Average Error: 4.0 → 1.2
Time: 18.6s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot 9 \le -2.434616547682554976717028694110922515392:\\ \;\;\;\;\left(27 \cdot a\right) \cdot b + \left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot t\right) \cdot y\right)\\ \mathbf{elif}\;y \cdot 9 \le 1.245717551989869811727447027402159666676 \cdot 10^{-192}:\\ \;\;\;\;\left(\left(27 \cdot a\right) \cdot b - \left(y \cdot t\right) \cdot \left(z \cdot 9\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - \sqrt{y} \cdot \left(\left(9 \cdot \left(z \cdot t\right)\right) \cdot \sqrt{y}\right)\right)\\ \end{array}\]
\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}\;y \cdot 9 \le -2.434616547682554976717028694110922515392:\\
\;\;\;\;\left(27 \cdot a\right) \cdot b + \left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot t\right) \cdot y\right)\\

\mathbf{elif}\;y \cdot 9 \le 1.245717551989869811727447027402159666676 \cdot 10^{-192}:\\
\;\;\;\;\left(\left(27 \cdot a\right) \cdot b - \left(y \cdot t\right) \cdot \left(z \cdot 9\right)\right) + x \cdot 2\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r36154892 = x;
        double r36154893 = 2.0;
        double r36154894 = r36154892 * r36154893;
        double r36154895 = y;
        double r36154896 = 9.0;
        double r36154897 = r36154895 * r36154896;
        double r36154898 = z;
        double r36154899 = r36154897 * r36154898;
        double r36154900 = t;
        double r36154901 = r36154899 * r36154900;
        double r36154902 = r36154894 - r36154901;
        double r36154903 = a;
        double r36154904 = 27.0;
        double r36154905 = r36154903 * r36154904;
        double r36154906 = b;
        double r36154907 = r36154905 * r36154906;
        double r36154908 = r36154902 + r36154907;
        return r36154908;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r36154909 = y;
        double r36154910 = 9.0;
        double r36154911 = r36154909 * r36154910;
        double r36154912 = -2.434616547682555;
        bool r36154913 = r36154911 <= r36154912;
        double r36154914 = 27.0;
        double r36154915 = a;
        double r36154916 = r36154914 * r36154915;
        double r36154917 = b;
        double r36154918 = r36154916 * r36154917;
        double r36154919 = x;
        double r36154920 = 2.0;
        double r36154921 = r36154919 * r36154920;
        double r36154922 = z;
        double r36154923 = r36154922 * r36154910;
        double r36154924 = t;
        double r36154925 = r36154923 * r36154924;
        double r36154926 = r36154925 * r36154909;
        double r36154927 = r36154921 - r36154926;
        double r36154928 = r36154918 + r36154927;
        double r36154929 = 1.2457175519898698e-192;
        bool r36154930 = r36154911 <= r36154929;
        double r36154931 = r36154909 * r36154924;
        double r36154932 = r36154931 * r36154923;
        double r36154933 = r36154918 - r36154932;
        double r36154934 = r36154933 + r36154921;
        double r36154935 = r36154914 * r36154917;
        double r36154936 = r36154915 * r36154935;
        double r36154937 = sqrt(r36154909);
        double r36154938 = r36154922 * r36154924;
        double r36154939 = r36154910 * r36154938;
        double r36154940 = r36154939 * r36154937;
        double r36154941 = r36154937 * r36154940;
        double r36154942 = r36154936 - r36154941;
        double r36154943 = r36154921 + r36154942;
        double r36154944 = r36154930 ? r36154934 : r36154943;
        double r36154945 = r36154913 ? r36154928 : r36154944;
        return r36154945;
}

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

Original4.0
Target2.7
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811188954625810696587370427881 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y 9.0) < -2.434616547682555

    1. Initial program 8.2

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

    3. Applied associate-*l*8.1

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

    5. Applied associate-*l*0.7

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

    if -2.434616547682555 < (* y 9.0) < 1.2457175519898698e-192

    1. Initial program 0.7

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

    3. Applied associate-*l*0.8

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

    5. Applied associate-*l*6.0

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

    7. Applied sub-neg6.0

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

    8. Applied associate-+l+6.0

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

    9. Simplified0.6

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

    if 1.2457175519898698e-192 < (* y 9.0)

    1. Initial program 5.1

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

    3. Applied associate-*l*5.1

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

    5. Applied sub-neg5.1

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

    6. Applied associate-+l+5.1

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

    7. Simplified2.0

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

    9. Applied add-sqr-sqrt2.1

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

    10. Applied associate-*r*2.1

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \le -2.434616547682554976717028694110922515392:\\ \;\;\;\;\left(27 \cdot a\right) \cdot b + \left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot t\right) \cdot y\right)\\ \mathbf{elif}\;y \cdot 9 \le 1.245717551989869811727447027402159666676 \cdot 10^{-192}:\\ \;\;\;\;\left(\left(27 \cdot a\right) \cdot b - \left(y \cdot t\right) \cdot \left(z \cdot 9\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - \sqrt{y} \cdot \left(\left(9 \cdot \left(z \cdot t\right)\right) \cdot \sqrt{y}\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(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)))