Average Error: 3.7 → 0.6
Time: 4.0s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -8.9800446771093483 \cdot 10^{217} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 7.947264576269877 \cdot 10^{204}\right):\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot x - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]
\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -8.9800446771093483 \cdot 10^{217} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 7.947264576269877 \cdot 10^{204}\right):\\
\;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + 27 \cdot \left(a \cdot b\right)\\

\mathbf{else}:\\
\;\;\;\;\left(2 \cdot x - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r757640 = x;
        double r757641 = 2.0;
        double r757642 = r757640 * r757641;
        double r757643 = y;
        double r757644 = 9.0;
        double r757645 = r757643 * r757644;
        double r757646 = z;
        double r757647 = r757645 * r757646;
        double r757648 = t;
        double r757649 = r757647 * r757648;
        double r757650 = r757642 - r757649;
        double r757651 = a;
        double r757652 = 27.0;
        double r757653 = r757651 * r757652;
        double r757654 = b;
        double r757655 = r757653 * r757654;
        double r757656 = r757650 + r757655;
        return r757656;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r757657 = y;
        double r757658 = 9.0;
        double r757659 = r757657 * r757658;
        double r757660 = z;
        double r757661 = r757659 * r757660;
        double r757662 = -8.980044677109348e+217;
        bool r757663 = r757661 <= r757662;
        double r757664 = 7.947264576269877e+204;
        bool r757665 = r757661 <= r757664;
        double r757666 = !r757665;
        bool r757667 = r757663 || r757666;
        double r757668 = x;
        double r757669 = 2.0;
        double r757670 = r757668 * r757669;
        double r757671 = t;
        double r757672 = r757660 * r757671;
        double r757673 = r757659 * r757672;
        double r757674 = r757670 - r757673;
        double r757675 = 27.0;
        double r757676 = a;
        double r757677 = b;
        double r757678 = r757676 * r757677;
        double r757679 = r757675 * r757678;
        double r757680 = r757674 + r757679;
        double r757681 = r757669 * r757668;
        double r757682 = r757660 * r757657;
        double r757683 = r757671 * r757682;
        double r757684 = r757658 * r757683;
        double r757685 = r757681 - r757684;
        double r757686 = r757676 * r757675;
        double r757687 = r757686 * r757677;
        double r757688 = r757685 + r757687;
        double r757689 = r757667 ? r757680 : r757688;
        return r757689;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.7
Target2.7
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* (* y 9.0) z) < -8.980044677109348e+217 or 7.947264576269877e+204 < (* (* y 9.0) z)

    1. Initial program 28.2

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
    2. Using strategy rm

    3. Applied associate-*l*1.1

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b\]

    4. Taylor expanded around 0 1.0

      \[\leadsto \left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \color{blue}{27 \cdot \left(a \cdot b\right)}\]

    if -8.980044677109348e+217 < (* (* y 9.0) z) < 7.947264576269877e+204

    1. Initial program 0.5

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
    2. Using strategy rm

    3. Applied associate-*l*3.8

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b\]

    4. Taylor expanded around inf 0.5

      \[\leadsto \color{blue}{\left(2 \cdot x - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)} + \left(a \cdot 27\right) \cdot b\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -8.9800446771093483 \cdot 10^{217} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 7.947264576269877 \cdot 10^{204}\right):\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot x - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< y 7.590524218811189e-161) (+ (- (* x 2) (* (* (* y 9) z) t)) (* a (* 27 b))) (+ (- (* x 2) (* 9 (* y (* t z)))) (* (* a 27) b)))

  (+ (- (* x 2) (* (* (* y 9) z) t)) (* (* a 27) b)))