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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -2.885407554804660517455724314669671165557 \cdot 10^{71}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \le 5.930939844067445722258493130712277239397 \cdot 10^{90}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot z\right)}{\sqrt{z \cdot z - a \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;z \le -2.885407554804660517455724314669671165557 \cdot 10^{71}:\\
\;\;\;\;x \cdot \left(-y\right)\\

\mathbf{elif}\;z \le 5.930939844067445722258493130712277239397 \cdot 10^{90}:\\
\;\;\;\;\frac{x \cdot \left(y \cdot z\right)}{\sqrt{z \cdot z - a \cdot t}}\\

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

\end{array}

double f(double x, double y, double z, double t, double a) {
        double r19982260 = x;
        double r19982261 = y;
        double r19982262 = r19982260 * r19982261;
        double r19982263 = z;
        double r19982264 = r19982262 * r19982263;
        double r19982265 = r19982263 * r19982263;
        double r19982266 = t;
        double r19982267 = a;
        double r19982268 = r19982266 * r19982267;
        double r19982269 = r19982265 - r19982268;
        double r19982270 = sqrt(r19982269);
        double r19982271 = r19982264 / r19982270;
        return r19982271;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r19982272 = z;
        double r19982273 = -2.8854075548046605e+71;
        bool r19982274 = r19982272 <= r19982273;
        double r19982275 = x;
        double r19982276 = y;
        double r19982277 = -r19982276;
        double r19982278 = r19982275 * r19982277;
        double r19982279 = 5.930939844067446e+90;
        bool r19982280 = r19982272 <= r19982279;
        double r19982281 = r19982276 * r19982272;
        double r19982282 = r19982275 * r19982281;
        double r19982283 = r19982272 * r19982272;
        double r19982284 = a;
        double r19982285 = t;
        double r19982286 = r19982284 * r19982285;
        double r19982287 = r19982283 - r19982286;
        double r19982288 = sqrt(r19982287);
        double r19982289 = r19982282 / r19982288;
        double r19982290 = r19982275 * r19982276;
        double r19982291 = r19982280 ? r19982289 : r19982290;
        double r19982292 = r19982274 ? r19982278 : r19982291;
        return r19982292;
}

Original	24.9
Target	7.9
Herbie	7.7

Derivation

Split input into 3 regimes
if z < -2.8854075548046605e+71
1. Initial program 39.6
  \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}}\]
2. Using strategy rm
3. Applied *-un-lft-identity39.6
  \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\sqrt{\color{blue}{1 \cdot \left(z \cdot z - t \cdot a\right)}}}\]
4. Applied sqrt-prod39.6
  \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\color{blue}{\sqrt{1} \cdot \sqrt{z \cdot z - t \cdot a}}}\]
5. Applied times-frac36.6
  \[\leadsto \color{blue}{\frac{x \cdot y}{\sqrt{1}} \cdot \frac{z}{\sqrt{z \cdot z - t \cdot a}}}\]
6. Simplified36.6
  \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot \frac{z}{\sqrt{z \cdot z - t \cdot a}}\]
7. Using strategy rm
8. Applied add-sqr-sqrt36.6
  \[\leadsto \left(y \cdot x\right) \cdot \frac{z}{\sqrt{\color{blue}{\sqrt{z \cdot z - t \cdot a} \cdot \sqrt{z \cdot z - t \cdot a}}}}\]
9. Applied sqrt-prod36.7
  \[\leadsto \left(y \cdot x\right) \cdot \frac{z}{\color{blue}{\sqrt{\sqrt{z \cdot z - t \cdot a}} \cdot \sqrt{\sqrt{z \cdot z - t \cdot a}}}}\]
10. Applied *-un-lft-identity36.7
  \[\leadsto \left(y \cdot x\right) \cdot \frac{\color{blue}{1 \cdot z}}{\sqrt{\sqrt{z \cdot z - t \cdot a}} \cdot \sqrt{\sqrt{z \cdot z - t \cdot a}}}\]
11. Applied times-frac36.7
  \[\leadsto \left(y \cdot x\right) \cdot \color{blue}{\left(\frac{1}{\sqrt{\sqrt{z \cdot z - t \cdot a}}} \cdot \frac{z}{\sqrt{\sqrt{z \cdot z - t \cdot a}}}\right)}\]
12. Taylor expanded around -inf 3.3
  \[\leadsto \color{blue}{-1 \cdot \left(x \cdot y\right)}\]
13. Simplified3.3
  \[\leadsto \color{blue}{-x \cdot y}\]
if -2.8854075548046605e+71 < z < 5.930939844067446e+90
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 associate-*l*11.8
  \[\leadsto \frac{\color{blue}{x \cdot \left(y \cdot z\right)}}{\sqrt{z \cdot z - t \cdot a}}\]
if 5.930939844067446e+90 < z
1. Initial program 43.0
  \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}}\]
2. Using strategy rm
3. Applied *-un-lft-identity43.0
  \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\sqrt{\color{blue}{1 \cdot \left(z \cdot z - t \cdot a\right)}}}\]
4. Applied sqrt-prod43.0
  \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\color{blue}{\sqrt{1} \cdot \sqrt{z \cdot z - t \cdot a}}}\]
5. Applied times-frac40.5
  \[\leadsto \color{blue}{\frac{x \cdot y}{\sqrt{1}} \cdot \frac{z}{\sqrt{z \cdot z - t \cdot a}}}\]
6. Simplified40.5
  \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot \frac{z}{\sqrt{z \cdot z - t \cdot a}}\]
7. Using strategy rm
8. Applied associate-*l*40.5
  \[\leadsto \color{blue}{y \cdot \left(x \cdot \frac{z}{\sqrt{z \cdot z - t \cdot a}}\right)}\]
9. Taylor expanded around inf 2.5
  \[\leadsto y \cdot \color{blue}{x}\]
Recombined 3 regimes into one program.
Final simplification7.7
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.885407554804660517455724314669671165557 \cdot 10^{71}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \le 5.930939844067445722258493130712277239397 \cdot 10^{90}:\\ \;\;\;\;\frac{x \cdot \left(y \cdot z\right)}{\sqrt{z \cdot z - a \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array}\]

Error

Try it out

Target

Derivation

`if z < -2.8854075548046605e+71`

`if -2.8854075548046605e+71 < z < 5.930939844067446e+90`

`if 5.930939844067446e+90 < z`

Reproduce

In
Out