\[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]

↓

\[\begin{array}{l} \mathbf{if}\;y \le -7.155484423493136172297234653917029205289 \cdot 10^{-54}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{\left(z \cdot 2\right) \cdot z - t \cdot y}{y}}{z \cdot 2}}\\ \mathbf{elif}\;y \le 1.488359269655058698602859488441319618704 \cdot 10^{-214}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{\left(z \cdot 2\right) \cdot z - t \cdot y}{y}}{z \cdot 2}}\\ \end{array}\]

x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}

↓

\begin{array}{l}
\mathbf{if}\;y \le -7.155484423493136172297234653917029205289 \cdot 10^{-54}:\\
\;\;\;\;x - \frac{1}{\frac{\frac{\left(z \cdot 2\right) \cdot z - t \cdot y}{y}}{z \cdot 2}}\\

\mathbf{elif}\;y \le 1.488359269655058698602859488441319618704 \cdot 10^{-214}:\\
\;\;\;\;x\\

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

\end{array}

double f(double x, double y, double z, double t) {
        double r20189638 = x;
        double r20189639 = y;
        double r20189640 = 2.0;
        double r20189641 = r20189639 * r20189640;
        double r20189642 = z;
        double r20189643 = r20189641 * r20189642;
        double r20189644 = r20189642 * r20189640;
        double r20189645 = r20189644 * r20189642;
        double r20189646 = t;
        double r20189647 = r20189639 * r20189646;
        double r20189648 = r20189645 - r20189647;
        double r20189649 = r20189643 / r20189648;
        double r20189650 = r20189638 - r20189649;
        return r20189650;
}

↓

double f(double x, double y, double z, double t) {
        double r20189651 = y;
        double r20189652 = -7.155484423493136e-54;
        bool r20189653 = r20189651 <= r20189652;
        double r20189654 = x;
        double r20189655 = 1.0;
        double r20189656 = z;
        double r20189657 = 2.0;
        double r20189658 = r20189656 * r20189657;
        double r20189659 = r20189658 * r20189656;
        double r20189660 = t;
        double r20189661 = r20189660 * r20189651;
        double r20189662 = r20189659 - r20189661;
        double r20189663 = r20189662 / r20189651;
        double r20189664 = r20189663 / r20189658;
        double r20189665 = r20189655 / r20189664;
        double r20189666 = r20189654 - r20189665;
        double r20189667 = 1.4883592696550587e-214;
        bool r20189668 = r20189651 <= r20189667;
        double r20189669 = r20189668 ? r20189654 : r20189666;
        double r20189670 = r20189653 ? r20189666 : r20189669;
        return r20189670;
}

Original	11.6
Target	0.1
Herbie	7.1

Derivation

Split input into 2 regimes
if y < -7.155484423493136e-54 or 1.4883592696550587e-214 < y
1. Initial program 13.7
  \[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
2. Using strategy rm
3. Applied clear-num13.7
  \[\leadsto x - \color{blue}{\frac{1}{\frac{\left(z \cdot 2\right) \cdot z - y \cdot t}{\left(y \cdot 2\right) \cdot z}}}\]
4. Simplified7.0
  \[\leadsto x - \frac{1}{\color{blue}{\frac{\frac{z \cdot \left(z \cdot 2\right) - t \cdot y}{y}}{z \cdot 2}}}\]
if -7.155484423493136e-54 < y < 1.4883592696550587e-214
1. Initial program 6.1
  \[x - \frac{\left(y \cdot 2\right) \cdot z}{\left(z \cdot 2\right) \cdot z - y \cdot t}\]
2. Simplified4.4
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z \cdot 2}{\mathsf{fma}\left(-y, t, \left(z \cdot 2\right) \cdot z\right)}, -y, x\right)}\]
3. Taylor expanded around 0 7.2
  \[\leadsto \color{blue}{x}\]
Recombined 2 regimes into one program.
Final simplification7.1
\[\leadsto \begin{array}{l} \mathbf{if}\;y \le -7.155484423493136172297234653917029205289 \cdot 10^{-54}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{\left(z \cdot 2\right) \cdot z - t \cdot y}{y}}{z \cdot 2}}\\ \mathbf{elif}\;y \le 1.488359269655058698602859488441319618704 \cdot 10^{-214}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{\left(z \cdot 2\right) \cdot z - t \cdot y}{y}}{z \cdot 2}}\\ \end{array}\]

Error

Try it out

Target

Derivation

`if y < -7.155484423493136e-54 or 1.4883592696550587e-214 < y`

`if -7.155484423493136e-54 < y < 1.4883592696550587e-214`

Reproduce

In
Out