Average Error: 4.1 → 1.0
Time: 4.3s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot 9 \le -1.80294560403524109 \cdot 10^{-79} \lor \neg \left(y \cdot 9 \le 4.4323646665533492 \cdot 10^{-78}\right):\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot x + 27 \cdot \left(a \cdot b\right)\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array}\]
\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 -1.80294560403524109 \cdot 10^{-79} \lor \neg \left(y \cdot 9 \le 4.4323646665533492 \cdot 10^{-78}\right):\\
\;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r1009751 = x;
        double r1009752 = 2.0;
        double r1009753 = r1009751 * r1009752;
        double r1009754 = y;
        double r1009755 = 9.0;
        double r1009756 = r1009754 * r1009755;
        double r1009757 = z;
        double r1009758 = r1009756 * r1009757;
        double r1009759 = t;
        double r1009760 = r1009758 * r1009759;
        double r1009761 = r1009753 - r1009760;
        double r1009762 = a;
        double r1009763 = 27.0;
        double r1009764 = r1009762 * r1009763;
        double r1009765 = b;
        double r1009766 = r1009764 * r1009765;
        double r1009767 = r1009761 + r1009766;
        return r1009767;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1009768 = y;
        double r1009769 = 9.0;
        double r1009770 = r1009768 * r1009769;
        double r1009771 = -1.802945604035241e-79;
        bool r1009772 = r1009770 <= r1009771;
        double r1009773 = 4.432364666553349e-78;
        bool r1009774 = r1009770 <= r1009773;
        double r1009775 = !r1009774;
        bool r1009776 = r1009772 || r1009775;
        double r1009777 = x;
        double r1009778 = 2.0;
        double r1009779 = r1009777 * r1009778;
        double r1009780 = z;
        double r1009781 = r1009769 * r1009780;
        double r1009782 = t;
        double r1009783 = r1009781 * r1009782;
        double r1009784 = r1009768 * r1009783;
        double r1009785 = r1009779 - r1009784;
        double r1009786 = a;
        double r1009787 = 27.0;
        double r1009788 = r1009786 * r1009787;
        double r1009789 = b;
        double r1009790 = r1009788 * r1009789;
        double r1009791 = r1009785 + r1009790;
        double r1009792 = r1009778 * r1009777;
        double r1009793 = r1009786 * r1009789;
        double r1009794 = r1009787 * r1009793;
        double r1009795 = r1009792 + r1009794;
        double r1009796 = r1009780 * r1009768;
        double r1009797 = r1009782 * r1009796;
        double r1009798 = r1009769 * r1009797;
        double r1009799 = r1009795 - r1009798;
        double r1009800 = r1009776 ? r1009791 : r1009799;
        return r1009800;
}

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

Original4.1
Target2.8
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y 9.0) < -1.802945604035241e-79 or 4.432364666553349e-78 < (* y 9.0)

    1. Initial program 6.8

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

    3. Applied associate-*l*1.3

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

    5. Applied associate-*l*1.3

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

    7. Applied associate-*r*1.3

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

    if -1.802945604035241e-79 < (* y 9.0) < 4.432364666553349e-78

    1. Initial program 0.6

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

    3. Applied sub-neg0.6

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

    4. Applied associate-+l+0.6

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

    5. Simplified0.6

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

    6. Taylor expanded around inf 0.6

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \le -1.80294560403524109 \cdot 10^{-79} \lor \neg \left(y \cdot 9 \le 4.4323646665533492 \cdot 10^{-78}\right):\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot x + 27 \cdot \left(a \cdot b\right)\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020025 
(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)))