Average Error: 3.6 → 0.7
Time: 4.7s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -1.509627698880911586338015526628233224088 \cdot 10^{129} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 2.414314480791499273783363683236492721004 \cdot 10^{188}\right):\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + {\left(27 \cdot \left(a \cdot b\right)\right)}^{1}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]
\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 -1.509627698880911586338015526628233224088 \cdot 10^{129} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 2.414314480791499273783363683236492721004 \cdot 10^{188}\right):\\
\;\;\;\;\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}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r769006 = x;
        double r769007 = 2.0;
        double r769008 = r769006 * r769007;
        double r769009 = y;
        double r769010 = 9.0;
        double r769011 = r769009 * r769010;
        double r769012 = z;
        double r769013 = r769011 * r769012;
        double r769014 = t;
        double r769015 = r769013 * r769014;
        double r769016 = r769008 - r769015;
        double r769017 = a;
        double r769018 = 27.0;
        double r769019 = r769017 * r769018;
        double r769020 = b;
        double r769021 = r769019 * r769020;
        double r769022 = r769016 + r769021;
        return r769022;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r769023 = y;
        double r769024 = 9.0;
        double r769025 = r769023 * r769024;
        double r769026 = z;
        double r769027 = r769025 * r769026;
        double r769028 = -1.5096276988809116e+129;
        bool r769029 = r769027 <= r769028;
        double r769030 = 2.4143144807914993e+188;
        bool r769031 = r769027 <= r769030;
        double r769032 = !r769031;
        bool r769033 = r769029 || r769032;
        double r769034 = x;
        double r769035 = 2.0;
        double r769036 = r769034 * r769035;
        double r769037 = r769024 * r769026;
        double r769038 = t;
        double r769039 = r769037 * r769038;
        double r769040 = r769023 * r769039;
        double r769041 = r769036 - r769040;
        double r769042 = 27.0;
        double r769043 = a;
        double r769044 = b;
        double r769045 = r769043 * r769044;
        double r769046 = r769042 * r769045;
        double r769047 = 1.0;
        double r769048 = pow(r769046, r769047);
        double r769049 = r769041 + r769048;
        double r769050 = r769023 * r769037;
        double r769051 = r769050 * r769038;
        double r769052 = r769036 - r769051;
        double r769053 = r769043 * r769042;
        double r769054 = r769053 * r769044;
        double r769055 = r769052 + r769054;
        double r769056 = r769033 ? r769049 : r769055;
        return r769056;
}

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

Original3.6
Target2.6
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 2 regimes

  2. if (* (* y 9.0) z) < -1.5096276988809116e+129 or 2.4143144807914993e+188 < (* (* y 9.0) z)

    1. Initial program 19.0

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

    3. Applied associate-*l*2.3

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

    5. Applied associate-*l*1.8

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

    7. Applied associate-*r*1.9

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

    9. Applied pow11.9

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

    10. Applied pow11.9

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

    11. Applied pow11.9

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

    12. Applied pow-prod-down1.9

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

    13. Applied pow-prod-down1.9

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

    14. Simplified1.7

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

    if -1.5096276988809116e+129 < (* (* y 9.0) z) < 2.4143144807914993e+188

    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

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -1.509627698880911586338015526628233224088 \cdot 10^{129} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 2.414314480791499273783363683236492721004 \cdot 10^{188}\right):\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + {\left(27 \cdot \left(a \cdot b\right)\right)}^{1}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(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)))