Average Error: 1.9 → 1.2
Time: 4.7s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.67032308676182466 \cdot 10^{79}:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot \left(z \cdot b + t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \end{array}\]
\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 -1.67032308676182466 \cdot 10^{79}:\\
\;\;\;\;\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 r805827 = x;
        double r805828 = y;
        double r805829 = z;
        double r805830 = r805828 * r805829;
        double r805831 = r805827 + r805830;
        double r805832 = t;
        double r805833 = a;
        double r805834 = r805832 * r805833;
        double r805835 = r805831 + r805834;
        double r805836 = r805833 * r805829;
        double r805837 = b;
        double r805838 = r805836 * r805837;
        double r805839 = r805835 + r805838;
        return r805839;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r805840 = a;
        double r805841 = -1.6703230867618247e+79;
        bool r805842 = r805840 <= r805841;
        double r805843 = x;
        double r805844 = y;
        double r805845 = z;
        double r805846 = r805844 * r805845;
        double r805847 = r805843 + r805846;
        double r805848 = b;
        double r805849 = r805845 * r805848;
        double r805850 = t;
        double r805851 = r805849 + r805850;
        double r805852 = r805840 * r805851;
        double r805853 = r805847 + r805852;
        double r805854 = r805850 * r805840;
        double r805855 = r805847 + r805854;
        double r805856 = r805840 * r805845;
        double r805857 = r805856 * r805848;
        double r805858 = r805855 + r805857;
        double r805859 = r805842 ? r805853 : r805858;
        return r805859;
}

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

Original1.9
Target0.3
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 < -1.6703230867618247e+79

    1. Initial program 6.2

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

    3. Applied associate-+l+6.2

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

    4. Simplified0.1

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

    if -1.6703230867618247e+79 < a

    1. Initial program 1.3

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.67032308676182466 \cdot 10^{79}:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot \left(z \cdot b + t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t a b)
  :name "Graphics.Rasterific.CubicBezier:cachedBezierAt from Rasterific-0.6.1"
  :precision binary64

  :herbie-target
  (if (< z -11820553527347888000) (+ (* 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)))