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

↓

\[\begin{array}{l} \mathbf{if}\;z \le -1.356781841784474027900731484822658034209 \cdot 10^{-77} \lor \neg \left(z \le 4.670252803328497878057690068138751516781 \cdot 10^{62}\right):\\ \;\;\;\;\mathsf{fma}\left(t, a, \mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(z, b, t\right) + \left(z \cdot y + x\right)\\ \end{array}\]

\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 -1.356781841784474027900731484822658034209 \cdot 10^{-77} \lor \neg \left(z \le 4.670252803328497878057690068138751516781 \cdot 10^{62}\right):\\
\;\;\;\;\mathsf{fma}\left(t, a, \mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), x\right)\right)\\

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

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r431922 = x;
        double r431923 = y;
        double r431924 = z;
        double r431925 = r431923 * r431924;
        double r431926 = r431922 + r431925;
        double r431927 = t;
        double r431928 = a;
        double r431929 = r431927 * r431928;
        double r431930 = r431926 + r431929;
        double r431931 = r431928 * r431924;
        double r431932 = b;
        double r431933 = r431931 * r431932;
        double r431934 = r431930 + r431933;
        return r431934;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r431935 = z;
        double r431936 = -1.356781841784474e-77;
        bool r431937 = r431935 <= r431936;
        double r431938 = 4.670252803328498e+62;
        bool r431939 = r431935 <= r431938;
        double r431940 = !r431939;
        bool r431941 = r431937 || r431940;
        double r431942 = t;
        double r431943 = a;
        double r431944 = b;
        double r431945 = y;
        double r431946 = fma(r431943, r431944, r431945);
        double r431947 = x;
        double r431948 = fma(r431935, r431946, r431947);
        double r431949 = fma(r431942, r431943, r431948);
        double r431950 = fma(r431935, r431944, r431942);
        double r431951 = r431943 * r431950;
        double r431952 = r431935 * r431945;
        double r431953 = r431952 + r431947;
        double r431954 = r431951 + r431953;
        double r431955 = r431941 ? r431949 : r431954;
        return r431955;
}

Original	2.3
Target	0.3
Herbie	0.2

Derivation

Split input into 2 regimes
if z < -1.356781841784474e-77 or 4.670252803328498e+62 < z
1. Initial program 5.0
  \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
2. Simplified0.3
  \[\leadsto \color{blue}{\mathsf{fma}\left(t, a, \mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), x\right)\right)}\]
if -1.356781841784474e-77 < z < 4.670252803328498e+62
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+0.5
  \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + \left(a \cdot z\right) \cdot b\right)}\]
4. Simplified0.2
  \[\leadsto \left(x + y \cdot z\right) + \color{blue}{a \cdot \mathsf{fma}\left(z, b, t\right)}\]
Recombined 2 regimes into one program.
Final simplification0.2
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.356781841784474027900731484822658034209 \cdot 10^{-77} \lor \neg \left(z \le 4.670252803328497878057690068138751516781 \cdot 10^{62}\right):\\ \;\;\;\;\mathsf{fma}\left(t, a, \mathsf{fma}\left(z, \mathsf{fma}\left(a, b, y\right), x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \mathsf{fma}\left(z, b, t\right) + \left(z \cdot y + x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 +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 < -1.356781841784474e-77 or 4.670252803328498e+62 < z`

`if -1.356781841784474e-77 < z < 4.670252803328498e+62`

Reproduce