Average Error: 1.9 → 1.6
Time: 4.9s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -1.6607943700588965 \cdot 10^{-190}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \end{array}\]
\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 -1.6607943700588965 \cdot 10^{-190}:\\
\;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + a \cdot \left(z \cdot b\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 r669337 = x;
        double r669338 = y;
        double r669339 = z;
        double r669340 = r669338 * r669339;
        double r669341 = r669337 + r669340;
        double r669342 = t;
        double r669343 = a;
        double r669344 = r669342 * r669343;
        double r669345 = r669341 + r669344;
        double r669346 = r669343 * r669339;
        double r669347 = b;
        double r669348 = r669346 * r669347;
        double r669349 = r669345 + r669348;
        return r669349;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r669350 = a;
        double r669351 = -1.6607943700588965e-190;
        bool r669352 = r669350 <= r669351;
        double r669353 = x;
        double r669354 = y;
        double r669355 = z;
        double r669356 = r669354 * r669355;
        double r669357 = r669353 + r669356;
        double r669358 = t;
        double r669359 = r669358 * r669350;
        double r669360 = r669357 + r669359;
        double r669361 = b;
        double r669362 = r669355 * r669361;
        double r669363 = r669350 * r669362;
        double r669364 = r669360 + r669363;
        double r669365 = r669350 * r669355;
        double r669366 = r669365 * r669361;
        double r669367 = r669360 + r669366;
        double r669368 = r669352 ? r669364 : r669367;
        return r669368;
}

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
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888000:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.75897431883642871 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -1.6607943700588965e-190

    1. Initial program 2.3

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

    3. Applied associate-*l*1.7

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

    if -1.6607943700588965e-190 < a

    1. Initial program 1.6

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

  4. Final simplification1.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -1.6607943700588965 \cdot 10^{-190}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + a \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(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)))