Average Error: 12.1 → 11.2
Time: 27.1s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -5.790815325220392908858165475828676773669 \cdot 10^{105}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot j\right) \cdot c + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \le -1.53784447253032729710026066052934139026 \cdot 10^{-198}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;y \le 4.328665951797104146389136561894216279411 \cdot 10^{-260}:\\ \;\;\;\;\left(\left(x \cdot \left(z \cdot y\right) + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \le 9.417727496660265300992831427606688521337 \cdot 10^{-4}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-\left(\left(i \cdot j\right) \cdot \sqrt{y}\right) \cdot \sqrt{y}\right)\right)\\ \end{array}\]
\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)
↓
\begin{array}{l}
\mathbf{if}\;y \le -5.790815325220392908858165475828676773669 \cdot 10^{105}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot j\right) \cdot c + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\

\mathbf{elif}\;y \le -1.53784447253032729710026066052934139026 \cdot 10^{-198}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

\mathbf{elif}\;y \le 4.328665951797104146389136561894216279411 \cdot 10^{-260}:\\
\;\;\;\;\left(\left(x \cdot \left(z \cdot y\right) + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\

\mathbf{elif}\;y \le 9.417727496660265300992831427606688521337 \cdot 10^{-4}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-\left(\left(i \cdot j\right) \cdot \sqrt{y}\right) \cdot \sqrt{y}\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 r80236 = x;
        double r80237 = y;
        double r80238 = z;
        double r80239 = r80237 * r80238;
        double r80240 = t;
        double r80241 = a;
        double r80242 = r80240 * r80241;
        double r80243 = r80239 - r80242;
        double r80244 = r80236 * r80243;
        double r80245 = b;
        double r80246 = c;
        double r80247 = r80246 * r80238;
        double r80248 = i;
        double r80249 = r80248 * r80241;
        double r80250 = r80247 - r80249;
        double r80251 = r80245 * r80250;
        double r80252 = r80244 - r80251;
        double r80253 = j;
        double r80254 = r80246 * r80240;
        double r80255 = r80248 * r80237;
        double r80256 = r80254 - r80255;
        double r80257 = r80253 * r80256;
        double r80258 = r80252 + r80257;
        return r80258;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r80259 = y;
        double r80260 = -5.790815325220393e+105;
        bool r80261 = r80259 <= r80260;
        double r80262 = x;
        double r80263 = z;
        double r80264 = r80259 * r80263;
        double r80265 = t;
        double r80266 = a;
        double r80267 = r80265 * r80266;
        double r80268 = r80264 - r80267;
        double r80269 = r80262 * r80268;
        double r80270 = b;
        double r80271 = c;
        double r80272 = r80271 * r80263;
        double r80273 = i;
        double r80274 = r80273 * r80266;
        double r80275 = r80272 - r80274;
        double r80276 = r80270 * r80275;
        double r80277 = r80269 - r80276;
        double r80278 = j;
        double r80279 = r80265 * r80278;
        double r80280 = r80279 * r80271;
        double r80281 = r80278 * r80259;
        double r80282 = r80273 * r80281;
        double r80283 = -r80282;
        double r80284 = r80280 + r80283;
        double r80285 = r80277 + r80284;
        double r80286 = -1.5378444725303273e-198;
        bool r80287 = r80259 <= r80286;
        double r80288 = r80270 * r80271;
        double r80289 = r80263 * r80288;
        double r80290 = -r80274;
        double r80291 = r80270 * r80290;
        double r80292 = r80289 + r80291;
        double r80293 = r80269 - r80292;
        double r80294 = r80271 * r80265;
        double r80295 = r80273 * r80259;
        double r80296 = r80294 - r80295;
        double r80297 = r80278 * r80296;
        double r80298 = r80293 + r80297;
        double r80299 = 4.328665951797104e-260;
        bool r80300 = r80259 <= r80299;
        double r80301 = r80263 * r80259;
        double r80302 = r80262 * r80301;
        double r80303 = r80262 * r80265;
        double r80304 = r80266 * r80303;
        double r80305 = -r80304;
        double r80306 = r80302 + r80305;
        double r80307 = r80306 - r80276;
        double r80308 = r80278 * r80271;
        double r80309 = r80265 * r80308;
        double r80310 = r80309 + r80283;
        double r80311 = r80307 + r80310;
        double r80312 = 0.0009417727496660265;
        bool r80313 = r80259 <= r80312;
        double r80314 = r80273 * r80278;
        double r80315 = sqrt(r80259);
        double r80316 = r80314 * r80315;
        double r80317 = r80316 * r80315;
        double r80318 = -r80317;
        double r80319 = r80309 + r80318;
        double r80320 = r80277 + r80319;
        double r80321 = r80313 ? r80298 : r80320;
        double r80322 = r80300 ? r80311 : r80321;
        double r80323 = r80287 ? r80298 : r80322;
        double r80324 = r80261 ? r80285 : r80323;
        return r80324;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 4 regimes

  2. if y < -5.790815325220393e+105

    1. Initial program 21.9

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

    3. Applied sub-neg21.9

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

    4. Applied distribute-lft-in21.9

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

    5. Simplified21.6

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

    6. Simplified20.9

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

    8. Applied associate-*r*20.6

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

    if -5.790815325220393e+105 < y < -1.5378444725303273e-198 or 4.328665951797104e-260 < y < 0.0009417727496660265

    1. Initial program 9.3

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

    3. Applied sub-neg9.3

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

    4. Applied distribute-lft-in9.3

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

    5. Simplified8.9

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

    if -1.5378444725303273e-198 < y < 4.328665951797104e-260

    1. Initial program 9.5

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

    3. Applied sub-neg9.5

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

    4. Applied distribute-lft-in9.5

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

    5. Simplified10.0

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

    6. Simplified9.9

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

    8. Applied sub-neg9.9

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

    9. Applied distribute-lft-in9.9

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

    10. Simplified9.9

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

    11. Simplified11.0

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

    if 0.0009417727496660265 < y

    1. Initial program 16.5

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

    3. Applied sub-neg16.5

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

    4. Applied distribute-lft-in16.5

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

    5. Simplified16.4

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

    6. Simplified16.2

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

    8. Applied associate-*r*12.2

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

    10. Applied add-sqr-sqrt12.3

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

    11. Applied associate-*r*12.3

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

  4. Final simplification11.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5.790815325220392908858165475828676773669 \cdot 10^{105}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\left(t \cdot j\right) \cdot c + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \le -1.53784447253032729710026066052934139026 \cdot 10^{-198}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;y \le 4.328665951797104146389136561894216279411 \cdot 10^{-260}:\\ \;\;\;\;\left(\left(x \cdot \left(z \cdot y\right) + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \mathbf{elif}\;y \le 9.417727496660265300992831427606688521337 \cdot 10^{-4}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-\left(\left(i \cdot j\right) \cdot \sqrt{y}\right) \cdot \sqrt{y}\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))