Average Error: 2.3 → 2.4
Time: 10.1s
Precision: 64
\[\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.578567063737235255180370993029824399964 \cdot 10^{-145} \lor \neg \left(y \le 3.947860033410908928699063785796365012728 \cdot 10^{-45}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\sqrt[3]{\left(a \cdot z\right) \cdot b} \cdot \sqrt[3]{\left(a \cdot z\right) \cdot b}\right) \cdot \sqrt[3]{\left(a \cdot z\right) \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot \left(t + z \cdot b\right)\\ \end{array}\]
\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(a \cdot z\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;y \le -1.578567063737235255180370993029824399964 \cdot 10^{-145} \lor \neg \left(y \le 3.947860033410908928699063785796365012728 \cdot 10^{-45}\right):\\
\;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\sqrt[3]{\left(a \cdot z\right) \cdot b} \cdot \sqrt[3]{\left(a \cdot z\right) \cdot b}\right) \cdot \sqrt[3]{\left(a \cdot z\right) \cdot b}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r453127 = x;
        double r453128 = y;
        double r453129 = z;
        double r453130 = r453128 * r453129;
        double r453131 = r453127 + r453130;
        double r453132 = t;
        double r453133 = a;
        double r453134 = r453132 * r453133;
        double r453135 = r453131 + r453134;
        double r453136 = r453133 * r453129;
        double r453137 = b;
        double r453138 = r453136 * r453137;
        double r453139 = r453135 + r453138;
        return r453139;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r453140 = y;
        double r453141 = -1.5785670637372353e-145;
        bool r453142 = r453140 <= r453141;
        double r453143 = 3.947860033410909e-45;
        bool r453144 = r453140 <= r453143;
        double r453145 = !r453144;
        bool r453146 = r453142 || r453145;
        double r453147 = x;
        double r453148 = z;
        double r453149 = r453140 * r453148;
        double r453150 = r453147 + r453149;
        double r453151 = t;
        double r453152 = a;
        double r453153 = r453151 * r453152;
        double r453154 = r453150 + r453153;
        double r453155 = r453152 * r453148;
        double r453156 = b;
        double r453157 = r453155 * r453156;
        double r453158 = cbrt(r453157);
        double r453159 = r453158 * r453158;
        double r453160 = r453159 * r453158;
        double r453161 = r453154 + r453160;
        double r453162 = r453148 * r453156;
        double r453163 = r453151 + r453162;
        double r453164 = r453152 * r453163;
        double r453165 = r453150 + r453164;
        double r453166 = r453146 ? r453161 : r453165;
        return r453166;
}

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

Original2.3
Target0.4
Herbie2.4
\[\begin{array}{l} \mathbf{if}\;z \lt -11820553527347888128:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \mathbf{elif}\;z \lt 4.758974318836428710669076838657752600596 \cdot 10^{-122}:\\ \;\;\;\;\left(b \cdot z + t\right) \cdot a + \left(z \cdot y + x\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot a + y\right) + \left(x + t \cdot a\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.5785670637372353e-145 or 3.947860033410909e-45 < y

    1. Initial program 1.7

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

    3. Applied add-cube-cbrt1.9

      \[\leadsto \left(\left(x + y \cdot z\right) + t \cdot a\right) + \color{blue}{\left(\sqrt[3]{\left(a \cdot z\right) \cdot b} \cdot \sqrt[3]{\left(a \cdot z\right) \cdot b}\right) \cdot \sqrt[3]{\left(a \cdot z\right) \cdot b}}\]

    if -1.5785670637372353e-145 < y < 3.947860033410909e-45

    1. Initial program 3.1

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

    3. Applied associate-+l+3.1

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

    4. Simplified3.2

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

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.578567063737235255180370993029824399964 \cdot 10^{-145} \lor \neg \left(y \le 3.947860033410908928699063785796365012728 \cdot 10^{-45}\right):\\ \;\;\;\;\left(\left(x + y \cdot z\right) + t \cdot a\right) + \left(\sqrt[3]{\left(a \cdot z\right) \cdot b} \cdot \sqrt[3]{\left(a \cdot z\right) \cdot b}\right) \cdot \sqrt[3]{\left(a \cdot z\right) \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y \cdot z\right) + a \cdot \left(t + z \cdot b\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019212 
(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)))