Average Error: 3.6 → 0.7
Time: 4.8s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -1.509627698880911586338015526628233224088 \cdot 10^{129} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 2.414314480791499273783363683236492721004 \cdot 10^{188}\right):\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + {\left(27 \cdot \left(a \cdot b\right)\right)}^{1}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]
\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 r718403 = x;
        double r718404 = 2.0;
        double r718405 = r718403 * r718404;
        double r718406 = y;
        double r718407 = 9.0;
        double r718408 = r718406 * r718407;
        double r718409 = z;
        double r718410 = r718408 * r718409;
        double r718411 = t;
        double r718412 = r718410 * r718411;
        double r718413 = r718405 - r718412;
        double r718414 = a;
        double r718415 = 27.0;
        double r718416 = r718414 * r718415;
        double r718417 = b;
        double r718418 = r718416 * r718417;
        double r718419 = r718413 + r718418;
        return r718419;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r718420 = y;
        double r718421 = 9.0;
        double r718422 = r718420 * r718421;
        double r718423 = z;
        double r718424 = r718422 * r718423;
        double r718425 = -1.5096276988809116e+129;
        bool r718426 = r718424 <= r718425;
        double r718427 = 2.4143144807914993e+188;
        bool r718428 = r718424 <= r718427;
        double r718429 = !r718428;
        bool r718430 = r718426 || r718429;
        double r718431 = x;
        double r718432 = 2.0;
        double r718433 = r718431 * r718432;
        double r718434 = r718421 * r718423;
        double r718435 = t;
        double r718436 = r718434 * r718435;
        double r718437 = r718420 * r718436;
        double r718438 = r718433 - r718437;
        double r718439 = 27.0;
        double r718440 = a;
        double r718441 = b;
        double r718442 = r718440 * r718441;
        double r718443 = r718439 * r718442;
        double r718444 = 1.0;
        double r718445 = pow(r718443, r718444);
        double r718446 = r718438 + r718445;
        double r718447 = r718420 * r718434;
        double r718448 = r718447 * r718435;
        double r718449 = r718433 - r718448;
        double r718450 = r718440 * r718439;
        double r718451 = r718450 * r718441;
        double r718452 = r718449 + r718451;
        double r718453 = r718430 ? r718446 : r718452;
        return r718453;
}

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)))