Average Error: 3.9 → 0.6
Time: 3.5s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -6.8994864051139462 \cdot 10^{137} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 1.29661849668913275 \cdot 10^{228}\right):\\ \;\;\;\;\left(2 \cdot x - 9 \cdot \left(\left(t \cdot z\right) \cdot y\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + 27 \cdot \left(a \cdot b\right)\\ \end{array}\]
\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 -6.8994864051139462 \cdot 10^{137} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 1.29661849668913275 \cdot 10^{228}\right):\\
\;\;\;\;\left(2 \cdot x - 9 \cdot \left(\left(t \cdot z\right) \cdot y\right)\right) + \left(a \cdot 27\right) \cdot b\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r754210 = x;
        double r754211 = 2.0;
        double r754212 = r754210 * r754211;
        double r754213 = y;
        double r754214 = 9.0;
        double r754215 = r754213 * r754214;
        double r754216 = z;
        double r754217 = r754215 * r754216;
        double r754218 = t;
        double r754219 = r754217 * r754218;
        double r754220 = r754212 - r754219;
        double r754221 = a;
        double r754222 = 27.0;
        double r754223 = r754221 * r754222;
        double r754224 = b;
        double r754225 = r754223 * r754224;
        double r754226 = r754220 + r754225;
        return r754226;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r754227 = y;
        double r754228 = 9.0;
        double r754229 = r754227 * r754228;
        double r754230 = z;
        double r754231 = r754229 * r754230;
        double r754232 = -6.899486405113946e+137;
        bool r754233 = r754231 <= r754232;
        double r754234 = 1.2966184966891327e+228;
        bool r754235 = r754231 <= r754234;
        double r754236 = !r754235;
        bool r754237 = r754233 || r754236;
        double r754238 = 2.0;
        double r754239 = x;
        double r754240 = r754238 * r754239;
        double r754241 = t;
        double r754242 = r754241 * r754230;
        double r754243 = r754242 * r754227;
        double r754244 = r754228 * r754243;
        double r754245 = r754240 - r754244;
        double r754246 = a;
        double r754247 = 27.0;
        double r754248 = r754246 * r754247;
        double r754249 = b;
        double r754250 = r754248 * r754249;
        double r754251 = r754245 + r754250;
        double r754252 = r754239 * r754238;
        double r754253 = r754231 * r754241;
        double r754254 = r754252 - r754253;
        double r754255 = r754246 * r754249;
        double r754256 = r754247 * r754255;
        double r754257 = r754254 + r754256;
        double r754258 = r754237 ? r754251 : r754257;
        return r754258;
}

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

Original3.9
Target2.9
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) < -6.899486405113946e+137 or 1.2966184966891327e+228 < (* (* y 9.0) z)

    1. Initial program 23.9

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

    2. Taylor expanded around inf 23.1

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

    4. Applied associate-*r*1.7

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

    if -6.899486405113946e+137 < (* (* y 9.0) z) < 1.2966184966891327e+228

    1. Initial program 0.4

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

    2. Taylor expanded around 0 0.4

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -6.8994864051139462 \cdot 10^{137} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 1.29661849668913275 \cdot 10^{228}\right):\\ \;\;\;\;\left(2 \cdot x - 9 \cdot \left(\left(t \cdot z\right) \cdot y\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + 27 \cdot \left(a \cdot b\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020018 
(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)))