\[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -6.064026063174626 \cdot 10^{45}:\\ \;\;\;\;x - \frac{\log \left(\sqrt{\left(1 - y\right) + y \cdot e^{z}}\right) + \log \left(\sqrt{\left(1 - y\right) + y \cdot e^{z}}\right)}{t}\\ \mathbf{elif}\;z \le 6.7485748775422916 \cdot 10^{-44}:\\ \;\;\;\;x - \left(1 \cdot \left(\left(z \cdot y\right) \cdot \frac{1}{t}\right) + \frac{\log 1}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\log \left(1 + y \cdot \left(\frac{1}{2} \cdot {z}^{2} + z\right)\right)}{t}\\ \end{array}\]

x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t}

↓

\begin{array}{l}
\mathbf{if}\;z \le -6.064026063174626 \cdot 10^{45}:\\
\;\;\;\;x - \frac{\log \left(\sqrt{\left(1 - y\right) + y \cdot e^{z}}\right) + \log \left(\sqrt{\left(1 - y\right) + y \cdot e^{z}}\right)}{t}\\

\mathbf{elif}\;z \le 6.7485748775422916 \cdot 10^{-44}:\\
\;\;\;\;x - \left(1 \cdot \left(\left(z \cdot y\right) \cdot \frac{1}{t}\right) + \frac{\log 1}{t}\right)\\

\mathbf{else}:\\
\;\;\;\;x - \frac{\log \left(1 + y \cdot \left(\frac{1}{2} \cdot {z}^{2} + z\right)\right)}{t}\\

\end{array}

double f(double x, double y, double z, double t) {
        double r331605 = x;
        double r331606 = 1.0;
        double r331607 = y;
        double r331608 = r331606 - r331607;
        double r331609 = z;
        double r331610 = exp(r331609);
        double r331611 = r331607 * r331610;
        double r331612 = r331608 + r331611;
        double r331613 = log(r331612);
        double r331614 = t;
        double r331615 = r331613 / r331614;
        double r331616 = r331605 - r331615;
        return r331616;
}

↓

double f(double x, double y, double z, double t) {
        double r331617 = z;
        double r331618 = -6.064026063174626e+45;
        bool r331619 = r331617 <= r331618;
        double r331620 = x;
        double r331621 = 1.0;
        double r331622 = y;
        double r331623 = r331621 - r331622;
        double r331624 = exp(r331617);
        double r331625 = r331622 * r331624;
        double r331626 = r331623 + r331625;
        double r331627 = sqrt(r331626);
        double r331628 = log(r331627);
        double r331629 = r331628 + r331628;
        double r331630 = t;
        double r331631 = r331629 / r331630;
        double r331632 = r331620 - r331631;
        double r331633 = 6.748574877542292e-44;
        bool r331634 = r331617 <= r331633;
        double r331635 = r331617 * r331622;
        double r331636 = 1.0;
        double r331637 = r331636 / r331630;
        double r331638 = r331635 * r331637;
        double r331639 = r331621 * r331638;
        double r331640 = log(r331621);
        double r331641 = r331640 / r331630;
        double r331642 = r331639 + r331641;
        double r331643 = r331620 - r331642;
        double r331644 = 0.5;
        double r331645 = 2.0;
        double r331646 = pow(r331617, r331645);
        double r331647 = r331644 * r331646;
        double r331648 = r331647 + r331617;
        double r331649 = r331622 * r331648;
        double r331650 = r331621 + r331649;
        double r331651 = log(r331650);
        double r331652 = r331651 / r331630;
        double r331653 = r331620 - r331652;
        double r331654 = r331634 ? r331643 : r331653;
        double r331655 = r331619 ? r331632 : r331654;
        return r331655;
}

Original	24.6
Target	16.0
Herbie	9.2

Derivation

Split input into 3 regimes
if z < -6.064026063174626e+45
1. Initial program 11.5
  \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t}\]
2. Using strategy rm
3. Applied add-sqr-sqrt11.6
  \[\leadsto x - \frac{\log \color{blue}{\left(\sqrt{\left(1 - y\right) + y \cdot e^{z}} \cdot \sqrt{\left(1 - y\right) + y \cdot e^{z}}\right)}}{t}\]
4. Applied log-prod11.6
  \[\leadsto x - \frac{\color{blue}{\log \left(\sqrt{\left(1 - y\right) + y \cdot e^{z}}\right) + \log \left(\sqrt{\left(1 - y\right) + y \cdot e^{z}}\right)}}{t}\]
if -6.064026063174626e+45 < z < 6.748574877542292e-44
1. Initial program 29.2
  \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t}\]
2. Taylor expanded around 0 8.2
  \[\leadsto x - \frac{\color{blue}{0.5 \cdot \left({z}^{2} \cdot y\right) + \left(1 \cdot \left(z \cdot y\right) + \log 1\right)}}{t}\]
3. Simplified8.2
  \[\leadsto x - \frac{\color{blue}{\log 1 + y \cdot \left(0.5 \cdot {z}^{2} + 1 \cdot z\right)}}{t}\]
4. Taylor expanded around 0 8.0
  \[\leadsto \color{blue}{x - \left(1 \cdot \frac{z \cdot y}{t} + \frac{\log 1}{t}\right)}\]
5. Using strategy rm
6. Applied div-inv8.0
  \[\leadsto x - \left(1 \cdot \color{blue}{\left(\left(z \cdot y\right) \cdot \frac{1}{t}\right)} + \frac{\log 1}{t}\right)\]
if 6.748574877542292e-44 < z
1. Initial program 25.7
  \[x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t}\]
2. Taylor expanded around 0 13.5
  \[\leadsto x - \frac{\log \color{blue}{\left(\frac{1}{2} \cdot \left({z}^{2} \cdot y\right) + \left(z \cdot y + 1\right)\right)}}{t}\]
3. Simplified13.5
  \[\leadsto x - \frac{\log \color{blue}{\left(1 + y \cdot \left(\frac{1}{2} \cdot {z}^{2} + z\right)\right)}}{t}\]
Recombined 3 regimes into one program.
Final simplification9.2
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.064026063174626 \cdot 10^{45}:\\ \;\;\;\;x - \frac{\log \left(\sqrt{\left(1 - y\right) + y \cdot e^{z}}\right) + \log \left(\sqrt{\left(1 - y\right) + y \cdot e^{z}}\right)}{t}\\ \mathbf{elif}\;z \le 6.7485748775422916 \cdot 10^{-44}:\\ \;\;\;\;x - \left(1 \cdot \left(\left(z \cdot y\right) \cdot \frac{1}{t}\right) + \frac{\log 1}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\log \left(1 + y \cdot \left(\frac{1}{2} \cdot {z}^{2} + z\right)\right)}{t}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if z < -6.064026063174626e+45`

`if -6.064026063174626e+45 < z < 6.748574877542292e-44`

`if 6.748574877542292e-44 < z`

Reproduce

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