Average Error: 2.1 → 0.3
Time: 3.8s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -628.151350085825356 \lor \neg \left(b \le 2.74830277152988734 \cdot 10^{70}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \end{array}\]
\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 -628.151350085825356 \lor \neg \left(b \le 2.74830277152988734 \cdot 10^{70}\right):\\
\;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r730471 = x;
        double r730472 = y;
        double r730473 = z;
        double r730474 = r730472 * r730473;
        double r730475 = r730471 + r730474;
        double r730476 = t;
        double r730477 = a;
        double r730478 = r730476 * r730477;
        double r730479 = r730475 + r730478;
        double r730480 = r730477 * r730473;
        double r730481 = b;
        double r730482 = r730480 * r730481;
        double r730483 = r730479 + r730482;
        return r730483;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r730484 = b;
        double r730485 = -628.1513500858254;
        bool r730486 = r730484 <= r730485;
        double r730487 = 2.7483027715298873e+70;
        bool r730488 = r730484 <= r730487;
        double r730489 = !r730488;
        bool r730490 = r730486 || r730489;
        double r730491 = x;
        double r730492 = y;
        double r730493 = z;
        double r730494 = r730492 * r730493;
        double r730495 = r730491 + r730494;
        double r730496 = t;
        double r730497 = a;
        double r730498 = r730496 * r730497;
        double r730499 = r730495 + r730498;
        double r730500 = r730497 * r730493;
        double r730501 = r730500 * r730484;
        double r730502 = r730499 + r730501;
        double r730503 = r730493 * r730484;
        double r730504 = r730496 + r730503;
        double r730505 = r730497 * r730504;
        double r730506 = r730491 + r730505;
        double r730507 = r730494 + r730506;
        double r730508 = r730490 ? r730502 : r730507;
        return r730508;
}

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

Original2.1
Target0.4
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888000:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.75897431883642871 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if b < -628.1513500858254 or 2.7483027715298873e+70 < b

    1. Initial program 0.5

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

    if -628.1513500858254 < b < 2.7483027715298873e+70

    1. Initial program 3.2

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

    2. Simplified0.2

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -628.151350085825356 \lor \neg \left(b \le 2.74830277152988734 \cdot 10^{70}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot z + \left(x + a \cdot \left(t + z \cdot b\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 
(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)))