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

↓

\[\begin{array}{l} \mathbf{if}\;c \le -6.753357285253370739227878007540049072435 \cdot 10^{60}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, z \cdot t - c \cdot \left(a \cdot i + \left(i \cdot b\right) \cdot c\right)\right)\\ \mathbf{elif}\;c \le 120250148987918560:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, \mathsf{fma}\left(z, t, -i \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, z \cdot t - c \cdot \left(a \cdot i + \left(i \cdot b\right) \cdot c\right)\right)\\ \end{array}\]

2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)

↓

\begin{array}{l}
\mathbf{if}\;c \le -6.753357285253370739227878007540049072435 \cdot 10^{60}:\\
\;\;\;\;2 \cdot \mathsf{fma}\left(y, x, z \cdot t - c \cdot \left(a \cdot i + \left(i \cdot b\right) \cdot c\right)\right)\\

\mathbf{elif}\;c \le 120250148987918560:\\
\;\;\;\;2 \cdot \mathsf{fma}\left(y, x, \mathsf{fma}\left(z, t, -i \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot c\right)\right)\right)\\

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

\end{array}

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r80689468 = 2.0;
        double r80689469 = x;
        double r80689470 = y;
        double r80689471 = r80689469 * r80689470;
        double r80689472 = z;
        double r80689473 = t;
        double r80689474 = r80689472 * r80689473;
        double r80689475 = r80689471 + r80689474;
        double r80689476 = a;
        double r80689477 = b;
        double r80689478 = c;
        double r80689479 = r80689477 * r80689478;
        double r80689480 = r80689476 + r80689479;
        double r80689481 = r80689480 * r80689478;
        double r80689482 = i;
        double r80689483 = r80689481 * r80689482;
        double r80689484 = r80689475 - r80689483;
        double r80689485 = r80689468 * r80689484;
        return r80689485;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r80689486 = c;
        double r80689487 = -6.753357285253371e+60;
        bool r80689488 = r80689486 <= r80689487;
        double r80689489 = 2.0;
        double r80689490 = y;
        double r80689491 = x;
        double r80689492 = z;
        double r80689493 = t;
        double r80689494 = r80689492 * r80689493;
        double r80689495 = a;
        double r80689496 = i;
        double r80689497 = r80689495 * r80689496;
        double r80689498 = b;
        double r80689499 = r80689496 * r80689498;
        double r80689500 = r80689499 * r80689486;
        double r80689501 = r80689497 + r80689500;
        double r80689502 = r80689486 * r80689501;
        double r80689503 = r80689494 - r80689502;
        double r80689504 = fma(r80689490, r80689491, r80689503);
        double r80689505 = r80689489 * r80689504;
        double r80689506 = 1.2025014898791856e+17;
        bool r80689507 = r80689486 <= r80689506;
        double r80689508 = fma(r80689498, r80689486, r80689495);
        double r80689509 = r80689508 * r80689486;
        double r80689510 = r80689496 * r80689509;
        double r80689511 = -r80689510;
        double r80689512 = fma(r80689492, r80689493, r80689511);
        double r80689513 = fma(r80689490, r80689491, r80689512);
        double r80689514 = r80689489 * r80689513;
        double r80689515 = r80689507 ? r80689514 : r80689505;
        double r80689516 = r80689488 ? r80689505 : r80689515;
        return r80689516;
}

Original	6.8
Target	1.8
Herbie	1.5

Derivation

Split input into 2 regimes
if c < -6.753357285253371e+60 or 1.2025014898791856e+17 < c
1. Initial program 23.8
  \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
2. Simplified23.8
  \[\leadsto \color{blue}{2 \cdot \mathsf{fma}\left(y, x, z \cdot t - i \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot c\right)\right)}\]
3. Using strategy rm
4. Applied associate-*r*3.7
  \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \color{blue}{\left(i \cdot \mathsf{fma}\left(b, c, a\right)\right) \cdot c}\right)\]
5. Taylor expanded around inf 31.4
  \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \color{blue}{\left(i \cdot \left(b \cdot {c}^{2}\right) + a \cdot \left(i \cdot c\right)\right)}\right)\]
6. Simplified3.3
  \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, z \cdot t - \color{blue}{c \cdot \left(a \cdot i + \left(i \cdot b\right) \cdot c\right)}\right)\]
if -6.753357285253371e+60 < c < 1.2025014898791856e+17
1. Initial program 0.9
  \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
2. Simplified0.9
  \[\leadsto \color{blue}{2 \cdot \mathsf{fma}\left(y, x, z \cdot t - i \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot c\right)\right)}\]
3. Using strategy rm
4. Applied fma-neg0.9
  \[\leadsto 2 \cdot \mathsf{fma}\left(y, x, \color{blue}{\mathsf{fma}\left(z, t, -i \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot c\right)\right)}\right)\]
Recombined 2 regimes into one program.
Final simplification1.5
\[\leadsto \begin{array}{l} \mathbf{if}\;c \le -6.753357285253370739227878007540049072435 \cdot 10^{60}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, z \cdot t - c \cdot \left(a \cdot i + \left(i \cdot b\right) \cdot c\right)\right)\\ \mathbf{elif}\;c \le 120250148987918560:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, \mathsf{fma}\left(z, t, -i \cdot \left(\mathsf{fma}\left(b, c, a\right) \cdot c\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \mathsf{fma}\left(y, x, z \cdot t - c \cdot \left(a \cdot i + \left(i \cdot b\right) \cdot c\right)\right)\\ \end{array}\]

Error

Target

Derivation

`if c < -6.753357285253371e+60 or 1.2025014898791856e+17 < c`

`if -6.753357285253371e+60 < c < 1.2025014898791856e+17`

Reproduce