Average Error: 3.6 → 0.7
Time: 4.4s
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 r755350 = x;
        double r755351 = 2.0;
        double r755352 = r755350 * r755351;
        double r755353 = y;
        double r755354 = 9.0;
        double r755355 = r755353 * r755354;
        double r755356 = z;
        double r755357 = r755355 * r755356;
        double r755358 = t;
        double r755359 = r755357 * r755358;
        double r755360 = r755352 - r755359;
        double r755361 = a;
        double r755362 = 27.0;
        double r755363 = r755361 * r755362;
        double r755364 = b;
        double r755365 = r755363 * r755364;
        double r755366 = r755360 + r755365;
        return r755366;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r755367 = y;
        double r755368 = 9.0;
        double r755369 = r755367 * r755368;
        double r755370 = z;
        double r755371 = r755369 * r755370;
        double r755372 = -1.5096276988809116e+129;
        bool r755373 = r755371 <= r755372;
        double r755374 = 2.4143144807914993e+188;
        bool r755375 = r755371 <= r755374;
        double r755376 = !r755375;
        bool r755377 = r755373 || r755376;
        double r755378 = x;
        double r755379 = 2.0;
        double r755380 = r755378 * r755379;
        double r755381 = r755368 * r755370;
        double r755382 = t;
        double r755383 = r755381 * r755382;
        double r755384 = r755367 * r755383;
        double r755385 = r755380 - r755384;
        double r755386 = 27.0;
        double r755387 = a;
        double r755388 = b;
        double r755389 = r755387 * r755388;
        double r755390 = r755386 * r755389;
        double r755391 = 1.0;
        double r755392 = pow(r755390, r755391);
        double r755393 = r755385 + r755392;
        double r755394 = r755367 * r755381;
        double r755395 = r755394 * r755382;
        double r755396 = r755380 - r755395;
        double r755397 = r755387 * r755386;
        double r755398 = r755397 * r755388;
        double r755399 = r755396 + r755398;
        double r755400 = r755377 ? r755393 : r755399;
        return r755400;
}

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 
(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)))