Average Error: 5.4 → 1.2
Time: 1.1m
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le -4.6433365676357043 \cdot 10^{+297}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(z \cdot \left(x \cdot \left(18.0 \cdot t\right)\right)\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(k \cdot j\right) \cdot 27.0\\ \mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le 3.8550714784291394 \cdot 10^{+279}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(27.0 \cdot k\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(z \cdot \left(x \cdot \left(18.0 \cdot t\right)\right)\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(k \cdot j\right) \cdot 27.0\\ \end{array}\]
\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 \le -4.6433365676357043 \cdot 10^{+297}:\\
\;\;\;\;\left(\left(\left(y \cdot \left(z \cdot \left(x \cdot \left(18.0 \cdot t\right)\right)\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(k \cdot j\right) \cdot 27.0\\

\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 3.8550714784291394 \cdot 10^{+279}:\\
\;\;\;\;\left(\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\right) - \left(27.0 \cdot k\right) \cdot j\\

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

\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 r26447010 = x;
        double r26447011 = 18.0;
        double r26447012 = r26447010 * r26447011;
        double r26447013 = y;
        double r26447014 = r26447012 * r26447013;
        double r26447015 = z;
        double r26447016 = r26447014 * r26447015;
        double r26447017 = t;
        double r26447018 = r26447016 * r26447017;
        double r26447019 = a;
        double r26447020 = 4.0;
        double r26447021 = r26447019 * r26447020;
        double r26447022 = r26447021 * r26447017;
        double r26447023 = r26447018 - r26447022;
        double r26447024 = b;
        double r26447025 = c;
        double r26447026 = r26447024 * r26447025;
        double r26447027 = r26447023 + r26447026;
        double r26447028 = r26447010 * r26447020;
        double r26447029 = i;
        double r26447030 = r26447028 * r26447029;
        double r26447031 = r26447027 - r26447030;
        double r26447032 = j;
        double r26447033 = 27.0;
        double r26447034 = r26447032 * r26447033;
        double r26447035 = k;
        double r26447036 = r26447034 * r26447035;
        double r26447037 = r26447031 - r26447036;
        return r26447037;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r26447038 = t;
        double r26447039 = x;
        double r26447040 = 18.0;
        double r26447041 = r26447039 * r26447040;
        double r26447042 = y;
        double r26447043 = r26447041 * r26447042;
        double r26447044 = z;
        double r26447045 = r26447043 * r26447044;
        double r26447046 = r26447038 * r26447045;
        double r26447047 = a;
        double r26447048 = 4.0;
        double r26447049 = r26447047 * r26447048;
        double r26447050 = r26447049 * r26447038;
        double r26447051 = r26447046 - r26447050;
        double r26447052 = c;
        double r26447053 = b;
        double r26447054 = r26447052 * r26447053;
        double r26447055 = r26447051 + r26447054;
        double r26447056 = r26447039 * r26447048;
        double r26447057 = i;
        double r26447058 = r26447056 * r26447057;
        double r26447059 = r26447055 - r26447058;
        double r26447060 = -4.6433365676357043e+297;
        bool r26447061 = r26447059 <= r26447060;
        double r26447062 = r26447040 * r26447038;
        double r26447063 = r26447039 * r26447062;
        double r26447064 = r26447044 * r26447063;
        double r26447065 = r26447042 * r26447064;
        double r26447066 = r26447065 - r26447050;
        double r26447067 = r26447066 + r26447054;
        double r26447068 = r26447067 - r26447058;
        double r26447069 = k;
        double r26447070 = j;
        double r26447071 = r26447069 * r26447070;
        double r26447072 = 27.0;
        double r26447073 = r26447071 * r26447072;
        double r26447074 = r26447068 - r26447073;
        double r26447075 = 3.8550714784291394e+279;
        bool r26447076 = r26447059 <= r26447075;
        double r26447077 = r26447072 * r26447069;
        double r26447078 = r26447077 * r26447070;
        double r26447079 = r26447059 - r26447078;
        double r26447080 = r26447076 ? r26447079 : r26447074;
        double r26447081 = r26447061 ? r26447074 : r26447080;
        return r26447081;
}

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 2 regimes

  2. if (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < -4.6433365676357043e+297 or 3.8550714784291394e+279 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))

    1. Initial program 37.9

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

    2. Taylor expanded around -inf 37.8

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

    4. Applied add-cube-cbrt37.9

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

    5. Applied associate-*r*37.9

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

    7. Applied pow137.9

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \color{blue}{{\left(\sqrt[3]{t}\right)}^{1}} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    8. Applied pow137.9

      \[\leadsto \left(\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot \color{blue}{{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}^{1}}\right) \cdot {\left(\sqrt[3]{t}\right)}^{1} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    9. Applied pow137.9

      \[\leadsto \left(\left(\left(\left(\color{blue}{{\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right)}^{1}} \cdot {\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}^{1}\right) \cdot {\left(\sqrt[3]{t}\right)}^{1} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    10. Applied pow-prod-down37.9

      \[\leadsto \left(\left(\left(\color{blue}{{\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right)}^{1}} \cdot {\left(\sqrt[3]{t}\right)}^{1} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    11. Applied pow-prod-down37.9

      \[\leadsto \left(\left(\left(\color{blue}{{\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t}\right)}^{1}} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    12. Simplified6.7

      \[\leadsto \left(\left(\left({\color{blue}{\left(\left(\left(\left(t \cdot 18.0\right) \cdot x\right) \cdot z\right) \cdot y\right)}}^{1} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\]

    if -4.6433365676357043e+297 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < 3.8550714784291394e+279

    1. Initial program 0.3

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

    3. Applied associate-*l*0.3

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \color{blue}{j \cdot \left(27.0 \cdot k\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le -4.6433365676357043 \cdot 10^{+297}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(z \cdot \left(x \cdot \left(18.0 \cdot t\right)\right)\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(k \cdot j\right) \cdot 27.0\\ \mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le 3.8550714784291394 \cdot 10^{+279}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(27.0 \cdot k\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(y \cdot \left(z \cdot \left(x \cdot \left(18.0 \cdot t\right)\right)\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(k \cdot j\right) \cdot 27.0\\ \end{array}\]

Reproduce

herbie shell --seed 2019120 
(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)))