Average Error: 12.4 → 9.8
Time: 7.4s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -6.2838196173283195 \cdot 10^{123} \lor \neg \left(b \le 904684009115.72681\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{c \cdot z - i \cdot a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(b \cdot c\right) \cdot z + \left(b \cdot i\right) \cdot \left(-a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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}\;b \le -6.2838196173283195 \cdot 10^{123} \lor \neg \left(b \le 904684009115.72681\right):\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{c \cdot z - i \cdot a}\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) - \left(\left(b \cdot c\right) \cdot z + \left(b \cdot i\right) \cdot \left(-a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r138327 = x;
        double r138328 = y;
        double r138329 = z;
        double r138330 = r138328 * r138329;
        double r138331 = t;
        double r138332 = a;
        double r138333 = r138331 * r138332;
        double r138334 = r138330 - r138333;
        double r138335 = r138327 * r138334;
        double r138336 = b;
        double r138337 = c;
        double r138338 = r138337 * r138329;
        double r138339 = i;
        double r138340 = r138339 * r138332;
        double r138341 = r138338 - r138340;
        double r138342 = r138336 * r138341;
        double r138343 = r138335 - r138342;
        double r138344 = j;
        double r138345 = r138337 * r138331;
        double r138346 = r138339 * r138328;
        double r138347 = r138345 - r138346;
        double r138348 = r138344 * r138347;
        double r138349 = r138343 + r138348;
        return r138349;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r138350 = b;
        double r138351 = -6.28381961732832e+123;
        bool r138352 = r138350 <= r138351;
        double r138353 = 904684009115.7268;
        bool r138354 = r138350 <= r138353;
        double r138355 = !r138354;
        bool r138356 = r138352 || r138355;
        double r138357 = x;
        double r138358 = y;
        double r138359 = z;
        double r138360 = r138358 * r138359;
        double r138361 = t;
        double r138362 = a;
        double r138363 = r138361 * r138362;
        double r138364 = r138360 - r138363;
        double r138365 = r138357 * r138364;
        double r138366 = c;
        double r138367 = r138366 * r138359;
        double r138368 = i;
        double r138369 = r138368 * r138362;
        double r138370 = r138367 - r138369;
        double r138371 = cbrt(r138370);
        double r138372 = r138371 * r138371;
        double r138373 = r138372 * r138371;
        double r138374 = r138350 * r138373;
        double r138375 = r138365 - r138374;
        double r138376 = j;
        double r138377 = r138366 * r138361;
        double r138378 = r138368 * r138358;
        double r138379 = r138377 - r138378;
        double r138380 = r138376 * r138379;
        double r138381 = r138375 + r138380;
        double r138382 = r138350 * r138366;
        double r138383 = r138382 * r138359;
        double r138384 = r138350 * r138368;
        double r138385 = -r138362;
        double r138386 = r138384 * r138385;
        double r138387 = r138383 + r138386;
        double r138388 = r138365 - r138387;
        double r138389 = r138388 + r138380;
        double r138390 = r138356 ? r138381 : r138389;
        return r138390;
}

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 b < -6.28381961732832e+123 or 904684009115.7268 < b

    1. Initial program 7.5

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

    3. Applied add-cube-cbrt8.1

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

    if -6.28381961732832e+123 < b < 904684009115.7268

    1. Initial program 14.4

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

    3. Applied sub-neg14.4

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

    4. Applied distribute-lft-in14.4

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

    6. Applied distribute-rgt-neg-in14.4

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

    7. Applied associate-*r*12.3

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

    9. Applied associate-*r*10.5

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

  4. Final simplification9.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -6.2838196173283195 \cdot 10^{123} \lor \neg \left(b \le 904684009115.72681\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{c \cdot z - i \cdot a}\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(b \cdot c\right) \cdot z + \left(b \cdot i\right) \cdot \left(-a\right)\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(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)))))