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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -3.01373759864766076 \cdot 10^{106} \lor \neg \left(z \le 9.0608695367454199 \cdot 10^{67}\right):\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\mathsf{fma}\left(b - y, z, y\right)}}{\frac{1}{x \cdot y + z \cdot \left(t - a\right)}}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;z \le -3.01373759864766076 \cdot 10^{106} \lor \neg \left(z \le 9.0608695367454199 \cdot 10^{67}\right):\\
\;\;\;\;\frac{t}{b} - \frac{a}{b}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{1}{\mathsf{fma}\left(b - y, z, y\right)}}{\frac{1}{x \cdot y + z \cdot \left(t - a\right)}}\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r763495 = x;
        double r763496 = y;
        double r763497 = r763495 * r763496;
        double r763498 = z;
        double r763499 = t;
        double r763500 = a;
        double r763501 = r763499 - r763500;
        double r763502 = r763498 * r763501;
        double r763503 = r763497 + r763502;
        double r763504 = b;
        double r763505 = r763504 - r763496;
        double r763506 = r763498 * r763505;
        double r763507 = r763496 + r763506;
        double r763508 = r763503 / r763507;
        return r763508;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r763509 = z;
        double r763510 = -3.0137375986476608e+106;
        bool r763511 = r763509 <= r763510;
        double r763512 = 9.06086953674542e+67;
        bool r763513 = r763509 <= r763512;
        double r763514 = !r763513;
        bool r763515 = r763511 || r763514;
        double r763516 = t;
        double r763517 = b;
        double r763518 = r763516 / r763517;
        double r763519 = a;
        double r763520 = r763519 / r763517;
        double r763521 = r763518 - r763520;
        double r763522 = 1.0;
        double r763523 = y;
        double r763524 = r763517 - r763523;
        double r763525 = fma(r763524, r763509, r763523);
        double r763526 = r763522 / r763525;
        double r763527 = x;
        double r763528 = r763527 * r763523;
        double r763529 = r763516 - r763519;
        double r763530 = r763509 * r763529;
        double r763531 = r763528 + r763530;
        double r763532 = r763522 / r763531;
        double r763533 = r763526 / r763532;
        double r763534 = r763515 ? r763521 : r763533;
        return r763534;
}

Original	23.6
Target	18.0
Herbie	19.7

Derivation

Split input into 2 regimes
if z < -3.0137375986476608e+106 or 9.06086953674542e+67 < z
1. Initial program 45.6
  \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\]
2. Using strategy rm
3. Applied clear-num45.7
  \[\leadsto \color{blue}{\frac{1}{\frac{y + z \cdot \left(b - y\right)}{x \cdot y + z \cdot \left(t - a\right)}}}\]
4. Using strategy rm
5. Applied div-inv45.7
  \[\leadsto \frac{1}{\color{blue}{\left(y + z \cdot \left(b - y\right)\right) \cdot \frac{1}{x \cdot y + z \cdot \left(t - a\right)}}}\]
6. Applied associate-/r*45.7
  \[\leadsto \color{blue}{\frac{\frac{1}{y + z \cdot \left(b - y\right)}}{\frac{1}{x \cdot y + z \cdot \left(t - a\right)}}}\]
7. Simplified45.7
  \[\leadsto \frac{\color{blue}{\frac{1}{\mathsf{fma}\left(b - y, z, y\right)}}}{\frac{1}{x \cdot y + z \cdot \left(t - a\right)}}\]
8. Taylor expanded around inf 34.1
  \[\leadsto \color{blue}{\frac{t}{b} - \frac{a}{b}}\]
if -3.0137375986476608e+106 < z < 9.06086953674542e+67
1. Initial program 11.5
  \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\]
2. Using strategy rm
3. Applied clear-num11.6
  \[\leadsto \color{blue}{\frac{1}{\frac{y + z \cdot \left(b - y\right)}{x \cdot y + z \cdot \left(t - a\right)}}}\]
4. Using strategy rm
5. Applied div-inv11.8
  \[\leadsto \frac{1}{\color{blue}{\left(y + z \cdot \left(b - y\right)\right) \cdot \frac{1}{x \cdot y + z \cdot \left(t - a\right)}}}\]
6. Applied associate-/r*11.7
  \[\leadsto \color{blue}{\frac{\frac{1}{y + z \cdot \left(b - y\right)}}{\frac{1}{x \cdot y + z \cdot \left(t - a\right)}}}\]
7. Simplified11.7
  \[\leadsto \frac{\color{blue}{\frac{1}{\mathsf{fma}\left(b - y, z, y\right)}}}{\frac{1}{x \cdot y + z \cdot \left(t - a\right)}}\]
Recombined 2 regimes into one program.
Final simplification19.7
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.01373759864766076 \cdot 10^{106} \lor \neg \left(z \le 9.0608695367454199 \cdot 10^{67}\right):\\ \;\;\;\;\frac{t}{b} - \frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\mathsf{fma}\left(b - y, z, y\right)}}{\frac{1}{x \cdot y + z \cdot \left(t - a\right)}}\\ \end{array}\]

Error

Target

Derivation

`if z < -3.0137375986476608e+106 or 9.06086953674542e+67 < z`

`if -3.0137375986476608e+106 < z < 9.06086953674542e+67`

Reproduce