Average Error: 3.9 → 0.6
Time: 4.6s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -8.4160355144962912 \cdot 10^{233}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 1.79783517118745171 \cdot 10^{166}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + {\left(27 \cdot \left(a \cdot b\right)\right)}^{1}\\ \end{array}\]
\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(y \cdot 9\right) \cdot z \le -8.4160355144962912 \cdot 10^{233}:\\
\;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\

\mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 1.79783517118745171 \cdot 10^{166}:\\
\;\;\;\;\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 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + {\left(27 \cdot \left(a \cdot b\right)\right)}^{1}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r793913 = x;
        double r793914 = 2.0;
        double r793915 = r793913 * r793914;
        double r793916 = y;
        double r793917 = 9.0;
        double r793918 = r793916 * r793917;
        double r793919 = z;
        double r793920 = r793918 * r793919;
        double r793921 = t;
        double r793922 = r793920 * r793921;
        double r793923 = r793915 - r793922;
        double r793924 = a;
        double r793925 = 27.0;
        double r793926 = r793924 * r793925;
        double r793927 = b;
        double r793928 = r793926 * r793927;
        double r793929 = r793923 + r793928;
        return r793929;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r793930 = y;
        double r793931 = 9.0;
        double r793932 = r793930 * r793931;
        double r793933 = z;
        double r793934 = r793932 * r793933;
        double r793935 = -8.416035514496291e+233;
        bool r793936 = r793934 <= r793935;
        double r793937 = x;
        double r793938 = 2.0;
        double r793939 = r793937 * r793938;
        double r793940 = t;
        double r793941 = r793933 * r793940;
        double r793942 = r793932 * r793941;
        double r793943 = r793939 - r793942;
        double r793944 = a;
        double r793945 = 27.0;
        double r793946 = r793944 * r793945;
        double r793947 = b;
        double r793948 = r793946 * r793947;
        double r793949 = r793943 + r793948;
        double r793950 = 1.7978351711874517e+166;
        bool r793951 = r793934 <= r793950;
        double r793952 = r793934 * r793940;
        double r793953 = r793939 - r793952;
        double r793954 = r793945 * r793947;
        double r793955 = r793944 * r793954;
        double r793956 = r793953 + r793955;
        double r793957 = r793931 * r793933;
        double r793958 = r793957 * r793940;
        double r793959 = r793930 * r793958;
        double r793960 = r793939 - r793959;
        double r793961 = r793944 * r793947;
        double r793962 = r793945 * r793961;
        double r793963 = 1.0;
        double r793964 = pow(r793962, r793963);
        double r793965 = r793960 + r793964;
        double r793966 = r793951 ? r793956 : r793965;
        double r793967 = r793936 ? r793949 : r793966;
        return r793967;
}

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

Original3.9
Target2.7
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (* y 9.0) z) < -8.416035514496291e+233

    1. Initial program 34.0

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

    3. Applied associate-*l*1.2

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

    if -8.416035514496291e+233 < (* (* y 9.0) z) < 1.7978351711874517e+166

    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. Using strategy rm

    3. Applied associate-*l*0.4

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

    if 1.7978351711874517e+166 < (* (* y 9.0) z)

    1. Initial program 22.3

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

    3. Applied associate-*l*21.7

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

    5. Applied pow121.7

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

    6. Applied pow121.7

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

    7. Applied pow121.7

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

    8. Applied pow-prod-down21.7

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

    9. Applied pow-prod-down21.7

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

    10. Simplified21.7

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

    12. Applied associate-*l*1.9

      \[\leadsto \left(x \cdot 2 - \color{blue}{y \cdot \left(\left(9 \cdot z\right) \cdot t\right)}\right) + {\left(27 \cdot \left(a \cdot b\right)\right)}^{1}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -8.4160355144962912 \cdot 10^{233}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 1.79783517118745171 \cdot 10^{166}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + {\left(27 \cdot \left(a \cdot b\right)\right)}^{1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020035 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< y 7.590524218811189e-161) (+ (- (* x 2) (* (* (* y 9) z) t)) (* a (* 27 b))) (+ (- (* x 2) (* 9 (* y (* t z)))) (* (* a 27) b)))

  (+ (- (* x 2) (* (* (* y 9) z) t)) (* (* a 27) b)))