Average Error: 5.4 → 0.6
Time: 39.1s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le -5.404085228185933 \cdot 10^{+307}:\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(\left(t \cdot z\right) \cdot y\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le 5.729051567323238 \cdot 10^{+306}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(\left(t \cdot z\right) \cdot y\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\ \end{array}\]
\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 \le -5.404085228185933 \cdot 10^{+307}:\\
\;\;\;\;\left(\left(c \cdot b + \left(\left(\left(t \cdot z\right) \cdot y\right) \cdot \left(x \cdot 18.0\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)\\

\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 5.729051567323238 \cdot 10^{+306}:\\
\;\;\;\;\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) - 27.0 \cdot \left(j \cdot k\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(c \cdot b + \left(\left(\left(t \cdot z\right) \cdot y\right) \cdot \left(x \cdot 18.0\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 r5979047 = x;
        double r5979048 = 18.0;
        double r5979049 = r5979047 * r5979048;
        double r5979050 = y;
        double r5979051 = r5979049 * r5979050;
        double r5979052 = z;
        double r5979053 = r5979051 * r5979052;
        double r5979054 = t;
        double r5979055 = r5979053 * r5979054;
        double r5979056 = a;
        double r5979057 = 4.0;
        double r5979058 = r5979056 * r5979057;
        double r5979059 = r5979058 * r5979054;
        double r5979060 = r5979055 - r5979059;
        double r5979061 = b;
        double r5979062 = c;
        double r5979063 = r5979061 * r5979062;
        double r5979064 = r5979060 + r5979063;
        double r5979065 = r5979047 * r5979057;
        double r5979066 = i;
        double r5979067 = r5979065 * r5979066;
        double r5979068 = r5979064 - r5979067;
        double r5979069 = j;
        double r5979070 = 27.0;
        double r5979071 = r5979069 * r5979070;
        double r5979072 = k;
        double r5979073 = r5979071 * r5979072;
        double r5979074 = r5979068 - r5979073;
        return r5979074;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r5979075 = t;
        double r5979076 = x;
        double r5979077 = 18.0;
        double r5979078 = r5979076 * r5979077;
        double r5979079 = y;
        double r5979080 = r5979078 * r5979079;
        double r5979081 = z;
        double r5979082 = r5979080 * r5979081;
        double r5979083 = r5979075 * r5979082;
        double r5979084 = a;
        double r5979085 = 4.0;
        double r5979086 = r5979084 * r5979085;
        double r5979087 = r5979086 * r5979075;
        double r5979088 = r5979083 - r5979087;
        double r5979089 = c;
        double r5979090 = b;
        double r5979091 = r5979089 * r5979090;
        double r5979092 = r5979088 + r5979091;
        double r5979093 = r5979076 * r5979085;
        double r5979094 = i;
        double r5979095 = r5979093 * r5979094;
        double r5979096 = r5979092 - r5979095;
        double r5979097 = -5.404085228185933e+307;
        bool r5979098 = r5979096 <= r5979097;
        double r5979099 = r5979075 * r5979081;
        double r5979100 = r5979099 * r5979079;
        double r5979101 = r5979100 * r5979078;
        double r5979102 = r5979101 - r5979087;
        double r5979103 = r5979091 + r5979102;
        double r5979104 = r5979103 - r5979095;
        double r5979105 = 27.0;
        double r5979106 = j;
        double r5979107 = k;
        double r5979108 = r5979106 * r5979107;
        double r5979109 = r5979105 * r5979108;
        double r5979110 = r5979104 - r5979109;
        double r5979111 = 5.729051567323238e+306;
        bool r5979112 = r5979096 <= r5979111;
        double r5979113 = r5979096 - r5979109;
        double r5979114 = r5979112 ? r5979113 : r5979110;
        double r5979115 = r5979098 ? r5979110 : r5979114;
        return r5979115;
}

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)) < -5.404085228185933e+307 or 5.729051567323238e+306 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))

    1. Initial program 58.6

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

    3. Applied associate-*l*35.1

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

    4. Taylor expanded around 0 35.0

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

    6. Applied associate-*l*5.0

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

    if -5.404085228185933e+307 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < 5.729051567323238e+306

    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. Using strategy rm

    3. Applied associate-*l*3.4

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

    4. Taylor expanded around 0 3.2

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

    6. Applied associate-*r*0.2

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le -5.404085228185933 \cdot 10^{+307}:\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(\left(t \cdot z\right) \cdot y\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i \le 5.729051567323238 \cdot 10^{+306}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4.0\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(\left(t \cdot z\right) \cdot y\right) \cdot \left(x \cdot 18.0\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - 27.0 \cdot \left(j \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019144 +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)))