Average Error: 2.0 → 0.7
Time: 13.0s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -2.286916913862117754718909742314180276625 \cdot 10^{140} \lor \neg \left(b \le 2.423286906516461145384675984050168448583 \cdot 10^{84}\right):\\ \;\;\;\;\left(a \cdot z\right) \cdot b + \left(\left(x + y \cdot z\right) + a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot t + x\right) + z \cdot \left(y + a \cdot b\right)\\ \end{array}\]
\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 -2.286916913862117754718909742314180276625 \cdot 10^{140} \lor \neg \left(b \le 2.423286906516461145384675984050168448583 \cdot 10^{84}\right):\\
\;\;\;\;\left(a \cdot z\right) \cdot b + \left(\left(x + y \cdot z\right) + a \cdot t\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r620457 = x;
        double r620458 = y;
        double r620459 = z;
        double r620460 = r620458 * r620459;
        double r620461 = r620457 + r620460;
        double r620462 = t;
        double r620463 = a;
        double r620464 = r620462 * r620463;
        double r620465 = r620461 + r620464;
        double r620466 = r620463 * r620459;
        double r620467 = b;
        double r620468 = r620466 * r620467;
        double r620469 = r620465 + r620468;
        return r620469;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r620470 = b;
        double r620471 = -2.2869169138621178e+140;
        bool r620472 = r620470 <= r620471;
        double r620473 = 2.423286906516461e+84;
        bool r620474 = r620470 <= r620473;
        double r620475 = !r620474;
        bool r620476 = r620472 || r620475;
        double r620477 = a;
        double r620478 = z;
        double r620479 = r620477 * r620478;
        double r620480 = r620479 * r620470;
        double r620481 = x;
        double r620482 = y;
        double r620483 = r620482 * r620478;
        double r620484 = r620481 + r620483;
        double r620485 = t;
        double r620486 = r620477 * r620485;
        double r620487 = r620484 + r620486;
        double r620488 = r620480 + r620487;
        double r620489 = r620486 + r620481;
        double r620490 = r620477 * r620470;
        double r620491 = r620482 + r620490;
        double r620492 = r620478 * r620491;
        double r620493 = r620489 + r620492;
        double r620494 = r620476 ? r620488 : r620493;
        return r620494;
}

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

Original2.0
Target0.3
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888128:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.758974318836428710669076838657752600596 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if b < -2.2869169138621178e+140 or 2.423286906516461e+84 < b

    1. Initial program 0.9

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

    if -2.2869169138621178e+140 < b < 2.423286906516461e+84

    1. Initial program 2.3

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

    2. Simplified0.7

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -2.286916913862117754718909742314180276625 \cdot 10^{140} \lor \neg \left(b \le 2.423286906516461145384675984050168448583 \cdot 10^{84}\right):\\ \;\;\;\;\left(a \cdot z\right) \cdot b + \left(\left(x + y \cdot z\right) + a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot t + x\right) + z \cdot \left(y + a \cdot b\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019179 
(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)))