Average Error: 4.9 → 4.9
Time: 35.5s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[t \cdot \left(\left(x \cdot z\right) \cdot \left(18.0 \cdot y\right) - a \cdot 4.0\right) + \left(b \cdot c - \left(\left(k \cdot j\right) \cdot 27.0 + \left(x \cdot i\right) \cdot 4.0\right)\right)\]
\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k
↓
t \cdot \left(\left(x \cdot z\right) \cdot \left(18.0 \cdot y\right) - a \cdot 4.0\right) + \left(b \cdot c - \left(\left(k \cdot j\right) \cdot 27.0 + \left(x \cdot i\right) \cdot 4.0\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r6276453 = x;
        double r6276454 = 18.0;
        double r6276455 = r6276453 * r6276454;
        double r6276456 = y;
        double r6276457 = r6276455 * r6276456;
        double r6276458 = z;
        double r6276459 = r6276457 * r6276458;
        double r6276460 = t;
        double r6276461 = r6276459 * r6276460;
        double r6276462 = a;
        double r6276463 = 4.0;
        double r6276464 = r6276462 * r6276463;
        double r6276465 = r6276464 * r6276460;
        double r6276466 = r6276461 - r6276465;
        double r6276467 = b;
        double r6276468 = c;
        double r6276469 = r6276467 * r6276468;
        double r6276470 = r6276466 + r6276469;
        double r6276471 = r6276453 * r6276463;
        double r6276472 = i;
        double r6276473 = r6276471 * r6276472;
        double r6276474 = r6276470 - r6276473;
        double r6276475 = j;
        double r6276476 = 27.0;
        double r6276477 = r6276475 * r6276476;
        double r6276478 = k;
        double r6276479 = r6276477 * r6276478;
        double r6276480 = r6276474 - r6276479;
        return r6276480;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r6276481 = t;
        double r6276482 = x;
        double r6276483 = z;
        double r6276484 = r6276482 * r6276483;
        double r6276485 = 18.0;
        double r6276486 = y;
        double r6276487 = r6276485 * r6276486;
        double r6276488 = r6276484 * r6276487;
        double r6276489 = a;
        double r6276490 = 4.0;
        double r6276491 = r6276489 * r6276490;
        double r6276492 = r6276488 - r6276491;
        double r6276493 = r6276481 * r6276492;
        double r6276494 = b;
        double r6276495 = c;
        double r6276496 = r6276494 * r6276495;
        double r6276497 = k;
        double r6276498 = j;
        double r6276499 = r6276497 * r6276498;
        double r6276500 = 27.0;
        double r6276501 = r6276499 * r6276500;
        double r6276502 = i;
        double r6276503 = r6276482 * r6276502;
        double r6276504 = r6276503 * r6276490;
        double r6276505 = r6276501 + r6276504;
        double r6276506 = r6276496 - r6276505;
        double r6276507 = r6276493 + r6276506;
        return r6276507;
}

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

Bits error versus k

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 4.9

    \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]

  2. Simplified5.0

    \[\leadsto \color{blue}{\left(b \cdot c - \left(k \cdot \left(j \cdot 27.0\right) + \left(i \cdot x\right) \cdot 4.0\right)\right) + \left(\left(y \cdot x\right) \cdot \left(z \cdot 18.0\right) - a \cdot 4.0\right) \cdot t}\]
  3. Using strategy rm

  4. Applied associate-*l*5.0

    \[\leadsto \left(b \cdot c - \left(k \cdot \left(j \cdot 27.0\right) + \left(i \cdot x\right) \cdot 4.0\right)\right) + \left(\color{blue}{y \cdot \left(x \cdot \left(z \cdot 18.0\right)\right)} - a \cdot 4.0\right) \cdot t\]
  5. Using strategy rm

  6. Applied associate-*r*4.9

    \[\leadsto \left(b \cdot c - \left(\color{blue}{\left(k \cdot j\right) \cdot 27.0} + \left(i \cdot x\right) \cdot 4.0\right)\right) + \left(y \cdot \left(x \cdot \left(z \cdot 18.0\right)\right) - a \cdot 4.0\right) \cdot t\]
  7. Using strategy rm

  8. Applied associate-*r*4.8

    \[\leadsto \left(b \cdot c - \left(\left(k \cdot j\right) \cdot 27.0 + \left(i \cdot x\right) \cdot 4.0\right)\right) + \left(y \cdot \color{blue}{\left(\left(x \cdot z\right) \cdot 18.0\right)} - a \cdot 4.0\right) \cdot t\]

  9. Applied associate-*r*4.8

    \[\leadsto \left(b \cdot c - \left(\left(k \cdot j\right) \cdot 27.0 + \left(i \cdot x\right) \cdot 4.0\right)\right) + \left(\color{blue}{\left(y \cdot \left(x \cdot z\right)\right) \cdot 18.0} - a \cdot 4.0\right) \cdot t\]
  10. Using strategy rm

  11. Applied *-commutative4.8

    \[\leadsto \left(b \cdot c - \left(\left(k \cdot j\right) \cdot 27.0 + \left(i \cdot x\right) \cdot 4.0\right)\right) + \left(\color{blue}{\left(\left(x \cdot z\right) \cdot y\right)} \cdot 18.0 - a \cdot 4.0\right) \cdot t\]

  12. Applied associate-*l*4.9

    \[\leadsto \left(b \cdot c - \left(\left(k \cdot j\right) \cdot 27.0 + \left(i \cdot x\right) \cdot 4.0\right)\right) + \left(\color{blue}{\left(x \cdot z\right) \cdot \left(y \cdot 18.0\right)} - a \cdot 4.0\right) \cdot t\]

  13. Final simplification4.9

    \[\leadsto t \cdot \left(\left(x \cdot z\right) \cdot \left(18.0 \cdot y\right) - a \cdot 4.0\right) + \left(b \cdot c - \left(\left(k \cdot j\right) \cdot 27.0 + \left(x \cdot i\right) \cdot 4.0\right)\right)\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1"
  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))