Average Error: 4.0 → 1.2
Time: 17.7s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot 9 \le -2.434616547682554976717028694110922515392:\\ \;\;\;\;\left(27 \cdot a\right) \cdot b + \left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot t\right) \cdot y\right)\\ \mathbf{elif}\;y \cdot 9 \le 1.245717551989869811727447027402159666676 \cdot 10^{-192}:\\ \;\;\;\;\left(\left(27 \cdot a\right) \cdot b - \left(y \cdot t\right) \cdot \left(z \cdot 9\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - \sqrt{y} \cdot \left(\left(9 \cdot \left(z \cdot t\right)\right) \cdot \sqrt{y}\right)\right)\\ \end{array}\]
\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}\;y \cdot 9 \le -2.434616547682554976717028694110922515392:\\
\;\;\;\;\left(27 \cdot a\right) \cdot b + \left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot t\right) \cdot y\right)\\

\mathbf{elif}\;y \cdot 9 \le 1.245717551989869811727447027402159666676 \cdot 10^{-192}:\\
\;\;\;\;\left(\left(27 \cdot a\right) \cdot b - \left(y \cdot t\right) \cdot \left(z \cdot 9\right)\right) + x \cdot 2\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r34171600 = x;
        double r34171601 = 2.0;
        double r34171602 = r34171600 * r34171601;
        double r34171603 = y;
        double r34171604 = 9.0;
        double r34171605 = r34171603 * r34171604;
        double r34171606 = z;
        double r34171607 = r34171605 * r34171606;
        double r34171608 = t;
        double r34171609 = r34171607 * r34171608;
        double r34171610 = r34171602 - r34171609;
        double r34171611 = a;
        double r34171612 = 27.0;
        double r34171613 = r34171611 * r34171612;
        double r34171614 = b;
        double r34171615 = r34171613 * r34171614;
        double r34171616 = r34171610 + r34171615;
        return r34171616;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r34171617 = y;
        double r34171618 = 9.0;
        double r34171619 = r34171617 * r34171618;
        double r34171620 = -2.434616547682555;
        bool r34171621 = r34171619 <= r34171620;
        double r34171622 = 27.0;
        double r34171623 = a;
        double r34171624 = r34171622 * r34171623;
        double r34171625 = b;
        double r34171626 = r34171624 * r34171625;
        double r34171627 = x;
        double r34171628 = 2.0;
        double r34171629 = r34171627 * r34171628;
        double r34171630 = z;
        double r34171631 = r34171630 * r34171618;
        double r34171632 = t;
        double r34171633 = r34171631 * r34171632;
        double r34171634 = r34171633 * r34171617;
        double r34171635 = r34171629 - r34171634;
        double r34171636 = r34171626 + r34171635;
        double r34171637 = 1.2457175519898698e-192;
        bool r34171638 = r34171619 <= r34171637;
        double r34171639 = r34171617 * r34171632;
        double r34171640 = r34171639 * r34171631;
        double r34171641 = r34171626 - r34171640;
        double r34171642 = r34171641 + r34171629;
        double r34171643 = r34171622 * r34171625;
        double r34171644 = r34171623 * r34171643;
        double r34171645 = sqrt(r34171617);
        double r34171646 = r34171630 * r34171632;
        double r34171647 = r34171618 * r34171646;
        double r34171648 = r34171647 * r34171645;
        double r34171649 = r34171645 * r34171648;
        double r34171650 = r34171644 - r34171649;
        double r34171651 = r34171629 + r34171650;
        double r34171652 = r34171638 ? r34171642 : r34171651;
        double r34171653 = r34171621 ? r34171636 : r34171652;
        return r34171653;
}

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

Original4.0
Target2.7
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811188954625810696587370427881 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y 9.0) < -2.434616547682555

    1. Initial program 8.2

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

    3. Applied associate-*l*8.1

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

    5. Applied associate-*l*0.7

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

    if -2.434616547682555 < (* y 9.0) < 1.2457175519898698e-192

    1. Initial program 0.7

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

    3. Applied associate-*l*0.8

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

    5. Applied associate-*l*6.0

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

    7. Applied sub-neg6.0

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

    8. Applied associate-+l+6.0

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

    9. Simplified0.6

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

    if 1.2457175519898698e-192 < (* y 9.0)

    1. Initial program 5.1

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

    3. Applied associate-*l*5.1

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

    5. Applied sub-neg5.1

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

    6. Applied associate-+l+5.1

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

    7. Simplified2.0

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

    9. Applied add-sqr-sqrt2.1

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

    10. Applied associate-*r*2.1

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \le -2.434616547682554976717028694110922515392:\\ \;\;\;\;\left(27 \cdot a\right) \cdot b + \left(x \cdot 2 - \left(\left(z \cdot 9\right) \cdot t\right) \cdot y\right)\\ \mathbf{elif}\;y \cdot 9 \le 1.245717551989869811727447027402159666676 \cdot 10^{-192}:\\ \;\;\;\;\left(\left(27 \cdot a\right) \cdot b - \left(y \cdot t\right) \cdot \left(z \cdot 9\right)\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(a \cdot \left(27 \cdot b\right) - \sqrt{y} \cdot \left(\left(9 \cdot \left(z \cdot t\right)\right) \cdot \sqrt{y}\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(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)))