Average Error: 5.5 → 1.0
Time: 24.5s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i = -\infty:\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(y \cdot \left(\left(t \cdot x\right) \cdot z\right)\right) \cdot 18 - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i \le 5.292429442197061463553396675246931672241 \cdot 10^{278}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i\right) - \left(27 \cdot k\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot \left(t \cdot z\right)\right) \cdot y\right) \cdot 18 - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i\right) - \left(27 \cdot j\right) \cdot k\\ \end{array}\]
\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k
↓
\begin{array}{l}
\mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i = -\infty:\\
\;\;\;\;\left(\left(c \cdot b + \left(\left(y \cdot \left(\left(t \cdot x\right) \cdot z\right)\right) \cdot 18 - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - 27 \cdot \left(j \cdot k\right)\\

\mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i \le 5.292429442197061463553396675246931672241 \cdot 10^{278}:\\
\;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i\right) - \left(27 \cdot k\right) \cdot j\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(\left(\left(x \cdot \left(t \cdot z\right)\right) \cdot y\right) \cdot 18 - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i\right) - \left(27 \cdot j\right) \cdot k\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r35881536 = x;
        double r35881537 = 18.0;
        double r35881538 = r35881536 * r35881537;
        double r35881539 = y;
        double r35881540 = r35881538 * r35881539;
        double r35881541 = z;
        double r35881542 = r35881540 * r35881541;
        double r35881543 = t;
        double r35881544 = r35881542 * r35881543;
        double r35881545 = a;
        double r35881546 = 4.0;
        double r35881547 = r35881545 * r35881546;
        double r35881548 = r35881547 * r35881543;
        double r35881549 = r35881544 - r35881548;
        double r35881550 = b;
        double r35881551 = c;
        double r35881552 = r35881550 * r35881551;
        double r35881553 = r35881549 + r35881552;
        double r35881554 = r35881536 * r35881546;
        double r35881555 = i;
        double r35881556 = r35881554 * r35881555;
        double r35881557 = r35881553 - r35881556;
        double r35881558 = j;
        double r35881559 = 27.0;
        double r35881560 = r35881558 * r35881559;
        double r35881561 = k;
        double r35881562 = r35881560 * r35881561;
        double r35881563 = r35881557 - r35881562;
        return r35881563;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r35881564 = t;
        double r35881565 = x;
        double r35881566 = 18.0;
        double r35881567 = r35881565 * r35881566;
        double r35881568 = y;
        double r35881569 = r35881567 * r35881568;
        double r35881570 = z;
        double r35881571 = r35881569 * r35881570;
        double r35881572 = r35881564 * r35881571;
        double r35881573 = a;
        double r35881574 = 4.0;
        double r35881575 = r35881573 * r35881574;
        double r35881576 = r35881575 * r35881564;
        double r35881577 = r35881572 - r35881576;
        double r35881578 = c;
        double r35881579 = b;
        double r35881580 = r35881578 * r35881579;
        double r35881581 = r35881577 + r35881580;
        double r35881582 = r35881565 * r35881574;
        double r35881583 = i;
        double r35881584 = r35881582 * r35881583;
        double r35881585 = r35881581 - r35881584;
        double r35881586 = -inf.0;
        bool r35881587 = r35881585 <= r35881586;
        double r35881588 = r35881564 * r35881565;
        double r35881589 = r35881588 * r35881570;
        double r35881590 = r35881568 * r35881589;
        double r35881591 = r35881590 * r35881566;
        double r35881592 = r35881591 - r35881576;
        double r35881593 = r35881580 + r35881592;
        double r35881594 = r35881593 - r35881584;
        double r35881595 = 27.0;
        double r35881596 = j;
        double r35881597 = k;
        double r35881598 = r35881596 * r35881597;
        double r35881599 = r35881595 * r35881598;
        double r35881600 = r35881594 - r35881599;
        double r35881601 = 5.2924294421970615e+278;
        bool r35881602 = r35881585 <= r35881601;
        double r35881603 = r35881595 * r35881597;
        double r35881604 = r35881603 * r35881596;
        double r35881605 = r35881585 - r35881604;
        double r35881606 = r35881564 * r35881570;
        double r35881607 = r35881565 * r35881606;
        double r35881608 = r35881607 * r35881568;
        double r35881609 = r35881608 * r35881566;
        double r35881610 = r35881609 - r35881576;
        double r35881611 = r35881610 + r35881580;
        double r35881612 = r35881611 - r35881584;
        double r35881613 = r35881595 * r35881596;
        double r35881614 = r35881613 * r35881597;
        double r35881615 = r35881612 - r35881614;
        double r35881616 = r35881602 ? r35881605 : r35881615;
        double r35881617 = r35881587 ? r35881600 : r35881616;
        return r35881617;
}

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

Target

Original5.5
Target1.4
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;t \lt -1.62108153975413982700795070153457058168 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{elif}\;t \lt 165.6802794380522243500308832153677940369:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < -inf.0

    1. Initial program 64.0

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    2. Taylor expanded around inf 42.7

      \[\leadsto \left(\left(\left(\color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    3. Using strategy rm

    4. Applied associate-*r*19.6

      \[\leadsto \left(\left(\left(18 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot \left(z \cdot y\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    5. Using strategy rm

    6. Applied associate-*r*4.8

      \[\leadsto \left(\left(\left(18 \cdot \color{blue}{\left(\left(\left(t \cdot x\right) \cdot z\right) \cdot y\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    7. Taylor expanded around 0 4.6

      \[\leadsto \left(\left(\left(18 \cdot \left(\left(\left(t \cdot x\right) \cdot z\right) \cdot y\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \color{blue}{27 \cdot \left(j \cdot k\right)}\]

    if -inf.0 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) < 5.2924294421970615e+278

    1. Initial program 0.3

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*0.3

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \color{blue}{j \cdot \left(27 \cdot k\right)}\]

    if 5.2924294421970615e+278 < (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i))

    1. Initial program 32.5

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    2. Taylor expanded around inf 23.2

      \[\leadsto \left(\left(\left(\color{blue}{18 \cdot \left(t \cdot \left(x \cdot \left(z \cdot y\right)\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    3. Using strategy rm

    4. Applied associate-*r*15.3

      \[\leadsto \left(\left(\left(18 \cdot \color{blue}{\left(\left(t \cdot x\right) \cdot \left(z \cdot y\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    5. Using strategy rm

    6. Applied associate-*r*7.2

      \[\leadsto \left(\left(\left(18 \cdot \color{blue}{\left(\left(\left(t \cdot x\right) \cdot z\right) \cdot y\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
    7. Using strategy rm

    8. Applied *-un-lft-identity7.2

      \[\leadsto \left(\left(\left(18 \cdot \left(\left(\left(t \cdot x\right) \cdot z\right) \cdot \color{blue}{\left(1 \cdot y\right)}\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    9. Applied associate-*r*7.2

      \[\leadsto \left(\left(\left(18 \cdot \color{blue}{\left(\left(\left(\left(t \cdot x\right) \cdot z\right) \cdot 1\right) \cdot y\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    10. Simplified7.3

      \[\leadsto \left(\left(\left(18 \cdot \left(\color{blue}{\left(\left(t \cdot z\right) \cdot x\right)} \cdot y\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i = -\infty:\\ \;\;\;\;\left(\left(c \cdot b + \left(\left(y \cdot \left(\left(t \cdot x\right) \cdot z\right)\right) \cdot 18 - \left(a \cdot 4\right) \cdot t\right)\right) - \left(x \cdot 4\right) \cdot i\right) - 27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i \le 5.292429442197061463553396675246931672241 \cdot 10^{278}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i\right) - \left(27 \cdot k\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(x \cdot \left(t \cdot z\right)\right) \cdot y\right) \cdot 18 - \left(a \cdot 4\right) \cdot t\right) + c \cdot b\right) - \left(x \cdot 4\right) \cdot i\right) - \left(27 \cdot j\right) \cdot k\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))