Average Error: 5.4 → 1.2
Time: 1.2m
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 r18838081 = x;
        double r18838082 = 18.0;
        double r18838083 = r18838081 * r18838082;
        double r18838084 = y;
        double r18838085 = r18838083 * r18838084;
        double r18838086 = z;
        double r18838087 = r18838085 * r18838086;
        double r18838088 = t;
        double r18838089 = r18838087 * r18838088;
        double r18838090 = a;
        double r18838091 = 4.0;
        double r18838092 = r18838090 * r18838091;
        double r18838093 = r18838092 * r18838088;
        double r18838094 = r18838089 - r18838093;
        double r18838095 = b;
        double r18838096 = c;
        double r18838097 = r18838095 * r18838096;
        double r18838098 = r18838094 + r18838097;
        double r18838099 = r18838081 * r18838091;
        double r18838100 = i;
        double r18838101 = r18838099 * r18838100;
        double r18838102 = r18838098 - r18838101;
        double r18838103 = j;
        double r18838104 = 27.0;
        double r18838105 = r18838103 * r18838104;
        double r18838106 = k;
        double r18838107 = r18838105 * r18838106;
        double r18838108 = r18838102 - r18838107;
        return r18838108;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r18838109 = t;
        double r18838110 = x;
        double r18838111 = 18.0;
        double r18838112 = r18838110 * r18838111;
        double r18838113 = y;
        double r18838114 = r18838112 * r18838113;
        double r18838115 = z;
        double r18838116 = r18838114 * r18838115;
        double r18838117 = r18838109 * r18838116;
        double r18838118 = a;
        double r18838119 = 4.0;
        double r18838120 = r18838118 * r18838119;
        double r18838121 = r18838120 * r18838109;
        double r18838122 = r18838117 - r18838121;
        double r18838123 = c;
        double r18838124 = b;
        double r18838125 = r18838123 * r18838124;
        double r18838126 = r18838122 + r18838125;
        double r18838127 = r18838110 * r18838119;
        double r18838128 = i;
        double r18838129 = r18838127 * r18838128;
        double r18838130 = r18838126 - r18838129;
        double r18838131 = -4.6433365676357043e+297;
        bool r18838132 = r18838130 <= r18838131;
        double r18838133 = r18838111 * r18838109;
        double r18838134 = r18838110 * r18838133;
        double r18838135 = r18838115 * r18838134;
        double r18838136 = r18838113 * r18838135;
        double r18838137 = r18838136 - r18838121;
        double r18838138 = r18838137 + r18838125;
        double r18838139 = r18838138 - r18838129;
        double r18838140 = k;
        double r18838141 = j;
        double r18838142 = r18838140 * r18838141;
        double r18838143 = 27.0;
        double r18838144 = r18838142 * r18838143;
        double r18838145 = r18838139 - r18838144;
        double r18838146 = 3.8550714784291394e+279;
        bool r18838147 = r18838130 <= r18838146;
        double r18838148 = r18838143 * r18838140;
        double r18838149 = r18838148 * r18838141;
        double r18838150 = r18838130 - r18838149;
        double r18838151 = r18838147 ? r18838150 : r18838145;
        double r18838152 = r18838132 ? r18838145 : r18838151;
        return r18838152;
}

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 +o rules:numerics
(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)))