Average Error: 2.1 → 0.4
Time: 5.2s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.56568825374803224 \cdot 10^{-24} \lor \neg \left(a \le 6.8883938354389204 \cdot 10^{-97}\right):\\ \;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(a \cdot z\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{b}\\ \end{array}\]
\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 -1.56568825374803224 \cdot 10^{-24} \lor \neg \left(a \le 6.8883938354389204 \cdot 10^{-97}\right):\\
\;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(a \cdot z\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{b}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r706959 = x;
        double r706960 = y;
        double r706961 = z;
        double r706962 = r706960 * r706961;
        double r706963 = r706959 + r706962;
        double r706964 = t;
        double r706965 = a;
        double r706966 = r706964 * r706965;
        double r706967 = r706963 + r706966;
        double r706968 = r706965 * r706961;
        double r706969 = b;
        double r706970 = r706968 * r706969;
        double r706971 = r706967 + r706970;
        return r706971;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r706972 = a;
        double r706973 = -1.5656882537480322e-24;
        bool r706974 = r706972 <= r706973;
        double r706975 = 6.88839383543892e-97;
        bool r706976 = r706972 <= r706975;
        double r706977 = !r706976;
        bool r706978 = r706974 || r706977;
        double r706979 = y;
        double r706980 = z;
        double r706981 = r706979 * r706980;
        double r706982 = x;
        double r706983 = t;
        double r706984 = b;
        double r706985 = r706980 * r706984;
        double r706986 = r706983 + r706985;
        double r706987 = r706972 * r706986;
        double r706988 = r706982 + r706987;
        double r706989 = r706981 + r706988;
        double r706990 = r706982 + r706981;
        double r706991 = r706983 * r706972;
        double r706992 = r706990 + r706991;
        double r706993 = r706972 * r706980;
        double r706994 = cbrt(r706984);
        double r706995 = r706994 * r706994;
        double r706996 = r706993 * r706995;
        double r706997 = r706996 * r706994;
        double r706998 = r706992 + r706997;
        double r706999 = r706978 ? r706989 : r706998;
        return r706999;
}

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

Original2.1
Target0.4
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888000:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.75897431883642871 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -1.5656882537480322e-24 or 6.88839383543892e-97 < a

    1. Initial program 3.9

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

    2. Simplified0.5

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

    if -1.5656882537480322e-24 < a < 6.88839383543892e-97

    1. Initial program 0.3

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

    3. Applied add-cube-cbrt0.4

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \sqrt[3]{b}\right)}\]

    4. Applied associate-*r*0.4

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.56568825374803224 \cdot 10^{-24} \lor \neg \left(a \le 6.8883938354389204 \cdot 10^{-97}\right):\\ \;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\left(a \cdot z\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{b}\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 
(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)))