\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]

↓

\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -2.37460898105936542 \cdot 10^{120} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 2.15379248506655815 \cdot 10^{115}\right):\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \end{array}\]

\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b

↓

\begin{array}{l}
\mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -2.37460898105936542 \cdot 10^{120} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 2.15379248506655815 \cdot 10^{115}\right):\\
\;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r815447 = x;
        double r815448 = 2.0;
        double r815449 = r815447 * r815448;
        double r815450 = y;
        double r815451 = 9.0;
        double r815452 = r815450 * r815451;
        double r815453 = z;
        double r815454 = r815452 * r815453;
        double r815455 = t;
        double r815456 = r815454 * r815455;
        double r815457 = r815449 - r815456;
        double r815458 = a;
        double r815459 = 27.0;
        double r815460 = r815458 * r815459;
        double r815461 = b;
        double r815462 = r815460 * r815461;
        double r815463 = r815457 + r815462;
        return r815463;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r815464 = y;
        double r815465 = 9.0;
        double r815466 = r815464 * r815465;
        double r815467 = z;
        double r815468 = r815466 * r815467;
        double r815469 = -2.3746089810593654e+120;
        bool r815470 = r815468 <= r815469;
        double r815471 = 2.153792485066558e+115;
        bool r815472 = r815468 <= r815471;
        double r815473 = !r815472;
        bool r815474 = r815470 || r815473;
        double r815475 = a;
        double r815476 = 27.0;
        double r815477 = b;
        double r815478 = r815476 * r815477;
        double r815479 = x;
        double r815480 = 2.0;
        double r815481 = r815479 * r815480;
        double r815482 = t;
        double r815483 = r815467 * r815482;
        double r815484 = r815465 * r815483;
        double r815485 = r815464 * r815484;
        double r815486 = r815481 - r815485;
        double r815487 = fma(r815475, r815478, r815486);
        double r815488 = r815475 * r815477;
        double r815489 = r815476 * r815488;
        double r815490 = r815467 * r815464;
        double r815491 = r815482 * r815490;
        double r815492 = r815465 * r815491;
        double r815493 = r815489 - r815492;
        double r815494 = fma(r815480, r815479, r815493);
        double r815495 = r815474 ? r815487 : r815494;
        return r815495;
}

Original	4.0
Target	2.8
Herbie	0.9

Derivation

Split input into 2 regimes
if (* (* y 9.0) z) < -2.3746089810593654e+120 or 2.153792485066558e+115 < (* (* y 9.0) z)
1. Initial program 16.9
  \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
2. Simplified17.0
  \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)}\]
3. Using strategy rm
4. Applied associate-*l*3.2
  \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right)\]
5. Using strategy rm
6. Applied associate-*l*2.8
  \[\leadsto \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)}\right)\]
if -2.3746089810593654e+120 < (* (* y 9.0) z) < 2.153792485066558e+115
1. Initial program 0.4
  \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
2. Simplified0.5
  \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)}\]
3. Taylor expanded around inf 0.4
  \[\leadsto \color{blue}{\left(2 \cdot x + 27 \cdot \left(a \cdot b\right)\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)}\]
4. Simplified0.4
  \[\leadsto \color{blue}{\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)}\]
Recombined 2 regimes into one program.
Final simplification0.9
\[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -2.37460898105936542 \cdot 10^{120} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 2.15379248506655815 \cdot 10^{115}\right):\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(2, x, 27 \cdot \left(a \cdot b\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \end{array}\]

Error

Target

Derivation

`if (* (* y 9.0) z) < -2.3746089810593654e+120 or 2.153792485066558e+115 < (* (* y 9.0) z)`

`if -2.3746089810593654e+120 < (* (* y 9.0) z) < 2.153792485066558e+115`

Reproduce