Average Error: 2.2 → 0.3
Time: 11.3s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -6.443929933701575879273593458019847563077 \cdot 10^{-29} \lor \neg \left(b \le 5.207363882734844879707840428975175994284 \cdot 10^{45}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + a \cdot \left(z \cdot b\right)\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;b \le -6.443929933701575879273593458019847563077 \cdot 10^{-29} \lor \neg \left(b \le 5.207363882734844879707840428975175994284 \cdot 10^{45}\right):\\
\;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r470337 = x;
        double r470338 = y;
        double r470339 = z;
        double r470340 = r470338 * r470339;
        double r470341 = r470337 + r470340;
        double r470342 = t;
        double r470343 = a;
        double r470344 = r470342 * r470343;
        double r470345 = r470341 + r470344;
        double r470346 = r470343 * r470339;
        double r470347 = b;
        double r470348 = r470346 * r470347;
        double r470349 = r470345 + r470348;
        return r470349;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r470350 = b;
        double r470351 = -6.443929933701576e-29;
        bool r470352 = r470350 <= r470351;
        double r470353 = 5.207363882734845e+45;
        bool r470354 = r470350 <= r470353;
        double r470355 = !r470354;
        bool r470356 = r470352 || r470355;
        double r470357 = x;
        double r470358 = y;
        double r470359 = z;
        double r470360 = r470358 * r470359;
        double r470361 = r470357 + r470360;
        double r470362 = t;
        double r470363 = a;
        double r470364 = r470362 * r470363;
        double r470365 = r470361 + r470364;
        double r470366 = r470363 * r470359;
        double r470367 = r470366 * r470350;
        double r470368 = r470365 + r470367;
        double r470369 = r470359 * r470350;
        double r470370 = r470363 * r470369;
        double r470371 = r470365 + r470370;
        double r470372 = r470356 ? r470368 : r470371;
        return r470372;
}

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
Target0.3
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888128:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.758974318836428710669076838657752600596 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if b < -6.443929933701576e-29 or 5.207363882734845e+45 < b

    1. Initial program 0.7

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

    if -6.443929933701576e-29 < b < 5.207363882734845e+45

    1. Initial program 3.4

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

    3. Applied associate-*l*0.1

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -6.443929933701575879273593458019847563077 \cdot 10^{-29} \lor \neg \left(b \le 5.207363882734844879707840428975175994284 \cdot 10^{45}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + a \cdot \left(z \cdot b\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019305 
(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 4.75897431883642871e-122) (+ (* (+ (* b z) t) a) (+ (* z y) x)) (+ (* z (+ (* b a) y)) (+ x (* t a)))))

  (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)))