Average Error: 3.7 → 1.3
Time: 9.7s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot 9 \le -8.63828739859890366 \cdot 10^{64} \lor \neg \left(y \cdot 9 \le 4.26640526336584695 \cdot 10^{171}\right):\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 + \left(-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]
\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}\;y \cdot 9 \le -8.63828739859890366 \cdot 10^{64} \lor \neg \left(y \cdot 9 \le 4.26640526336584695 \cdot 10^{171}\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}:\\
\;\;\;\;\left(x \cdot 2 + \left(-9 \cdot \left(t \cdot \left(z \cdot y\right)\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 r796300 = x;
        double r796301 = 2.0;
        double r796302 = r796300 * r796301;
        double r796303 = y;
        double r796304 = 9.0;
        double r796305 = r796303 * r796304;
        double r796306 = z;
        double r796307 = r796305 * r796306;
        double r796308 = t;
        double r796309 = r796307 * r796308;
        double r796310 = r796302 - r796309;
        double r796311 = a;
        double r796312 = 27.0;
        double r796313 = r796311 * r796312;
        double r796314 = b;
        double r796315 = r796313 * r796314;
        double r796316 = r796310 + r796315;
        return r796316;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r796317 = y;
        double r796318 = 9.0;
        double r796319 = r796317 * r796318;
        double r796320 = -8.638287398598904e+64;
        bool r796321 = r796319 <= r796320;
        double r796322 = 4.266405263365847e+171;
        bool r796323 = r796319 <= r796322;
        double r796324 = !r796323;
        bool r796325 = r796321 || r796324;
        double r796326 = x;
        double r796327 = 2.0;
        double r796328 = r796326 * r796327;
        double r796329 = z;
        double r796330 = t;
        double r796331 = r796329 * r796330;
        double r796332 = r796319 * r796331;
        double r796333 = r796328 - r796332;
        double r796334 = a;
        double r796335 = 27.0;
        double r796336 = r796334 * r796335;
        double r796337 = b;
        double r796338 = r796336 * r796337;
        double r796339 = r796333 + r796338;
        double r796340 = r796329 * r796317;
        double r796341 = r796330 * r796340;
        double r796342 = r796318 * r796341;
        double r796343 = -r796342;
        double r796344 = r796328 + r796343;
        double r796345 = r796344 + r796338;
        double r796346 = r796325 ? r796339 : r796345;
        return r796346;
}

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
Target2.6
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y 9.0) < -8.638287398598904e+64 or 4.266405263365847e+171 < (* y 9.0)

    1. Initial program 10.7

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

    3. Applied associate-*l*1.0

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

    if -8.638287398598904e+64 < (* y 9.0) < 4.266405263365847e+171

    1. Initial program 1.4

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

    3. Applied sub-neg1.4

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

    4. Simplified1.4

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

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \le -8.63828739859890366 \cdot 10^{64} \lor \neg \left(y \cdot 9 \le 4.26640526336584695 \cdot 10^{171}\right):\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 + \left(-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 
(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)))