Average Error: 3.7 → 0.7
Time: 4.6s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -2.45757297895094979 \cdot 10^{136} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 7.2920232258789333 \cdot 10^{208}\right):\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right)\\ \end{array}\]
\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 -2.45757297895094979 \cdot 10^{136} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 7.2920232258789333 \cdot 10^{208}\right):\\
\;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r873957 = x;
        double r873958 = 2.0;
        double r873959 = r873957 * r873958;
        double r873960 = y;
        double r873961 = 9.0;
        double r873962 = r873960 * r873961;
        double r873963 = z;
        double r873964 = r873962 * r873963;
        double r873965 = t;
        double r873966 = r873964 * r873965;
        double r873967 = r873959 - r873966;
        double r873968 = a;
        double r873969 = 27.0;
        double r873970 = r873968 * r873969;
        double r873971 = b;
        double r873972 = r873970 * r873971;
        double r873973 = r873967 + r873972;
        return r873973;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r873974 = y;
        double r873975 = 9.0;
        double r873976 = r873974 * r873975;
        double r873977 = z;
        double r873978 = r873976 * r873977;
        double r873979 = -2.45757297895095e+136;
        bool r873980 = r873978 <= r873979;
        double r873981 = 7.292023225878933e+208;
        bool r873982 = r873978 <= r873981;
        double r873983 = !r873982;
        bool r873984 = r873980 || r873983;
        double r873985 = x;
        double r873986 = 2.0;
        double r873987 = r873985 * r873986;
        double r873988 = t;
        double r873989 = r873977 * r873988;
        double r873990 = r873976 * r873989;
        double r873991 = r873987 - r873990;
        double r873992 = a;
        double r873993 = 27.0;
        double r873994 = r873992 * r873993;
        double r873995 = b;
        double r873996 = r873994 * r873995;
        double r873997 = r873991 + r873996;
        double r873998 = r873993 * r873995;
        double r873999 = r873975 * r873977;
        double r874000 = r873974 * r873999;
        double r874001 = r874000 * r873988;
        double r874002 = r873987 - r874001;
        double r874003 = fma(r873992, r873998, r874002);
        double r874004 = r873984 ? r873997 : r874003;
        return r874004;
}

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

Target

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

Derivation

  1. Split input into 2 regimes

  2. if (* (* y 9.0) z) < -2.45757297895095e+136 or 7.292023225878933e+208 < (* (* y 9.0) z)

    1. Initial program 21.9

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

    3. Applied associate-*l*2.0

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

    if -2.45757297895095e+136 < (* (* y 9.0) z) < 7.292023225878933e+208

    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. Simplified0.4

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)}\]
    3. Using strategy rm

    4. Applied associate-*l*0.4

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -2.45757297895094979 \cdot 10^{136} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 7.2920232258789333 \cdot 10^{208}\right):\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(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)))