[\leadsto \color{blue}{\left(\left(x \cdot y\right) \cdot \frac{1}{\sqrt{\sqrt[3]{z \cdot z - t \cdot a} \cdot \sqrt[3]{z \cdot z - t \cdot a}}}\right) \cdot \frac{z}{\sqrt{\sqrt[3]{z \cdot z - t \cdot a}}}}\]
13. Simplified10.6
  \[\leadsto \color{blue}{\frac{x \cdot y}{\left|\sqrt[3]{z \cdot z - t \cdot a}\right|}} \cdot \frac{z}{\sqrt{\sqrt[3]{z \cdot z - t \cdot a}}}\]
if 4.518132542240334e+112 < z
1. Initial program 45.6
  \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}}\]
2. Taylor expanded around inf 2.3
  \[\leadsto \color{blue}{x \cdot y}\]
Recombined 3 regimes into one program.
Final simplification7.1
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.1890101961612443 \cdot 10^{88}:\\ \;\;\;\;-1 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;z \le 4.5181325422403336 \cdot 10^{112}:\\ \;\;\;\;\frac{x \cdot y}{\left|\sqrt[3]{z \cdot z - t \cdot a}\right|} \cdot \frac{z}{\sqrt{\sqrt[3]{z \cdot z - t \cdot a}}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array}\]

Error

Try it out

Target

Derivation

`if z < -2.1890101961612443e+88`

`if -2.1890101961612443e+88 < z < 4.518132542240334e+112`

`if 4.518132542240334e+112 < z`

Reproduce

In
Out