Average Error: 3.7 → 0.8
Time: 21.8s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t = -\infty \lor \neg \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \le 9.922659411281920326792191469870571772034 \cdot 10^{264}\right):\\ \;\;\;\;\left(x \cdot 2 - \left(t \cdot y\right) \cdot \left(z \cdot 9\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27 + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \end{array}\]
\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t = -\infty \lor \neg \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \le 9.922659411281920326792191469870571772034 \cdot 10^{264}\right):\\
\;\;\;\;\left(x \cdot 2 - \left(t \cdot y\right) \cdot \left(z \cdot 9\right)\right) + \left(a \cdot 27\right) \cdot b\\

\mathbf{else}:\\
\;\;\;\;\left(a \cdot b\right) \cdot 27 + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r596880 = x;
        double r596881 = 2.0;
        double r596882 = r596880 * r596881;
        double r596883 = y;
        double r596884 = 9.0;
        double r596885 = r596883 * r596884;
        double r596886 = z;
        double r596887 = r596885 * r596886;
        double r596888 = t;
        double r596889 = r596887 * r596888;
        double r596890 = r596882 - r596889;
        double r596891 = a;
        double r596892 = 27.0;
        double r596893 = r596891 * r596892;
        double r596894 = b;
        double r596895 = r596893 * r596894;
        double r596896 = r596890 + r596895;
        return r596896;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r596897 = y;
        double r596898 = 9.0;
        double r596899 = r596897 * r596898;
        double r596900 = z;
        double r596901 = r596899 * r596900;
        double r596902 = t;
        double r596903 = r596901 * r596902;
        double r596904 = -inf.0;
        bool r596905 = r596903 <= r596904;
        double r596906 = 9.92265941128192e+264;
        bool r596907 = r596903 <= r596906;
        double r596908 = !r596907;
        bool r596909 = r596905 || r596908;
        double r596910 = x;
        double r596911 = 2.0;
        double r596912 = r596910 * r596911;
        double r596913 = r596902 * r596897;
        double r596914 = r596900 * r596898;
        double r596915 = r596913 * r596914;
        double r596916 = r596912 - r596915;
        double r596917 = a;
        double r596918 = 27.0;
        double r596919 = r596917 * r596918;
        double r596920 = b;
        double r596921 = r596919 * r596920;
        double r596922 = r596916 + r596921;
        double r596923 = r596917 * r596920;
        double r596924 = r596923 * r596918;
        double r596925 = r596912 - r596903;
        double r596926 = r596924 + r596925;
        double r596927 = r596909 ? r596922 : r596926;
        return r596927;
}

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

Original3.7
Target2.6
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811188954625810696587370427881 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (* (* y 9.0) z) t) < -inf.0 or 9.92265941128192e+264 < (* (* (* y 9.0) z) t)

    1. Initial program 47.7

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
    2. Using strategy rm

    3. Applied pow147.7

      \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \color{blue}{{z}^{1}}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]

    4. Applied pow147.7

      \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot \color{blue}{{9}^{1}}\right) \cdot {z}^{1}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]

    5. Applied pow147.7

      \[\leadsto \left(x \cdot 2 - \left(\left(\color{blue}{{y}^{1}} \cdot {9}^{1}\right) \cdot {z}^{1}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]

    6. Applied pow-prod-down47.7

      \[\leadsto \left(x \cdot 2 - \left(\color{blue}{{\left(y \cdot 9\right)}^{1}} \cdot {z}^{1}\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]

    7. Applied pow-prod-down47.7

      \[\leadsto \left(x \cdot 2 - \color{blue}{{\left(\left(y \cdot 9\right) \cdot z\right)}^{1}} \cdot t\right) + \left(a \cdot 27\right) \cdot b\]

    8. Simplified47.0

      \[\leadsto \left(x \cdot 2 - {\color{blue}{\left(\left(z \cdot 9\right) \cdot y\right)}}^{1} \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
    9. Using strategy rm

    10. Applied *-un-lft-identity47.0

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(1 \cdot {\left(\left(z \cdot 9\right) \cdot y\right)}^{1}\right)} \cdot t\right) + \left(a \cdot 27\right) \cdot b\]

    11. Applied associate-*l*47.0

      \[\leadsto \left(x \cdot 2 - \color{blue}{1 \cdot \left({\left(\left(z \cdot 9\right) \cdot y\right)}^{1} \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b\]

    12. Simplified5.9

      \[\leadsto \left(x \cdot 2 - 1 \cdot \color{blue}{\left(\left(9 \cdot z\right) \cdot \left(y \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b\]

    if -inf.0 < (* (* (* y 9.0) z) t) < 9.92265941128192e+264

    1. Initial program 0.5

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]

    2. Taylor expanded around 0 0.4

      \[\leadsto \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \color{blue}{27 \cdot \left(a \cdot b\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t = -\infty \lor \neg \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \le 9.922659411281920326792191469870571772034 \cdot 10^{264}\right):\\ \;\;\;\;\left(x \cdot 2 - \left(t \cdot y\right) \cdot \left(z \cdot 9\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot b\right) \cdot 27 + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"

  :herbie-target
  (if (< y 7.590524218811189e-161) (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b))) (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b)))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))