Average Error: 11.9 → 11.9
Time: 29.3s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;j \le -7.756528578962063 \cdot 10^{-141}:\\ \;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - a \cdot \left(x \cdot t\right)\right) - \left(\left(-a\right) \cdot \left(i \cdot b\right) + b \cdot \left(c \cdot z\right)\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\ \mathbf{elif}\;j \le -1.9251627712030188 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - a \cdot i\right)\\ \mathbf{elif}\;j \le -8.261919533682203 \cdot 10^{-282}:\\ \;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - a \cdot \left(x \cdot t\right)\right) - \left(\left(-a\right) \cdot \left(i \cdot b\right) + b \cdot \left(c \cdot z\right)\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\ \mathbf{elif}\;j \le 3.7368582959710634 \cdot 10^{-162}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - a \cdot \left(x \cdot t\right)\right) - \left(\left(-a\right) \cdot \left(i \cdot b\right) + b \cdot \left(c \cdot z\right)\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\ \end{array}\]
\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 -7.756528578962063 \cdot 10^{-141}:\\
\;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - a \cdot \left(x \cdot t\right)\right) - \left(\left(-a\right) \cdot \left(i \cdot b\right) + b \cdot \left(c \cdot z\right)\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\

\mathbf{elif}\;j \le -1.9251627712030188 \cdot 10^{-231}:\\
\;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - a \cdot i\right)\\

\mathbf{elif}\;j \le -8.261919533682203 \cdot 10^{-282}:\\
\;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - a \cdot \left(x \cdot t\right)\right) - \left(\left(-a\right) \cdot \left(i \cdot b\right) + b \cdot \left(c \cdot z\right)\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\

\mathbf{elif}\;j \le 3.7368582959710634 \cdot 10^{-162}:\\
\;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - a \cdot i\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - a \cdot \left(x \cdot t\right)\right) - \left(\left(-a\right) \cdot \left(i \cdot b\right) + b \cdot \left(c \cdot z\right)\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r1807347 = x;
        double r1807348 = y;
        double r1807349 = z;
        double r1807350 = r1807348 * r1807349;
        double r1807351 = t;
        double r1807352 = a;
        double r1807353 = r1807351 * r1807352;
        double r1807354 = r1807350 - r1807353;
        double r1807355 = r1807347 * r1807354;
        double r1807356 = b;
        double r1807357 = c;
        double r1807358 = r1807357 * r1807349;
        double r1807359 = i;
        double r1807360 = r1807359 * r1807352;
        double r1807361 = r1807358 - r1807360;
        double r1807362 = r1807356 * r1807361;
        double r1807363 = r1807355 - r1807362;
        double r1807364 = j;
        double r1807365 = r1807357 * r1807351;
        double r1807366 = r1807359 * r1807348;
        double r1807367 = r1807365 - r1807366;
        double r1807368 = r1807364 * r1807367;
        double r1807369 = r1807363 + r1807368;
        return r1807369;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r1807370 = j;
        double r1807371 = -7.756528578962063e-141;
        bool r1807372 = r1807370 <= r1807371;
        double r1807373 = x;
        double r1807374 = z;
        double r1807375 = r1807373 * r1807374;
        double r1807376 = y;
        double r1807377 = r1807375 * r1807376;
        double r1807378 = a;
        double r1807379 = t;
        double r1807380 = r1807373 * r1807379;
        double r1807381 = r1807378 * r1807380;
        double r1807382 = r1807377 - r1807381;
        double r1807383 = -r1807378;
        double r1807384 = i;
        double r1807385 = b;
        double r1807386 = r1807384 * r1807385;
        double r1807387 = r1807383 * r1807386;
        double r1807388 = c;
        double r1807389 = r1807388 * r1807374;
        double r1807390 = r1807385 * r1807389;
        double r1807391 = r1807387 + r1807390;
        double r1807392 = r1807382 - r1807391;
        double r1807393 = r1807388 * r1807379;
        double r1807394 = r1807376 * r1807384;
        double r1807395 = r1807393 - r1807394;
        double r1807396 = r1807370 * r1807395;
        double r1807397 = r1807392 + r1807396;
        double r1807398 = -1.9251627712030188e-231;
        bool r1807399 = r1807370 <= r1807398;
        double r1807400 = r1807376 * r1807374;
        double r1807401 = r1807379 * r1807378;
        double r1807402 = r1807400 - r1807401;
        double r1807403 = r1807373 * r1807402;
        double r1807404 = r1807378 * r1807384;
        double r1807405 = r1807389 - r1807404;
        double r1807406 = r1807385 * r1807405;
        double r1807407 = r1807403 - r1807406;
        double r1807408 = -8.261919533682203e-282;
        bool r1807409 = r1807370 <= r1807408;
        double r1807410 = 3.7368582959710634e-162;
        bool r1807411 = r1807370 <= r1807410;
        double r1807412 = r1807411 ? r1807407 : r1807397;
        double r1807413 = r1807409 ? r1807397 : r1807412;
        double r1807414 = r1807399 ? r1807407 : r1807413;
        double r1807415 = r1807372 ? r1807397 : r1807414;
        return r1807415;
}

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 < -7.756528578962063e-141 or -1.9251627712030188e-231 < j < -8.261919533682203e-282 or 3.7368582959710634e-162 < j

    1. Initial program 10.4

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

    3. Applied sub-neg10.4

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

    4. Applied distribute-lft-in10.4

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

    5. Taylor expanded around inf 10.2

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

    7. Applied associate-*r*10.3

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

    9. Applied distribute-lft-neg-in10.3

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

    10. Applied associate-*r*9.7

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

    if -7.756528578962063e-141 < j < -1.9251627712030188e-231 or -8.261919533682203e-282 < j < 3.7368582959710634e-162

    1. Initial program 15.6

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

    2. Taylor expanded around 0 17.3

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

  4. Final simplification11.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;j \le -7.756528578962063 \cdot 10^{-141}:\\ \;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - a \cdot \left(x \cdot t\right)\right) - \left(\left(-a\right) \cdot \left(i \cdot b\right) + b \cdot \left(c \cdot z\right)\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\ \mathbf{elif}\;j \le -1.9251627712030188 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - a \cdot i\right)\\ \mathbf{elif}\;j \le -8.261919533682203 \cdot 10^{-282}:\\ \;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - a \cdot \left(x \cdot t\right)\right) - \left(\left(-a\right) \cdot \left(i \cdot b\right) + b \cdot \left(c \cdot z\right)\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\ \mathbf{elif}\;j \le 3.7368582959710634 \cdot 10^{-162}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot z\right) \cdot y - a \cdot \left(x \cdot t\right)\right) - \left(\left(-a\right) \cdot \left(i \cdot b\right) + b \cdot \left(c \cdot z\right)\right)\right) + j \cdot \left(c \cdot t - y \cdot i\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))