Average Error: 5.8 → 4.2
Time: 13.1s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.6888285353026094 \cdot 10^{97} \lor \neg \left(z \le 4.5937779867099482 \cdot 10^{-105}\right):\\ \;\;\;\;\mathsf{fma}\left(t, \left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4, b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4, b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, \left(j \cdot 27\right) \cdot k\right)\right)\\ \end{array}\]
\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}\;z \le -3.6888285353026094 \cdot 10^{97} \lor \neg \left(z \le 4.5937779867099482 \cdot 10^{-105}\right):\\
\;\;\;\;\mathsf{fma}\left(t, \left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4, b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(t, \left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4, b \cdot c - \mathsf{fma}\left(x, 4 \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 r112271 = x;
        double r112272 = 18.0;
        double r112273 = r112271 * r112272;
        double r112274 = y;
        double r112275 = r112273 * r112274;
        double r112276 = z;
        double r112277 = r112275 * r112276;
        double r112278 = t;
        double r112279 = r112277 * r112278;
        double r112280 = a;
        double r112281 = 4.0;
        double r112282 = r112280 * r112281;
        double r112283 = r112282 * r112278;
        double r112284 = r112279 - r112283;
        double r112285 = b;
        double r112286 = c;
        double r112287 = r112285 * r112286;
        double r112288 = r112284 + r112287;
        double r112289 = r112271 * r112281;
        double r112290 = i;
        double r112291 = r112289 * r112290;
        double r112292 = r112288 - r112291;
        double r112293 = j;
        double r112294 = 27.0;
        double r112295 = r112293 * r112294;
        double r112296 = k;
        double r112297 = r112295 * r112296;
        double r112298 = r112292 - r112297;
        return r112298;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r112299 = z;
        double r112300 = -3.688828535302609e+97;
        bool r112301 = r112299 <= r112300;
        double r112302 = 4.593777986709948e-105;
        bool r112303 = r112299 <= r112302;
        double r112304 = !r112303;
        bool r112305 = r112301 || r112304;
        double r112306 = t;
        double r112307 = x;
        double r112308 = 18.0;
        double r112309 = r112307 * r112308;
        double r112310 = y;
        double r112311 = r112309 * r112310;
        double r112312 = r112311 * r112299;
        double r112313 = a;
        double r112314 = 4.0;
        double r112315 = r112313 * r112314;
        double r112316 = r112312 - r112315;
        double r112317 = b;
        double r112318 = c;
        double r112319 = r112317 * r112318;
        double r112320 = i;
        double r112321 = r112314 * r112320;
        double r112322 = j;
        double r112323 = 27.0;
        double r112324 = k;
        double r112325 = r112323 * r112324;
        double r112326 = r112322 * r112325;
        double r112327 = fma(r112307, r112321, r112326);
        double r112328 = r112319 - r112327;
        double r112329 = fma(r112306, r112316, r112328);
        double r112330 = r112310 * r112299;
        double r112331 = r112309 * r112330;
        double r112332 = r112331 - r112315;
        double r112333 = r112322 * r112323;
        double r112334 = r112333 * r112324;
        double r112335 = fma(r112307, r112321, r112334);
        double r112336 = r112319 - r112335;
        double r112337 = fma(r112306, r112332, r112336);
        double r112338 = r112305 ? r112329 : r112337;
        return r112338;
}

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

Derivation

  1. Split input into 2 regimes

  2. if z < -3.688828535302609e+97 or 4.593777986709948e-105 < z

    1. Initial program 6.8

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

    2. Simplified6.9

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

    4. Applied associate-*l*6.9

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

    if -3.688828535302609e+97 < z < 4.593777986709948e-105

    1. Initial program 4.9

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

    2. Simplified5.0

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

    4. Applied associate-*l*2.0

      \[\leadsto \mathsf{fma}\left(t, \color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4, b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, \left(j \cdot 27\right) \cdot k\right)\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification4.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.6888285353026094 \cdot 10^{97} \lor \neg \left(z \le 4.5937779867099482 \cdot 10^{-105}\right):\\ \;\;\;\;\mathsf{fma}\left(t, \left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4, b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, j \cdot \left(27 \cdot k\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4, b \cdot c - \mathsf{fma}\left(x, 4 \cdot i, \left(j \cdot 27\right) \cdot k\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(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)))