Average Error: 1.9 → 0.1
Time: 11.6s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -9.83355154561418 \cdot 10^{+29}:\\ \;\;\;\;\left(x + t \cdot a\right) + \left(b \cdot a + y\right) \cdot z\\ \mathbf{elif}\;z \le 1.2529910400748553 \cdot 10^{-43}:\\ \;\;\;\;\left(z \cdot y + x\right) + a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + t \cdot a\right) + \left(b \cdot a + y\right) \cdot z\\ \end{array}\]
\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 -9.83355154561418 \cdot 10^{+29}:\\
\;\;\;\;\left(x + t \cdot a\right) + \left(b \cdot a + y\right) \cdot z\\

\mathbf{elif}\;z \le 1.2529910400748553 \cdot 10^{-43}:\\
\;\;\;\;\left(z \cdot y + x\right) + a \cdot \left(t + b \cdot z\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r32941981 = x;
        double r32941982 = y;
        double r32941983 = z;
        double r32941984 = r32941982 * r32941983;
        double r32941985 = r32941981 + r32941984;
        double r32941986 = t;
        double r32941987 = a;
        double r32941988 = r32941986 * r32941987;
        double r32941989 = r32941985 + r32941988;
        double r32941990 = r32941987 * r32941983;
        double r32941991 = b;
        double r32941992 = r32941990 * r32941991;
        double r32941993 = r32941989 + r32941992;
        return r32941993;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r32941994 = z;
        double r32941995 = -9.83355154561418e+29;
        bool r32941996 = r32941994 <= r32941995;
        double r32941997 = x;
        double r32941998 = t;
        double r32941999 = a;
        double r32942000 = r32941998 * r32941999;
        double r32942001 = r32941997 + r32942000;
        double r32942002 = b;
        double r32942003 = r32942002 * r32941999;
        double r32942004 = y;
        double r32942005 = r32942003 + r32942004;
        double r32942006 = r32942005 * r32941994;
        double r32942007 = r32942001 + r32942006;
        double r32942008 = 1.2529910400748553e-43;
        bool r32942009 = r32941994 <= r32942008;
        double r32942010 = r32941994 * r32942004;
        double r32942011 = r32942010 + r32941997;
        double r32942012 = r32942002 * r32941994;
        double r32942013 = r32941998 + r32942012;
        double r32942014 = r32941999 * r32942013;
        double r32942015 = r32942011 + r32942014;
        double r32942016 = r32942009 ? r32942015 : r32942007;
        double r32942017 = r32941996 ? r32942007 : r32942016;
        return r32942017;
}

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
Target0.4
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;z \lt -1.1820553527347888 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -9.83355154561418e+29 or 1.2529910400748553e-43 < z

    1. Initial program 4.1

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

    2. Simplified0.2

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

    if -9.83355154561418e+29 < z < 1.2529910400748553e-43

    1. Initial program 0.4

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

    3. Applied associate-+l+0.4

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

    4. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -9.83355154561418 \cdot 10^{+29}:\\ \;\;\;\;\left(x + t \cdot a\right) + \left(b \cdot a + y\right) \cdot z\\ \mathbf{elif}\;z \le 1.2529910400748553 \cdot 10^{-43}:\\ \;\;\;\;\left(z \cdot y + x\right) + a \cdot \left(t + b \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + t \cdot a\right) + \left(b \cdot a + y\right) \cdot z\\ \end{array}\]

Reproduce

herbie shell --seed 2019165 
(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)))