Average Error: 5.1 → 2.1
Time: 24.8s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i = -\infty:\\ \;\;\;\;\left(\left(c \cdot b + \left(-t\right) \cdot \left(a \cdot 4.0\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(k \cdot 27.0\right) \cdot j\\ \mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le 8.513289245050075 \cdot 10^{+301}:\\ \;\;\;\;t \cdot \left(\left(y \cdot x\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right) + \left(c \cdot b - \left(\left(27.0 \cdot j\right) \cdot k + 4.0 \cdot \left(x \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot b + \left(e^{\log \left(\left(x \cdot 18.0\right) \cdot \left(\left(t \cdot z\right) \cdot y\right)\right)} - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\ \end{array}\]
\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k
↓
\begin{array}{l}
\mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i = -\infty:\\
\;\;\;\;\left(\left(c \cdot b + \left(-t\right) \cdot \left(a \cdot 4.0\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(k \cdot 27.0\right) \cdot j\\

\mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le 8.513289245050075 \cdot 10^{+301}:\\
\;\;\;\;t \cdot \left(\left(y \cdot x\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right) + \left(c \cdot b - \left(\left(27.0 \cdot j\right) \cdot k + 4.0 \cdot \left(x \cdot i\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(c \cdot b + \left(e^{\log \left(\left(x \cdot 18.0\right) \cdot \left(\left(t \cdot z\right) \cdot y\right)\right)} - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r5397684 = x;
        double r5397685 = 18.0;
        double r5397686 = r5397684 * r5397685;
        double r5397687 = y;
        double r5397688 = r5397686 * r5397687;
        double r5397689 = z;
        double r5397690 = r5397688 * r5397689;
        double r5397691 = t;
        double r5397692 = r5397690 * r5397691;
        double r5397693 = a;
        double r5397694 = 4.0;
        double r5397695 = r5397693 * r5397694;
        double r5397696 = r5397695 * r5397691;
        double r5397697 = r5397692 - r5397696;
        double r5397698 = b;
        double r5397699 = c;
        double r5397700 = r5397698 * r5397699;
        double r5397701 = r5397697 + r5397700;
        double r5397702 = r5397684 * r5397694;
        double r5397703 = i;
        double r5397704 = r5397702 * r5397703;
        double r5397705 = r5397701 - r5397704;
        double r5397706 = j;
        double r5397707 = 27.0;
        double r5397708 = r5397706 * r5397707;
        double r5397709 = k;
        double r5397710 = r5397708 * r5397709;
        double r5397711 = r5397705 - r5397710;
        return r5397711;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r5397712 = t;
        double r5397713 = x;
        double r5397714 = 18.0;
        double r5397715 = r5397713 * r5397714;
        double r5397716 = y;
        double r5397717 = r5397715 * r5397716;
        double r5397718 = z;
        double r5397719 = r5397717 * r5397718;
        double r5397720 = r5397712 * r5397719;
        double r5397721 = a;
        double r5397722 = 4.0;
        double r5397723 = r5397721 * r5397722;
        double r5397724 = r5397723 * r5397712;
        double r5397725 = r5397720 - r5397724;
        double r5397726 = c;
        double r5397727 = b;
        double r5397728 = r5397726 * r5397727;
        double r5397729 = r5397725 + r5397728;
        double r5397730 = r5397713 * r5397722;
        double r5397731 = i;
        double r5397732 = r5397730 * r5397731;
        double r5397733 = r5397729 - r5397732;
        double r5397734 = -inf.0;
        bool r5397735 = r5397733 <= r5397734;
        double r5397736 = -r5397712;
        double r5397737 = r5397736 * r5397723;
        double r5397738 = r5397728 + r5397737;
        double r5397739 = r5397738 - r5397732;
        double r5397740 = k;
        double r5397741 = 27.0;
        double r5397742 = r5397740 * r5397741;
        double r5397743 = j;
        double r5397744 = r5397742 * r5397743;
        double r5397745 = r5397739 - r5397744;
        double r5397746 = 8.513289245050075e+301;
        bool r5397747 = r5397733 <= r5397746;
        double r5397748 = r5397716 * r5397713;
        double r5397749 = r5397718 * r5397714;
        double r5397750 = r5397748 * r5397749;
        double r5397751 = r5397750 - r5397723;
        double r5397752 = r5397712 * r5397751;
        double r5397753 = r5397741 * r5397743;
        double r5397754 = r5397753 * r5397740;
        double r5397755 = r5397713 * r5397731;
        double r5397756 = r5397722 * r5397755;
        double r5397757 = r5397754 + r5397756;
        double r5397758 = r5397728 - r5397757;
        double r5397759 = r5397752 + r5397758;
        double r5397760 = r5397712 * r5397718;
        double r5397761 = r5397760 * r5397716;
        double r5397762 = r5397715 * r5397761;
        double r5397763 = log(r5397762);
        double r5397764 = exp(r5397763);
        double r5397765 = r5397764 - r5397724;
        double r5397766 = r5397728 + r5397765;
        double r5397767 = r5397766 - r5397732;
        double r5397768 = r5397743 * r5397740;
        double r5397769 = r5397741 * r5397768;
        double r5397770 = r5397767 - r5397769;
        double r5397771 = r5397747 ? r5397759 : r5397770;
        double r5397772 = r5397735 ? r5397745 : r5397771;
        return r5397772;
}

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

Bits error versus c

Bits error versus i

Bits error versus j

Bits error versus k

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < -inf.0

    1. Initial program 60.6

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*60.6

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \color{blue}{j \cdot \left(27.0 \cdot k\right)}\]

    4. Taylor expanded around 0 30.8

      \[\leadsto \left(\left(\left(\color{blue}{0} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\]

    if -inf.0 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < 8.513289245050075e+301

    1. Initial program 0.4

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

    2. Simplified0.4

      \[\leadsto \color{blue}{\left(b \cdot c - \left(k \cdot \left(j \cdot 27.0\right) + \left(i \cdot x\right) \cdot 4.0\right)\right) + \left(\left(y \cdot x\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right) \cdot t}\]

    if 8.513289245050075e+301 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))

    1. Initial program 48.9

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

    2. Taylor expanded around 0 48.9

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \color{blue}{27.0 \cdot \left(j \cdot k\right)}\]
    3. Using strategy rm

    4. Applied add-exp-log54.3

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot \color{blue}{e^{\log t}} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    5. Applied add-exp-log56.6

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot \color{blue}{e^{\log z}}\right) \cdot e^{\log t} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    6. Applied add-exp-log57.7

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot \color{blue}{e^{\log y}}\right) \cdot e^{\log z}\right) \cdot e^{\log t} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    7. Applied add-exp-log57.7

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot \color{blue}{e^{\log 18.0}}\right) \cdot e^{\log y}\right) \cdot e^{\log z}\right) \cdot e^{\log t} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    8. Applied add-exp-log58.4

      \[\leadsto \left(\left(\left(\left(\left(\left(\color{blue}{e^{\log x}} \cdot e^{\log 18.0}\right) \cdot e^{\log y}\right) \cdot e^{\log z}\right) \cdot e^{\log t} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    9. Applied prod-exp58.4

      \[\leadsto \left(\left(\left(\left(\left(\color{blue}{e^{\log x + \log 18.0}} \cdot e^{\log y}\right) \cdot e^{\log z}\right) \cdot e^{\log t} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    10. Applied prod-exp58.4

      \[\leadsto \left(\left(\left(\left(\color{blue}{e^{\left(\log x + \log 18.0\right) + \log y}} \cdot e^{\log z}\right) \cdot e^{\log t} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    11. Applied prod-exp56.9

      \[\leadsto \left(\left(\left(\color{blue}{e^{\left(\left(\log x + \log 18.0\right) + \log y\right) + \log z}} \cdot e^{\log t} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    12. Applied prod-exp52.2

      \[\leadsto \left(\left(\left(\color{blue}{e^{\left(\left(\left(\log x + \log 18.0\right) + \log y\right) + \log z\right) + \log t}} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    13. Simplified9.4

      \[\leadsto \left(\left(\left(e^{\color{blue}{\log \left(\left(18.0 \cdot x\right) \cdot \left(y \cdot \left(t \cdot z\right)\right)\right)}} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]
  3. Recombined 3 regimes into one program.

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i = -\infty:\\ \;\;\;\;\left(\left(c \cdot b + \left(-t\right) \cdot \left(a \cdot 4.0\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(k \cdot 27.0\right) \cdot j\\ \mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le 8.513289245050075 \cdot 10^{+301}:\\ \;\;\;\;t \cdot \left(\left(y \cdot x\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right) + \left(c \cdot b - \left(\left(27.0 \cdot j\right) \cdot k + 4.0 \cdot \left(x \cdot i\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot b + \left(e^{\log \left(\left(x \cdot 18.0\right) \cdot \left(\left(t \cdot z\right) \cdot y\right)\right)} - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))