Average Error: 3.8 → 0.5
Time: 46.0s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(9 \cdot y\right) \cdot z \le -1.597595584666146595866193934309833222462 \cdot 10^{291}:\\ \;\;\;\;\left(\left(\left(\sqrt{27} \cdot a\right) \cdot b\right) \cdot \sqrt{27} - \left(y \cdot t\right) \cdot \left(z \cdot 9\right)\right) + 2 \cdot x\\ \mathbf{elif}\;\left(9 \cdot y\right) \cdot z \le 2.754361265387212695662526964744883723394 \cdot 10^{288}:\\ \;\;\;\;\left(2 \cdot x - t \cdot \left(\left(9 \cdot y\right) \cdot z\right)\right) + a \cdot \left(b \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\sqrt{27} \cdot a\right) \cdot b\right) \cdot \sqrt{27} - \left(y \cdot t\right) \cdot \left(z \cdot 9\right)\right) + 2 \cdot x\\ \end{array}\]
\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(9 \cdot y\right) \cdot z \le -1.597595584666146595866193934309833222462 \cdot 10^{291}:\\
\;\;\;\;\left(\left(\left(\sqrt{27} \cdot a\right) \cdot b\right) \cdot \sqrt{27} - \left(y \cdot t\right) \cdot \left(z \cdot 9\right)\right) + 2 \cdot x\\

\mathbf{elif}\;\left(9 \cdot y\right) \cdot z \le 2.754361265387212695662526964744883723394 \cdot 10^{288}:\\
\;\;\;\;\left(2 \cdot x - t \cdot \left(\left(9 \cdot y\right) \cdot z\right)\right) + a \cdot \left(b \cdot 27\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r36937485 = x;
        double r36937486 = 2.0;
        double r36937487 = r36937485 * r36937486;
        double r36937488 = y;
        double r36937489 = 9.0;
        double r36937490 = r36937488 * r36937489;
        double r36937491 = z;
        double r36937492 = r36937490 * r36937491;
        double r36937493 = t;
        double r36937494 = r36937492 * r36937493;
        double r36937495 = r36937487 - r36937494;
        double r36937496 = a;
        double r36937497 = 27.0;
        double r36937498 = r36937496 * r36937497;
        double r36937499 = b;
        double r36937500 = r36937498 * r36937499;
        double r36937501 = r36937495 + r36937500;
        return r36937501;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r36937502 = 9.0;
        double r36937503 = y;
        double r36937504 = r36937502 * r36937503;
        double r36937505 = z;
        double r36937506 = r36937504 * r36937505;
        double r36937507 = -1.5975955846661466e+291;
        bool r36937508 = r36937506 <= r36937507;
        double r36937509 = 27.0;
        double r36937510 = sqrt(r36937509);
        double r36937511 = a;
        double r36937512 = r36937510 * r36937511;
        double r36937513 = b;
        double r36937514 = r36937512 * r36937513;
        double r36937515 = r36937514 * r36937510;
        double r36937516 = t;
        double r36937517 = r36937503 * r36937516;
        double r36937518 = r36937505 * r36937502;
        double r36937519 = r36937517 * r36937518;
        double r36937520 = r36937515 - r36937519;
        double r36937521 = 2.0;
        double r36937522 = x;
        double r36937523 = r36937521 * r36937522;
        double r36937524 = r36937520 + r36937523;
        double r36937525 = 2.7543612653872127e+288;
        bool r36937526 = r36937506 <= r36937525;
        double r36937527 = r36937516 * r36937506;
        double r36937528 = r36937523 - r36937527;
        double r36937529 = r36937513 * r36937509;
        double r36937530 = r36937511 * r36937529;
        double r36937531 = r36937528 + r36937530;
        double r36937532 = r36937526 ? r36937531 : r36937524;
        double r36937533 = r36937508 ? r36937524 : r36937532;
        return r36937533;
}

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

Original3.8
Target2.8
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811188954625810696587370427881 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (* y 9.0) z) < -1.5975955846661466e+291 or 2.7543612653872127e+288 < (* (* y 9.0) z)

    1. Initial program 53.5

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

    3. Applied sub-neg53.5

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

    4. Applied associate-+l+53.5

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

    5. Simplified0.8

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

    7. Applied add-sqr-sqrt0.8

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

    8. Applied associate-*r*0.8

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

    10. Applied associate-*l*0.9

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

    if -1.5975955846661466e+291 < (* (* y 9.0) z) < 2.7543612653872127e+288

    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*0.4

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(9 \cdot y\right) \cdot z \le -1.597595584666146595866193934309833222462 \cdot 10^{291}:\\ \;\;\;\;\left(\left(\left(\sqrt{27} \cdot a\right) \cdot b\right) \cdot \sqrt{27} - \left(y \cdot t\right) \cdot \left(z \cdot 9\right)\right) + 2 \cdot x\\ \mathbf{elif}\;\left(9 \cdot y\right) \cdot z \le 2.754361265387212695662526964744883723394 \cdot 10^{288}:\\ \;\;\;\;\left(2 \cdot x - t \cdot \left(\left(9 \cdot y\right) \cdot z\right)\right) + a \cdot \left(b \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\sqrt{27} \cdot a\right) \cdot b\right) \cdot \sqrt{27} - \left(y \cdot t\right) \cdot \left(z \cdot 9\right)\right) + 2 \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019200 
(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)))