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

↓

\[\begin{array}{l} \mathbf{if}\;y \cdot 9 \le -7.76493181041917186 \cdot 10^{-70} \lor \neg \left(y \cdot 9 \le 1.1033717482674748 \cdot 10^{-70}\right):\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array}\]

\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}\;y \cdot 9 \le -7.76493181041917186 \cdot 10^{-70} \lor \neg \left(y \cdot 9 \le 1.1033717482674748 \cdot 10^{-70}\right):\\
\;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right)\\

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

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r745373 = x;
        double r745374 = 2.0;
        double r745375 = r745373 * r745374;
        double r745376 = y;
        double r745377 = 9.0;
        double r745378 = r745376 * r745377;
        double r745379 = z;
        double r745380 = r745378 * r745379;
        double r745381 = t;
        double r745382 = r745380 * r745381;
        double r745383 = r745375 - r745382;
        double r745384 = a;
        double r745385 = 27.0;
        double r745386 = r745384 * r745385;
        double r745387 = b;
        double r745388 = r745386 * r745387;
        double r745389 = r745383 + r745388;
        return r745389;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r745390 = y;
        double r745391 = 9.0;
        double r745392 = r745390 * r745391;
        double r745393 = -7.764931810419172e-70;
        bool r745394 = r745392 <= r745393;
        double r745395 = 1.1033717482674748e-70;
        bool r745396 = r745392 <= r745395;
        double r745397 = !r745396;
        bool r745398 = r745394 || r745397;
        double r745399 = a;
        double r745400 = 27.0;
        double r745401 = r745399 * r745400;
        double r745402 = b;
        double r745403 = x;
        double r745404 = 2.0;
        double r745405 = r745403 * r745404;
        double r745406 = z;
        double r745407 = r745391 * r745406;
        double r745408 = t;
        double r745409 = r745407 * r745408;
        double r745410 = r745390 * r745409;
        double r745411 = r745405 - r745410;
        double r745412 = fma(r745401, r745402, r745411);
        double r745413 = r745399 * r745402;
        double r745414 = r745404 * r745403;
        double r745415 = fma(r745400, r745413, r745414);
        double r745416 = r745406 * r745390;
        double r745417 = r745408 * r745416;
        double r745418 = r745391 * r745417;
        double r745419 = r745415 - r745418;
        double r745420 = r745398 ? r745412 : r745419;
        return r745420;
}

Original	3.7
Target	2.5
Herbie	0.8

Derivation

Split input into 2 regimes
if (* y 9.0) < -7.764931810419172e-70 or 1.1033717482674748e-70 < (* y 9.0)
1. Initial program 6.3
  \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
2. Simplified6.3
  \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)}\]
3. Using strategy rm
4. Applied associate-*l*6.2
  \[\leadsto \mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right)\]
5. Using strategy rm
6. Applied associate-*l*1.1
  \[\leadsto \mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - \color{blue}{y \cdot \left(\left(9 \cdot z\right) \cdot t\right)}\right)\]
if -7.764931810419172e-70 < (* y 9.0) < 1.1033717482674748e-70
1. Initial program 0.5
  \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
2. Simplified0.5
  \[\leadsto \color{blue}{\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)}\]
3. Using strategy rm
4. Applied associate-*l*0.6
  \[\leadsto \mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} \cdot t\right)\]
5. Taylor expanded around inf 0.4
  \[\leadsto \color{blue}{\left(2 \cdot x + 27 \cdot \left(a \cdot b\right)\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)}\]
6. Simplified0.4
  \[\leadsto \color{blue}{\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)}\]
Recombined 2 regimes into one program.
Final simplification0.8
\[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \le -7.76493181041917186 \cdot 10^{-70} \lor \neg \left(y \cdot 9 \le 1.1033717482674748 \cdot 10^{-70}\right):\\ \;\;\;\;\mathsf{fma}\left(a \cdot 27, b, x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(27, a \cdot b, 2 \cdot x\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array}\]

Falling back on racket egraph because egg-herbie package not installed (more)

Error

Target

Derivation

`if (* y 9.0) < -7.764931810419172e-70 or 1.1033717482674748e-70 < (* y 9.0)`

`if -7.764931810419172e-70 < (* y 9.0) < 1.1033717482674748e-70`

Reproduce