Average Error: 5.9 → 2.1
Time: 6.7s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -9.1318127710871948 \cdot 10^{-10} \lor \neg \left(x \le 52701.756950327122\right):\\ \;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(\left(y \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\sqrt[3]{\left(x \cdot 18\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot 18\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot 18\right) \cdot y}\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array}\]
\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}\;x \le -9.1318127710871948 \cdot 10^{-10} \lor \neg \left(x \le 52701.756950327122\right):\\
\;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(\left(y \cdot z\right) \cdot t\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\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(\left(\left(\left(\sqrt[3]{\left(x \cdot 18\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot 18\right) \cdot y}\right) \cdot \sqrt[3]{\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\\

\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 r807636 = x;
        double r807637 = 18.0;
        double r807638 = r807636 * r807637;
        double r807639 = y;
        double r807640 = r807638 * r807639;
        double r807641 = z;
        double r807642 = r807640 * r807641;
        double r807643 = t;
        double r807644 = r807642 * r807643;
        double r807645 = a;
        double r807646 = 4.0;
        double r807647 = r807645 * r807646;
        double r807648 = r807647 * r807643;
        double r807649 = r807644 - r807648;
        double r807650 = b;
        double r807651 = c;
        double r807652 = r807650 * r807651;
        double r807653 = r807649 + r807652;
        double r807654 = r807636 * r807646;
        double r807655 = i;
        double r807656 = r807654 * r807655;
        double r807657 = r807653 - r807656;
        double r807658 = j;
        double r807659 = 27.0;
        double r807660 = r807658 * r807659;
        double r807661 = k;
        double r807662 = r807660 * r807661;
        double r807663 = r807657 - r807662;
        return r807663;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r807664 = x;
        double r807665 = -9.131812771087195e-10;
        bool r807666 = r807664 <= r807665;
        double r807667 = 52701.75695032712;
        bool r807668 = r807664 <= r807667;
        double r807669 = !r807668;
        bool r807670 = r807666 || r807669;
        double r807671 = 18.0;
        double r807672 = r807664 * r807671;
        double r807673 = y;
        double r807674 = z;
        double r807675 = r807673 * r807674;
        double r807676 = t;
        double r807677 = r807675 * r807676;
        double r807678 = r807672 * r807677;
        double r807679 = a;
        double r807680 = 4.0;
        double r807681 = r807679 * r807680;
        double r807682 = r807681 * r807676;
        double r807683 = r807678 - r807682;
        double r807684 = b;
        double r807685 = c;
        double r807686 = r807684 * r807685;
        double r807687 = r807683 + r807686;
        double r807688 = r807664 * r807680;
        double r807689 = i;
        double r807690 = r807688 * r807689;
        double r807691 = r807687 - r807690;
        double r807692 = j;
        double r807693 = 27.0;
        double r807694 = r807692 * r807693;
        double r807695 = k;
        double r807696 = r807694 * r807695;
        double r807697 = r807691 - r807696;
        double r807698 = r807672 * r807673;
        double r807699 = cbrt(r807698);
        double r807700 = r807699 * r807699;
        double r807701 = r807700 * r807699;
        double r807702 = r807701 * r807674;
        double r807703 = r807702 * r807676;
        double r807704 = r807703 - r807682;
        double r807705 = r807704 + r807686;
        double r807706 = r807705 - r807690;
        double r807707 = r807706 - r807696;
        double r807708 = r807670 ? r807697 : r807707;
        return r807708;
}

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

Original5.9
Target1.7
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;t \lt -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{elif}\;t \lt 165.680279438052224:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -9.131812771087195e-10 or 52701.75695032712 < x

    1. Initial program 12.2

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

    3. Applied associate-*l*7.4

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

    5. Applied associate-*l*2.2

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

    if -9.131812771087195e-10 < x < 52701.75695032712

    1. Initial program 1.9

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

    3. Applied add-cube-cbrt2.0

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(\left(\sqrt[3]{\left(x \cdot 18\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot 18\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot 18\right) \cdot y}\right)} \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -9.1318127710871948 \cdot 10^{-10} \lor \neg \left(x \le 52701.756950327122\right):\\ \;\;\;\;\left(\left(\left(\left(x \cdot 18\right) \cdot \left(\left(y \cdot z\right) \cdot t\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(\sqrt[3]{\left(x \cdot 18\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot 18\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot 18\right) \cdot y}\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18) y) z) t) (* (* a 4) t)) (* b c)) (* (* x 4) i)) (* (* j 27) k)))