Average Error: 2.0 → 1.4
Time: 10.0s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le 6.172014095867321 \cdot 10^{+119}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(a \cdot t + \left(x + y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(t + b \cdot z\right) + x\right) + y \cdot z\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;a \le 6.172014095867321 \cdot 10^{+119}:\\
\;\;\;\;\left(z \cdot a\right) \cdot b + \left(a \cdot t + \left(x + y \cdot z\right)\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r13242612 = x;
        double r13242613 = y;
        double r13242614 = z;
        double r13242615 = r13242613 * r13242614;
        double r13242616 = r13242612 + r13242615;
        double r13242617 = t;
        double r13242618 = a;
        double r13242619 = r13242617 * r13242618;
        double r13242620 = r13242616 + r13242619;
        double r13242621 = r13242618 * r13242614;
        double r13242622 = b;
        double r13242623 = r13242621 * r13242622;
        double r13242624 = r13242620 + r13242623;
        return r13242624;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r13242625 = a;
        double r13242626 = 6.172014095867321e+119;
        bool r13242627 = r13242625 <= r13242626;
        double r13242628 = z;
        double r13242629 = r13242628 * r13242625;
        double r13242630 = b;
        double r13242631 = r13242629 * r13242630;
        double r13242632 = t;
        double r13242633 = r13242625 * r13242632;
        double r13242634 = x;
        double r13242635 = y;
        double r13242636 = r13242635 * r13242628;
        double r13242637 = r13242634 + r13242636;
        double r13242638 = r13242633 + r13242637;
        double r13242639 = r13242631 + r13242638;
        double r13242640 = r13242630 * r13242628;
        double r13242641 = r13242632 + r13242640;
        double r13242642 = r13242625 * r13242641;
        double r13242643 = r13242642 + r13242634;
        double r13242644 = r13242643 + r13242636;
        double r13242645 = r13242627 ? r13242639 : r13242644;
        return r13242645;
}

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
Target0.4
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;z \lt -1.1820553527347888 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.7589743188364287 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < 6.172014095867321e+119

    1. Initial program 1.5

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

    if 6.172014095867321e+119 < a

    1. Initial program 7.0

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

    2. Simplified0.1

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le 6.172014095867321 \cdot 10^{+119}:\\ \;\;\;\;\left(z \cdot a\right) \cdot b + \left(a \cdot t + \left(x + y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot \left(t + b \cdot z\right) + x\right) + y \cdot z\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(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)))