Average Error: 2.2 → 0.5
Time: 38.8s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;a \le -689220297669389697679360:\\ \;\;\;\;\left(a \cdot t + \left(x + z \cdot y\right)\right) + a \cdot \left(b \cdot z\right)\\ \mathbf{elif}\;a \le 1.08509508461724670436922945007558543031 \cdot 10^{-107}:\\ \;\;\;\;\left(a \cdot t + \left(x + z \cdot y\right)\right) + \left(z \cdot a\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot t + \left(x + z \cdot y\right)\right) + a \cdot \left(b \cdot z\right)\\ \end{array}\]
\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 r35150109 = x;
        double r35150110 = y;
        double r35150111 = z;
        double r35150112 = r35150110 * r35150111;
        double r35150113 = r35150109 + r35150112;
        double r35150114 = t;
        double r35150115 = a;
        double r35150116 = r35150114 * r35150115;
        double r35150117 = r35150113 + r35150116;
        double r35150118 = r35150115 * r35150111;
        double r35150119 = b;
        double r35150120 = r35150118 * r35150119;
        double r35150121 = r35150117 + r35150120;
        return r35150121;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r35150122 = a;
        double r35150123 = -6.892202976693897e+23;
        bool r35150124 = r35150122 <= r35150123;
        double r35150125 = t;
        double r35150126 = r35150122 * r35150125;
        double r35150127 = x;
        double r35150128 = z;
        double r35150129 = y;
        double r35150130 = r35150128 * r35150129;
        double r35150131 = r35150127 + r35150130;
        double r35150132 = r35150126 + r35150131;
        double r35150133 = b;
        double r35150134 = r35150133 * r35150128;
        double r35150135 = r35150122 * r35150134;
        double r35150136 = r35150132 + r35150135;
        double r35150137 = 1.0850950846172467e-107;
        bool r35150138 = r35150122 <= r35150137;
        double r35150139 = r35150128 * r35150122;
        double r35150140 = r35150139 * r35150133;
        double r35150141 = r35150132 + r35150140;
        double r35150142 = r35150138 ? r35150141 : r35150136;
        double r35150143 = r35150124 ? r35150136 : r35150142;
        return r35150143;
}

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 
(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)))