Average Error: 12.5 → 9.0
Time: 26.8s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;j \le -3.558679195290626040559800458140671253204 \lor \neg \left(j \le 4.784801129022457779255706995671921542182 \cdot 10^{-23}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot z\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y} + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \end{array}\]
\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}\;j \le -3.558679195290626040559800458140671253204 \lor \neg \left(j \le 4.784801129022457779255706995671921542182 \cdot 10^{-23}\right):\\
\;\;\;\;\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(\left(\left(\left(x \cdot z\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y} + \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)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r78188 = x;
        double r78189 = y;
        double r78190 = z;
        double r78191 = r78189 * r78190;
        double r78192 = t;
        double r78193 = a;
        double r78194 = r78192 * r78193;
        double r78195 = r78191 - r78194;
        double r78196 = r78188 * r78195;
        double r78197 = b;
        double r78198 = c;
        double r78199 = r78198 * r78190;
        double r78200 = i;
        double r78201 = r78200 * r78193;
        double r78202 = r78199 - r78201;
        double r78203 = r78197 * r78202;
        double r78204 = r78196 - r78203;
        double r78205 = j;
        double r78206 = r78198 * r78192;
        double r78207 = r78200 * r78189;
        double r78208 = r78206 - r78207;
        double r78209 = r78205 * r78208;
        double r78210 = r78204 + r78209;
        return r78210;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r78211 = j;
        double r78212 = -3.558679195290626;
        bool r78213 = r78211 <= r78212;
        double r78214 = 4.784801129022458e-23;
        bool r78215 = r78211 <= r78214;
        double r78216 = !r78215;
        bool r78217 = r78213 || r78216;
        double r78218 = x;
        double r78219 = y;
        double r78220 = z;
        double r78221 = r78219 * r78220;
        double r78222 = t;
        double r78223 = a;
        double r78224 = r78222 * r78223;
        double r78225 = r78221 - r78224;
        double r78226 = r78218 * r78225;
        double r78227 = b;
        double r78228 = c;
        double r78229 = r78227 * r78228;
        double r78230 = r78220 * r78229;
        double r78231 = i;
        double r78232 = r78231 * r78223;
        double r78233 = -r78232;
        double r78234 = r78227 * r78233;
        double r78235 = r78230 + r78234;
        double r78236 = r78226 - r78235;
        double r78237 = r78228 * r78222;
        double r78238 = r78231 * r78219;
        double r78239 = r78237 - r78238;
        double r78240 = r78211 * r78239;
        double r78241 = r78236 + r78240;
        double r78242 = r78218 * r78220;
        double r78243 = cbrt(r78219);
        double r78244 = r78243 * r78243;
        double r78245 = r78242 * r78244;
        double r78246 = r78245 * r78243;
        double r78247 = r78218 * r78222;
        double r78248 = r78223 * r78247;
        double r78249 = -r78248;
        double r78250 = r78246 + r78249;
        double r78251 = r78228 * r78220;
        double r78252 = r78251 - r78232;
        double r78253 = r78227 * r78252;
        double r78254 = r78250 - r78253;
        double r78255 = r78211 * r78228;
        double r78256 = r78222 * r78255;
        double r78257 = r78211 * r78219;
        double r78258 = r78231 * r78257;
        double r78259 = -r78258;
        double r78260 = r78256 + r78259;
        double r78261 = r78254 + r78260;
        double r78262 = r78217 ? r78241 : r78261;
        return r78262;
}

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 2 regimes

  2. if j < -3.558679195290626 or 4.784801129022458e-23 < j

    1. Initial program 7.6

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

    3. Applied sub-neg7.6

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

    4. Applied distribute-lft-in7.6

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

    5. Simplified7.8

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

    if -3.558679195290626 < j < 4.784801129022458e-23

    1. Initial program 15.9

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

    3. Applied sub-neg15.9

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

    4. Applied distribute-lft-in15.9

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

    5. Simplified15.9

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

    6. Simplified15.8

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

    8. Applied associate-*r*15.3

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

    10. Applied add-cube-cbrt15.5

      \[\leadsto \left(\left(\left(x \cdot z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    11. Applied associate-*r*15.5

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

    13. Applied sub-neg15.5

      \[\leadsto \left(\left(\left(\left(x \cdot z\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y} + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \color{blue}{\left(c \cdot t + \left(-i \cdot y\right)\right)}\]

    14. Applied distribute-lft-in15.5

      \[\leadsto \left(\left(\left(\left(x \cdot z\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y} + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(j \cdot \left(c \cdot t\right) + j \cdot \left(-i \cdot y\right)\right)}\]

    15. Simplified13.0

      \[\leadsto \left(\left(\left(\left(x \cdot z\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y} + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\color{blue}{t \cdot \left(j \cdot c\right)} + j \cdot \left(-i \cdot y\right)\right)\]

    16. Simplified9.8

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

  4. Final simplification9.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;j \le -3.558679195290626040559800458140671253204 \lor \neg \left(j \le 4.784801129022457779255706995671921542182 \cdot 10^{-23}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(z \cdot \left(b \cdot c\right) + b \cdot \left(-i \cdot a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot z\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y} + \left(-a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(t \cdot \left(j \cdot c\right) + \left(-i \cdot \left(j \cdot y\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(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)))))