Average Error: 2.2 → 0.5
Time: 30.7s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -689220297669389697679360:\\ \;\;\;\;\left(a \cdot t + \left(x + z \cdot y\right)\right) + a \cdot \left(b \cdot z\right)\\ \mathbf{elif}\;a \le 1.08509508461724670436922945007558543031 \cdot 10^{-107}:\\ \;\;\;\;\left(a \cdot t + \left(x + z \cdot y\right)\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot t + \left(x + z \cdot y\right)\right) + a \cdot \left(b \cdot z\right)\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;a \le -689220297669389697679360:\\
\;\;\;\;\left(a \cdot t + \left(x + z \cdot y\right)\right) + a \cdot \left(b \cdot z\right)\\

\mathbf{elif}\;a \le 1.08509508461724670436922945007558543031 \cdot 10^{-107}:\\
\;\;\;\;\left(a \cdot t + \left(x + z \cdot y\right)\right) + \left(z \cdot a\right) \cdot b\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r27999387 = x;
        double r27999388 = y;
        double r27999389 = z;
        double r27999390 = r27999388 * r27999389;
        double r27999391 = r27999387 + r27999390;
        double r27999392 = t;
        double r27999393 = a;
        double r27999394 = r27999392 * r27999393;
        double r27999395 = r27999391 + r27999394;
        double r27999396 = r27999393 * r27999389;
        double r27999397 = b;
        double r27999398 = r27999396 * r27999397;
        double r27999399 = r27999395 + r27999398;
        return r27999399;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r27999400 = a;
        double r27999401 = -6.892202976693897e+23;
        bool r27999402 = r27999400 <= r27999401;
        double r27999403 = t;
        double r27999404 = r27999400 * r27999403;
        double r27999405 = x;
        double r27999406 = z;
        double r27999407 = y;
        double r27999408 = r27999406 * r27999407;
        double r27999409 = r27999405 + r27999408;
        double r27999410 = r27999404 + r27999409;
        double r27999411 = b;
        double r27999412 = r27999411 * r27999406;
        double r27999413 = r27999400 * r27999412;
        double r27999414 = r27999410 + r27999413;
        double r27999415 = 1.0850950846172467e-107;
        bool r27999416 = r27999400 <= r27999415;
        double r27999417 = r27999406 * r27999400;
        double r27999418 = r27999417 * r27999411;
        double r27999419 = r27999410 + r27999418;
        double r27999420 = r27999416 ? r27999419 : r27999414;
        double r27999421 = r27999402 ? r27999414 : r27999420;
        return r27999421;
}

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
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888128:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.758974318836428710669076838657752600596 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if a < -6.892202976693897e+23 or 1.0850950846172467e-107 < a

    1. Initial program 4.2

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

    3. Applied associate-*l*0.5

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

    if -6.892202976693897e+23 < a < 1.0850950846172467e-107

    1. Initial program 0.4

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;a \le -689220297669389697679360:\\ \;\;\;\;\left(a \cdot t + \left(x + z \cdot y\right)\right) + a \cdot \left(b \cdot z\right)\\ \mathbf{elif}\;a \le 1.08509508461724670436922945007558543031 \cdot 10^{-107}:\\ \;\;\;\;\left(a \cdot t + \left(x + z \cdot y\right)\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot t + \left(x + z \cdot y\right)\right) + a \cdot \left(b \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(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)))