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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -4.98598492962298202 \cdot 10^{-158} \lor \neg \left(z \le 6.9390753974297484 \cdot 10^{-149}\right):\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{\frac{a}{t - z}}, y, x\right)\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;z \le -4.98598492962298202 \cdot 10^{-158} \lor \neg \left(z \le 6.9390753974297484 \cdot 10^{-149}\right):\\
\;\;\;\;\left(t - z\right) \cdot \frac{y}{a} + x\\

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

\end{array}

double f(double x, double y, double z, double t, double a) {
        double r311347 = x;
        double r311348 = y;
        double r311349 = z;
        double r311350 = t;
        double r311351 = r311349 - r311350;
        double r311352 = r311348 * r311351;
        double r311353 = a;
        double r311354 = r311352 / r311353;
        double r311355 = r311347 - r311354;
        return r311355;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r311356 = z;
        double r311357 = -4.985984929622982e-158;
        bool r311358 = r311356 <= r311357;
        double r311359 = 6.939075397429748e-149;
        bool r311360 = r311356 <= r311359;
        double r311361 = !r311360;
        bool r311362 = r311358 || r311361;
        double r311363 = t;
        double r311364 = r311363 - r311356;
        double r311365 = y;
        double r311366 = a;
        double r311367 = r311365 / r311366;
        double r311368 = r311364 * r311367;
        double r311369 = x;
        double r311370 = r311368 + r311369;
        double r311371 = 1.0;
        double r311372 = r311366 / r311364;
        double r311373 = r311371 / r311372;
        double r311374 = fma(r311373, r311365, r311369);
        double r311375 = r311362 ? r311370 : r311374;
        return r311375;
}

Original	6.2
Target	0.7
Herbie	2.6

Derivation

Split input into 2 regimes
if z < -4.985984929622982e-158 or 6.939075397429748e-149 < z
1. Initial program 6.9
  \[x - \frac{y \cdot \left(z - t\right)}{a}\]
2. Simplified6.6
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - z}{a}, y, x\right)}\]
3. Using strategy rm
4. Applied clear-num6.6
  \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a}{t - z}}}, y, x\right)\]
5. Using strategy rm
6. Applied fma-udef6.6
  \[\leadsto \color{blue}{\frac{1}{\frac{a}{t - z}} \cdot y + x}\]
7. Simplified2.1
  \[\leadsto \color{blue}{\left(t - z\right) \cdot \frac{y}{a}} + x\]
if -4.985984929622982e-158 < z < 6.939075397429748e-149
1. Initial program 4.2
  \[x - \frac{y \cdot \left(z - t\right)}{a}\]
2. Simplified3.7
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{t - z}{a}, y, x\right)}\]
3. Using strategy rm
4. Applied clear-num3.8
  \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a}{t - z}}}, y, x\right)\]
Recombined 2 regimes into one program.
Final simplification2.6
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4.98598492962298202 \cdot 10^{-158} \lor \neg \left(z \le 6.9390753974297484 \cdot 10^{-149}\right):\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a} + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1}{\frac{a}{t - z}}, y, x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

  (- x (/ (* y (- z t)) a)))

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

Error

Target

Derivation

`if z < -4.985984929622982e-158 or 6.939075397429748e-149 < z`

`if -4.985984929622982e-158 < z < 6.939075397429748e-149`

Reproduce