Average Error: 3.7 → 0.7
Time: 5.1s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -3.448549789137693191269335221806774831746 \cdot 10^{254}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + {\left(27 \cdot \left(a \cdot b\right)\right)}^{1}\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 2.369062689999037946122298172350622575008 \cdot 10^{135}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + {\left(\sqrt{27} \cdot \left(\sqrt{27} \cdot \left(a \cdot b\right)\right)\right)}^{1}\\ \end{array}\]
\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 -3.448549789137693191269335221806774831746 \cdot 10^{254}:\\
\;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + {\left(27 \cdot \left(a \cdot b\right)\right)}^{1}\\

\mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 2.369062689999037946122298172350622575008 \cdot 10^{135}:\\
\;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + {\left(\sqrt{27} \cdot \left(\sqrt{27} \cdot \left(a \cdot b\right)\right)\right)}^{1}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r674859 = x;
        double r674860 = 2.0;
        double r674861 = r674859 * r674860;
        double r674862 = y;
        double r674863 = 9.0;
        double r674864 = r674862 * r674863;
        double r674865 = z;
        double r674866 = r674864 * r674865;
        double r674867 = t;
        double r674868 = r674866 * r674867;
        double r674869 = r674861 - r674868;
        double r674870 = a;
        double r674871 = 27.0;
        double r674872 = r674870 * r674871;
        double r674873 = b;
        double r674874 = r674872 * r674873;
        double r674875 = r674869 + r674874;
        return r674875;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r674876 = y;
        double r674877 = 9.0;
        double r674878 = r674876 * r674877;
        double r674879 = z;
        double r674880 = r674878 * r674879;
        double r674881 = -3.448549789137693e+254;
        bool r674882 = r674880 <= r674881;
        double r674883 = x;
        double r674884 = 2.0;
        double r674885 = r674883 * r674884;
        double r674886 = t;
        double r674887 = r674879 * r674886;
        double r674888 = r674877 * r674887;
        double r674889 = r674876 * r674888;
        double r674890 = r674885 - r674889;
        double r674891 = 27.0;
        double r674892 = a;
        double r674893 = b;
        double r674894 = r674892 * r674893;
        double r674895 = r674891 * r674894;
        double r674896 = 1.0;
        double r674897 = pow(r674895, r674896);
        double r674898 = r674890 + r674897;
        double r674899 = 2.369062689999038e+135;
        bool r674900 = r674880 <= r674899;
        double r674901 = r674877 * r674879;
        double r674902 = r674876 * r674901;
        double r674903 = r674902 * r674886;
        double r674904 = r674885 - r674903;
        double r674905 = r674892 * r674891;
        double r674906 = r674905 * r674893;
        double r674907 = r674904 + r674906;
        double r674908 = sqrt(r674891);
        double r674909 = r674908 * r674894;
        double r674910 = r674908 * r674909;
        double r674911 = pow(r674910, r674896);
        double r674912 = r674890 + r674911;
        double r674913 = r674900 ? r674907 : r674912;
        double r674914 = r674882 ? r674898 : r674913;
        return r674914;
}

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

Derivation

  1. Split input into 3 regimes

  2. if (* (* y 9.0) z) < -3.448549789137693e+254

    1. Initial program 41.3

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

    3. Applied associate-*l*1.2

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

    5. Applied associate-*l*0.9

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

    7. Applied pow10.9

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

    8. Applied pow10.9

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

    9. Applied pow10.9

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

    10. Applied pow-prod-down0.9

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

    11. Applied pow-prod-down0.9

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

    12. Simplified0.5

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

    if -3.448549789137693e+254 < (* (* y 9.0) z) < 2.369062689999038e+135

    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*0.5

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

    if 2.369062689999038e+135 < (* (* y 9.0) z)

    1. Initial program 16.1

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

    3. Applied associate-*l*2.1

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

    5. Applied associate-*l*1.9

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

    7. Applied pow11.9

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

    8. Applied pow11.9

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

    9. Applied pow11.9

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

    10. Applied pow-prod-down1.9

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

    11. Applied pow-prod-down1.9

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

    12. Simplified1.9

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

    14. Applied add-sqr-sqrt1.9

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

    15. Applied associate-*l*1.9

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -3.448549789137693191269335221806774831746 \cdot 10^{254}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + {\left(27 \cdot \left(a \cdot b\right)\right)}^{1}\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 2.369062689999037946122298172350622575008 \cdot 10^{135}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + {\left(\sqrt{27} \cdot \left(\sqrt{27} \cdot \left(a \cdot b\right)\right)\right)}^{1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020002 
(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)))