Average Error: 3.8 → 0.6
Time: 3.8s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z = -\infty:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 2.73534201683668052 \cdot 10^{138}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(27 \cdot \left(a \cdot b\right) - \left(\left(9 \cdot t\right) \cdot z\right) \cdot y\right)\\ \end{array}\]
\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}\;\left(y \cdot 9\right) \cdot z = -\infty:\\
\;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\

\mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 2.73534201683668052 \cdot 10^{138}:\\
\;\;\;\;\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}:\\
\;\;\;\;x \cdot 2 + \left(27 \cdot \left(a \cdot b\right) - \left(\left(9 \cdot t\right) \cdot z\right) \cdot y\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r665995 = x;
        double r665996 = 2.0;
        double r665997 = r665995 * r665996;
        double r665998 = y;
        double r665999 = 9.0;
        double r666000 = r665998 * r665999;
        double r666001 = z;
        double r666002 = r666000 * r666001;
        double r666003 = t;
        double r666004 = r666002 * r666003;
        double r666005 = r665997 - r666004;
        double r666006 = a;
        double r666007 = 27.0;
        double r666008 = r666006 * r666007;
        double r666009 = b;
        double r666010 = r666008 * r666009;
        double r666011 = r666005 + r666010;
        return r666011;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r666012 = y;
        double r666013 = 9.0;
        double r666014 = r666012 * r666013;
        double r666015 = z;
        double r666016 = r666014 * r666015;
        double r666017 = -inf.0;
        bool r666018 = r666016 <= r666017;
        double r666019 = x;
        double r666020 = 2.0;
        double r666021 = r666019 * r666020;
        double r666022 = t;
        double r666023 = r666015 * r666022;
        double r666024 = r666014 * r666023;
        double r666025 = r666021 - r666024;
        double r666026 = a;
        double r666027 = 27.0;
        double r666028 = r666026 * r666027;
        double r666029 = b;
        double r666030 = r666028 * r666029;
        double r666031 = r666025 + r666030;
        double r666032 = 2.7353420168366805e+138;
        bool r666033 = r666016 <= r666032;
        double r666034 = r666016 * r666022;
        double r666035 = r666021 - r666034;
        double r666036 = r666027 * r666029;
        double r666037 = r666026 * r666036;
        double r666038 = r666035 + r666037;
        double r666039 = r666026 * r666029;
        double r666040 = r666027 * r666039;
        double r666041 = r666013 * r666022;
        double r666042 = r666041 * r666015;
        double r666043 = r666042 * r666012;
        double r666044 = r666040 - r666043;
        double r666045 = r666021 + r666044;
        double r666046 = r666033 ? r666038 : r666045;
        double r666047 = r666018 ? r666031 : r666046;
        return r666047;
}

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
Target2.7
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (* y 9.0) z) < -inf.0

    1. Initial program 64.0

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

    3. Applied associate-*l*2.0

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

    if -inf.0 < (* (* y 9.0) z) < 2.7353420168366805e+138

    1. Initial program 0.4

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

    3. Applied associate-*l*0.5

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

    if 2.7353420168366805e+138 < (* (* y 9.0) z)

    1. Initial program 17.3

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

    3. Applied sub-neg17.3

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

    4. Applied associate-+l+17.3

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

    5. Simplified17.1

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

    6. Taylor expanded around inf 16.9

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

    8. Applied associate-*r*16.9

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

    10. Applied associate-*r*1.6

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z = -\infty:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 2.73534201683668052 \cdot 10^{138}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(27 \cdot \left(a \cdot b\right) - \left(\left(9 \cdot t\right) \cdot z\right) \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020024 
(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)))