Average Error: 5.4 → 4.2
Time: 9.1s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -7.5200119166880343 \cdot 10^{-93} \lor \neg \left(t \le 8.24455457144902905 \cdot 10^{-121}\right):\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \end{array}\]
\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}\;t \le -7.5200119166880343 \cdot 10^{-93} \lor \neg \left(t \le 8.24455457144902905 \cdot 10^{-121}\right):\\
\;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\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 r119146 = x;
        double r119147 = 18.0;
        double r119148 = r119146 * r119147;
        double r119149 = y;
        double r119150 = r119148 * r119149;
        double r119151 = z;
        double r119152 = r119150 * r119151;
        double r119153 = t;
        double r119154 = r119152 * r119153;
        double r119155 = a;
        double r119156 = 4.0;
        double r119157 = r119155 * r119156;
        double r119158 = r119157 * r119153;
        double r119159 = r119154 - r119158;
        double r119160 = b;
        double r119161 = c;
        double r119162 = r119160 * r119161;
        double r119163 = r119159 + r119162;
        double r119164 = r119146 * r119156;
        double r119165 = i;
        double r119166 = r119164 * r119165;
        double r119167 = r119163 - r119166;
        double r119168 = j;
        double r119169 = 27.0;
        double r119170 = r119168 * r119169;
        double r119171 = k;
        double r119172 = r119170 * r119171;
        double r119173 = r119167 - r119172;
        return r119173;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r119174 = t;
        double r119175 = -7.520011916688034e-93;
        bool r119176 = r119174 <= r119175;
        double r119177 = 8.244554571449029e-121;
        bool r119178 = r119174 <= r119177;
        double r119179 = !r119178;
        bool r119180 = r119176 || r119179;
        double r119181 = x;
        double r119182 = 18.0;
        double r119183 = r119181 * r119182;
        double r119184 = y;
        double r119185 = r119183 * r119184;
        double r119186 = z;
        double r119187 = r119185 * r119186;
        double r119188 = a;
        double r119189 = 4.0;
        double r119190 = r119188 * r119189;
        double r119191 = r119187 - r119190;
        double r119192 = r119174 * r119191;
        double r119193 = b;
        double r119194 = c;
        double r119195 = r119193 * r119194;
        double r119196 = r119181 * r119189;
        double r119197 = i;
        double r119198 = r119196 * r119197;
        double r119199 = j;
        double r119200 = 27.0;
        double r119201 = k;
        double r119202 = r119200 * r119201;
        double r119203 = r119199 * r119202;
        double r119204 = r119198 + r119203;
        double r119205 = r119195 - r119204;
        double r119206 = r119192 + r119205;
        double r119207 = 0.0;
        double r119208 = r119207 - r119190;
        double r119209 = r119174 * r119208;
        double r119210 = r119199 * r119200;
        double r119211 = r119210 * r119201;
        double r119212 = r119198 + r119211;
        double r119213 = r119195 - r119212;
        double r119214 = r119209 + r119213;
        double r119215 = r119180 ? r119206 : r119214;
        return r119215;
}

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 t < -7.520011916688034e-93 or 8.244554571449029e-121 < t

    1. Initial program 2.9

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

    2. Simplified2.9

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

    4. Applied associate-*l*3.0

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

    if -7.520011916688034e-93 < t < 8.244554571449029e-121

    1. Initial program 8.9

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

    2. Simplified8.9

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

    3. Taylor expanded around 0 5.9

      \[\leadsto t \cdot \left(\color{blue}{0} - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification4.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -7.5200119166880343 \cdot 10^{-93} \lor \neg \left(t \le 8.24455457144902905 \cdot 10^{-121}\right):\\ \;\;\;\;t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020003 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  :precision binary64
  (- (- (+ (- (* (* (* (* x 18) y) z) t) (* (* a 4) t)) (* b c)) (* (* x 4) i)) (* (* j 27) k)))