Average Error: 11.5 → 11.8
Time: 48.8s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\left(\sqrt[3]{\left(z \cdot y - t \cdot a\right) \cdot x} \cdot \left(\sqrt[3]{\left(z \cdot y - t \cdot a\right) \cdot x} \cdot \sqrt[3]{\left(z \cdot y - t \cdot a\right) \cdot x}\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(t \cdot c - i \cdot y\right) \cdot j\]
\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)
↓
\left(\sqrt[3]{\left(z \cdot y - t \cdot a\right) \cdot x} \cdot \left(\sqrt[3]{\left(z \cdot y - t \cdot a\right) \cdot x} \cdot \sqrt[3]{\left(z \cdot y - t \cdot a\right) \cdot x}\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right) + \left(t \cdot c - i \cdot y\right) \cdot j
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r10239375 = x;
        double r10239376 = y;
        double r10239377 = z;
        double r10239378 = r10239376 * r10239377;
        double r10239379 = t;
        double r10239380 = a;
        double r10239381 = r10239379 * r10239380;
        double r10239382 = r10239378 - r10239381;
        double r10239383 = r10239375 * r10239382;
        double r10239384 = b;
        double r10239385 = c;
        double r10239386 = r10239385 * r10239377;
        double r10239387 = i;
        double r10239388 = r10239387 * r10239380;
        double r10239389 = r10239386 - r10239388;
        double r10239390 = r10239384 * r10239389;
        double r10239391 = r10239383 - r10239390;
        double r10239392 = j;
        double r10239393 = r10239385 * r10239379;
        double r10239394 = r10239387 * r10239376;
        double r10239395 = r10239393 - r10239394;
        double r10239396 = r10239392 * r10239395;
        double r10239397 = r10239391 + r10239396;
        return r10239397;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r10239398 = z;
        double r10239399 = y;
        double r10239400 = r10239398 * r10239399;
        double r10239401 = t;
        double r10239402 = a;
        double r10239403 = r10239401 * r10239402;
        double r10239404 = r10239400 - r10239403;
        double r10239405 = x;
        double r10239406 = r10239404 * r10239405;
        double r10239407 = cbrt(r10239406);
        double r10239408 = r10239407 * r10239407;
        double r10239409 = r10239407 * r10239408;
        double r10239410 = b;
        double r10239411 = c;
        double r10239412 = r10239398 * r10239411;
        double r10239413 = i;
        double r10239414 = r10239413 * r10239402;
        double r10239415 = r10239412 - r10239414;
        double r10239416 = r10239410 * r10239415;
        double r10239417 = r10239409 - r10239416;
        double r10239418 = r10239401 * r10239411;
        double r10239419 = r10239413 * r10239399;
        double r10239420 = r10239418 - r10239419;
        double r10239421 = j;
        double r10239422 = r10239420 * r10239421;
        double r10239423 = r10239417 + r10239422;
        return r10239423;
}

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. Initial program 11.5

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

  3. Applied add-cube-cbrt11.8

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

  4. Final simplification11.8

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

Reproduce

herbie shell --seed 2019124 
(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)))))