Average Error: 2.2 → 0.4
Time: 10.5s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b = -\infty \lor \neg \left(\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le 5.116019414478908543360651182801591114306 \cdot 10^{293}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right) + \left(x + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b = -\infty \lor \neg \left(\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le 5.116019414478908543360651182801591114306 \cdot 10^{293}\right):\\
\;\;\;\;a \cdot \left(t + z \cdot b\right) + \left(x + y \cdot z\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 r404597 = x;
        double r404598 = y;
        double r404599 = z;
        double r404600 = r404598 * r404599;
        double r404601 = r404597 + r404600;
        double r404602 = t;
        double r404603 = a;
        double r404604 = r404602 * r404603;
        double r404605 = r404601 + r404604;
        double r404606 = r404603 * r404599;
        double r404607 = b;
        double r404608 = r404606 * r404607;
        double r404609 = r404605 + r404608;
        return r404609;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r404610 = x;
        double r404611 = y;
        double r404612 = z;
        double r404613 = r404611 * r404612;
        double r404614 = r404610 + r404613;
        double r404615 = t;
        double r404616 = a;
        double r404617 = r404615 * r404616;
        double r404618 = r404614 + r404617;
        double r404619 = r404616 * r404612;
        double r404620 = b;
        double r404621 = r404619 * r404620;
        double r404622 = r404618 + r404621;
        double r404623 = -inf.0;
        bool r404624 = r404622 <= r404623;
        double r404625 = 5.1160194144789085e+293;
        bool r404626 = r404622 <= r404625;
        double r404627 = !r404626;
        bool r404628 = r404624 || r404627;
        double r404629 = r404612 * r404620;
        double r404630 = r404615 + r404629;
        double r404631 = r404616 * r404630;
        double r404632 = r404631 + r404614;
        double r404633 = r404628 ? r404632 : r404622;
        return r404633;
}

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
Target0.4
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888128:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.758974318836428710669076838657752600596 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)) < -inf.0 or 5.1160194144789085e+293 < (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b))

    1. Initial program 34.0

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

    2. Simplified2.1

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

    if -inf.0 < (+ (+ (+ x (* y z)) (* t a)) (* (* a z) b)) < 5.1160194144789085e+293

    1. Initial program 0.3

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b = -\infty \lor \neg \left(\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b \le 5.116019414478908543360651182801591114306 \cdot 10^{293}\right):\\ \;\;\;\;a \cdot \left(t + z \cdot b\right) + \left(x + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(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)))