\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le -5.157691058688136 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(t, a, \mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), x\right)\right)\\ \mathbf{elif}\;z \le 2.415354527944333 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(b \cdot z\right) + \left(\left(z \cdot y + x\right) + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, a, \mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), x\right)\right)\\ \end{array}\]

\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b

↓

\begin{array}{l}
\mathbf{if}\;z \le -5.157691058688136 \cdot 10^{+22}:\\
\;\;\;\;\mathsf{fma}\left(t, a, \mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), x\right)\right)\\

\mathbf{elif}\;z \le 2.415354527944333 \cdot 10^{-97}:\\
\;\;\;\;a \cdot \left(b \cdot z\right) + \left(\left(z \cdot y + x\right) + t \cdot a\right)\\

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

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r22915333 = x;
        double r22915334 = y;
        double r22915335 = z;
        double r22915336 = r22915334 * r22915335;
        double r22915337 = r22915333 + r22915336;
        double r22915338 = t;
        double r22915339 = a;
        double r22915340 = r22915338 * r22915339;
        double r22915341 = r22915337 + r22915340;
        double r22915342 = r22915339 * r22915335;
        double r22915343 = b;
        double r22915344 = r22915342 * r22915343;
        double r22915345 = r22915341 + r22915344;
        return r22915345;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r22915346 = z;
        double r22915347 = -5.157691058688136e+22;
        bool r22915348 = r22915346 <= r22915347;
        double r22915349 = t;
        double r22915350 = a;
        double r22915351 = b;
        double r22915352 = y;
        double r22915353 = fma(r22915350, r22915351, r22915352);
        double r22915354 = x;
        double r22915355 = fma(r22915346, r22915353, r22915354);
        double r22915356 = fma(r22915349, r22915350, r22915355);
        double r22915357 = 2.415354527944333e-97;
        bool r22915358 = r22915346 <= r22915357;
        double r22915359 = r22915351 * r22915346;
        double r22915360 = r22915350 * r22915359;
        double r22915361 = r22915346 * r22915352;
        double r22915362 = r22915361 + r22915354;
        double r22915363 = r22915349 * r22915350;
        double r22915364 = r22915362 + r22915363;
        double r22915365 = r22915360 + r22915364;
        double r22915366 = r22915358 ? r22915365 : r22915356;
        double r22915367 = r22915348 ? r22915356 : r22915366;
        return r22915367;
}

Original	1.9
Target	0.4
Herbie	0.2

Derivation

Split input into 2 regimes
if z < -5.157691058688136e+22 or 2.415354527944333e-97 < z
1. Initial program 3.6
  \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
2. Simplified0.4
  \[\leadsto \color{blue}{\mathsf{fma}\left(t, a, \mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), x\right)\right)}\]
if -5.157691058688136e+22 < z < 2.415354527944333e-97
1. Initial program 0.5
  \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
2. Using strategy rm
3. Applied associate-*l*0.1
  \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{a \cdot \left(z \cdot b\right)}\]
Recombined 2 regimes into one program.
Final simplification0.2
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -5.157691058688136 \cdot 10^{+22}:\\ \;\;\;\;\mathsf{fma}\left(t, a, \mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), x\right)\right)\\ \mathbf{elif}\;z \le 2.415354527944333 \cdot 10^{-97}:\\ \;\;\;\;a \cdot \left(b \cdot z\right) + \left(\left(z \cdot y + x\right) + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, a, \mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), x\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"

  :herbie-target
  (if (< z -1.1820553527347888e+19) (+ (* z (+ (* b a) y)) (+ x (* t a))) (if (< z 4.7589743188364287e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))

Error

Target

Derivation

`if z < -5.157691058688136e+22 or 2.415354527944333e-97 < z`

`if -5.157691058688136e+22 < z < 2.415354527944333e-97`

Reproduce