Average Error: 2.2 → 1.2
Time: 12.3s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -3.6778195167685823 \cdot 10^{-6}:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot \left(z \cdot b + t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \end{array}\]
\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 -3.6778195167685823 \cdot 10^{-6}:\\
\;\;\;\;\left(x + y \cdot z\right) + a \cdot \left(z \cdot b + t\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r1361764 = x;
        double r1361765 = y;
        double r1361766 = z;
        double r1361767 = r1361765 * r1361766;
        double r1361768 = r1361764 + r1361767;
        double r1361769 = t;
        double r1361770 = a;
        double r1361771 = r1361769 * r1361770;
        double r1361772 = r1361768 + r1361771;
        double r1361773 = r1361770 * r1361766;
        double r1361774 = b;
        double r1361775 = r1361773 * r1361774;
        double r1361776 = r1361772 + r1361775;
        return r1361776;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1361777 = a;
        double r1361778 = -3.6778195167685823e-06;
        bool r1361779 = r1361777 <= r1361778;
        double r1361780 = x;
        double r1361781 = y;
        double r1361782 = z;
        double r1361783 = r1361781 * r1361782;
        double r1361784 = r1361780 + r1361783;
        double r1361785 = b;
        double r1361786 = r1361782 * r1361785;
        double r1361787 = t;
        double r1361788 = r1361786 + r1361787;
        double r1361789 = r1361777 * r1361788;
        double r1361790 = r1361784 + r1361789;
        double r1361791 = r1361787 * r1361777;
        double r1361792 = r1361784 + r1361791;
        double r1361793 = r1361777 * r1361782;
        double r1361794 = r1361793 * r1361785;
        double r1361795 = r1361792 + r1361794;
        double r1361796 = r1361779 ? r1361790 : r1361795;
        return r1361796;
}

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

Original2.2
Target0.4
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888000:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.75897431883642871 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -3.6778195167685823e-06

    1. Initial program 5.2

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

    3. Applied associate-+l+5.2

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

    4. Simplified0.1

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

    if -3.6778195167685823e-06 < a

    1. Initial program 1.5

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -3.6778195167685823 \cdot 10^{-6}:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot \left(z \cdot b + t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 
(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)))