Average Error: 2.0 → 1.2
Time: 38.0s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le 2.289140927704578058538453283100075846866 \cdot 10^{-92}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(a \cdot t + \left(x + y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot z + t\right) + \left(x + y \cdot z\right)\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;a \le 2.289140927704578058538453283100075846866 \cdot 10^{-92}:\\
\;\;\;\;\left(z \cdot a\right) \cdot b + \left(a \cdot t + \left(x + y \cdot z\right)\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r32090849 = x;
        double r32090850 = y;
        double r32090851 = z;
        double r32090852 = r32090850 * r32090851;
        double r32090853 = r32090849 + r32090852;
        double r32090854 = t;
        double r32090855 = a;
        double r32090856 = r32090854 * r32090855;
        double r32090857 = r32090853 + r32090856;
        double r32090858 = r32090855 * r32090851;
        double r32090859 = b;
        double r32090860 = r32090858 * r32090859;
        double r32090861 = r32090857 + r32090860;
        return r32090861;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r32090862 = a;
        double r32090863 = 2.289140927704578e-92;
        bool r32090864 = r32090862 <= r32090863;
        double r32090865 = z;
        double r32090866 = r32090865 * r32090862;
        double r32090867 = b;
        double r32090868 = r32090866 * r32090867;
        double r32090869 = t;
        double r32090870 = r32090862 * r32090869;
        double r32090871 = x;
        double r32090872 = y;
        double r32090873 = r32090872 * r32090865;
        double r32090874 = r32090871 + r32090873;
        double r32090875 = r32090870 + r32090874;
        double r32090876 = r32090868 + r32090875;
        double r32090877 = r32090867 * r32090865;
        double r32090878 = r32090877 + r32090869;
        double r32090879 = r32090862 * r32090878;
        double r32090880 = r32090879 + r32090874;
        double r32090881 = r32090864 ? r32090876 : r32090880;
        return r32090881;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original2.0
Target0.3
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888128:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.758974318836428710669076838657752600596 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < 2.289140927704578e-92

    1. Initial program 1.5

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

    if 2.289140927704578e-92 < a

    1. Initial program 3.5

      \[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
    2. Using strategy rm

    3. Applied associate-+l+3.5

      \[\leadsto \color{blue}{\left(x + y \cdot z\right) + \left(t \cdot a + \left(a \cdot z\right) \cdot b\right)}\]

    4. Simplified0.4

      \[\leadsto \left(x + y \cdot z\right) + \color{blue}{a \cdot \left(b \cdot z + t\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le 2.289140927704578058538453283100075846866 \cdot 10^{-92}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(a \cdot t + \left(x + y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot z + t\right) + \left(x + y \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(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)))