Average Error: 5.5 → 0.9
Time: 1.3m
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i = -\infty:\\ \;\;\;\;\left(\left(c \cdot b + \left(x \cdot \left(18 \cdot \left(\left(t \cdot z\right) \cdot y\right)\right) - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i \le 2.091817559392553810929566838550160622791 \cdot 10^{304}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i\right) - \left(k \cdot 27\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot b + \left(x \cdot \left(\left(y \cdot 18\right) \cdot \left(t \cdot z\right)\right) - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \end{array}\]
\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k
↓
\begin{array}{l}
\mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i = -\infty:\\
\;\;\;\;\left(\left(c \cdot b + \left(x \cdot \left(18 \cdot \left(\left(t \cdot z\right) \cdot y\right)\right) - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\

\mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i \le 2.091817559392553810929566838550160622791 \cdot 10^{304}:\\
\;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i\right) - \left(k \cdot 27\right) \cdot j\\

\mathbf{else}:\\
\;\;\;\;\left(\left(c \cdot b + \left(x \cdot \left(\left(y \cdot 18\right) \cdot \left(t \cdot z\right)\right) - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\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 r5189035 = x;
        double r5189036 = 18.0;
        double r5189037 = r5189035 * r5189036;
        double r5189038 = y;
        double r5189039 = r5189037 * r5189038;
        double r5189040 = z;
        double r5189041 = r5189039 * r5189040;
        double r5189042 = t;
        double r5189043 = r5189041 * r5189042;
        double r5189044 = a;
        double r5189045 = 4.0;
        double r5189046 = r5189044 * r5189045;
        double r5189047 = r5189046 * r5189042;
        double r5189048 = r5189043 - r5189047;
        double r5189049 = b;
        double r5189050 = c;
        double r5189051 = r5189049 * r5189050;
        double r5189052 = r5189048 + r5189051;
        double r5189053 = r5189035 * r5189045;
        double r5189054 = i;
        double r5189055 = r5189053 * r5189054;
        double r5189056 = r5189052 - r5189055;
        double r5189057 = j;
        double r5189058 = 27.0;
        double r5189059 = r5189057 * r5189058;
        double r5189060 = k;
        double r5189061 = r5189059 * r5189060;
        double r5189062 = r5189056 - r5189061;
        return r5189062;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r5189063 = t;
        double r5189064 = x;
        double r5189065 = 18.0;
        double r5189066 = r5189064 * r5189065;
        double r5189067 = y;
        double r5189068 = r5189066 * r5189067;
        double r5189069 = z;
        double r5189070 = r5189068 * r5189069;
        double r5189071 = r5189063 * r5189070;
        double r5189072 = a;
        double r5189073 = 4.0;
        double r5189074 = r5189072 * r5189073;
        double r5189075 = r5189074 * r5189063;
        double r5189076 = r5189071 - r5189075;
        double r5189077 = c;
        double r5189078 = b;
        double r5189079 = r5189077 * r5189078;
        double r5189080 = r5189076 + r5189079;
        double r5189081 = r5189064 * r5189073;
        double r5189082 = i;
        double r5189083 = r5189081 * r5189082;
        double r5189084 = r5189080 - r5189083;
        double r5189085 = -inf.0;
        bool r5189086 = r5189084 <= r5189085;
        double r5189087 = r5189063 * r5189069;
        double r5189088 = r5189087 * r5189067;
        double r5189089 = r5189065 * r5189088;
        double r5189090 = r5189064 * r5189089;
        double r5189091 = r5189090 - r5189075;
        double r5189092 = r5189079 + r5189091;
        double r5189093 = r5189092 - r5189083;
        double r5189094 = k;
        double r5189095 = j;
        double r5189096 = 27.0;
        double r5189097 = r5189095 * r5189096;
        double r5189098 = r5189094 * r5189097;
        double r5189099 = r5189093 - r5189098;
        double r5189100 = 2.0918175593925538e+304;
        bool r5189101 = r5189084 <= r5189100;
        double r5189102 = r5189094 * r5189096;
        double r5189103 = r5189102 * r5189095;
        double r5189104 = r5189084 - r5189103;
        double r5189105 = r5189067 * r5189065;
        double r5189106 = r5189105 * r5189087;
        double r5189107 = r5189064 * r5189106;
        double r5189108 = r5189107 - r5189075;
        double r5189109 = r5189079 + r5189108;
        double r5189110 = r5189109 - r5189083;
        double r5189111 = r5189110 - r5189098;
        double r5189112 = r5189101 ? r5189104 : r5189111;
        double r5189113 = r5189086 ? r5189099 : r5189112;
        return r5189113;
}

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 64.0

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*37.0

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    4. Using strategy rm

    5. Applied associate-*l*5.1

      \[\leadsto \left(\left(\left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    6. Using strategy rm

    7. Applied associate-*l*5.1

      \[\leadsto \left(\left(\left(\color{blue}{x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    if -inf.0 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < 2.0918175593925538e+304

    1. Initial program 0.3

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*0.3

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \color{blue}{j \cdot \left(27 \cdot k\right)}\]

    if 2.0918175593925538e+304 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))

    1. Initial program 56.2

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*31.4

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(x \cdot 18\right) \cdot y\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    4. Using strategy rm

    5. Applied associate-*l*9.1

      \[\leadsto \left(\left(\left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot \left(z \cdot t\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    6. Using strategy rm

    7. Applied associate-*l*8.4

      \[\leadsto \left(\left(\left(\color{blue}{x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    8. Using strategy rm

    9. Applied associate-*r*8.8

      \[\leadsto \left(\left(\left(x \cdot \color{blue}{\left(\left(18 \cdot y\right) \cdot \left(z \cdot t\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i = -\infty:\\ \;\;\;\;\left(\left(c \cdot b + \left(x \cdot \left(18 \cdot \left(\left(t \cdot z\right) \cdot y\right)\right) - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i \le 2.091817559392553810929566838550160622791 \cdot 10^{304}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i\right) - \left(k \cdot 27\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot b + \left(x \cdot \left(\left(y \cdot 18\right) \cdot \left(t \cdot z\right)\right) - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - k \cdot \left(j \cdot 27\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(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)))