Average Error: 3.7 → 1.3
Time: 7.5s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot 9 \le -8.63828739859890366 \cdot 10^{64} \lor \neg \left(y \cdot 9 \le 4.26640526336584695 \cdot 10^{171}\right):\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 + \left(-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]
\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 r1364278 = x;
        double r1364279 = 2.0;
        double r1364280 = r1364278 * r1364279;
        double r1364281 = y;
        double r1364282 = 9.0;
        double r1364283 = r1364281 * r1364282;
        double r1364284 = z;
        double r1364285 = r1364283 * r1364284;
        double r1364286 = t;
        double r1364287 = r1364285 * r1364286;
        double r1364288 = r1364280 - r1364287;
        double r1364289 = a;
        double r1364290 = 27.0;
        double r1364291 = r1364289 * r1364290;
        double r1364292 = b;
        double r1364293 = r1364291 * r1364292;
        double r1364294 = r1364288 + r1364293;
        return r1364294;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r1364295 = y;
        double r1364296 = 9.0;
        double r1364297 = r1364295 * r1364296;
        double r1364298 = -8.638287398598904e+64;
        bool r1364299 = r1364297 <= r1364298;
        double r1364300 = 4.266405263365847e+171;
        bool r1364301 = r1364297 <= r1364300;
        double r1364302 = !r1364301;
        bool r1364303 = r1364299 || r1364302;
        double r1364304 = x;
        double r1364305 = 2.0;
        double r1364306 = r1364304 * r1364305;
        double r1364307 = z;
        double r1364308 = t;
        double r1364309 = r1364307 * r1364308;
        double r1364310 = r1364297 * r1364309;
        double r1364311 = r1364306 - r1364310;
        double r1364312 = a;
        double r1364313 = 27.0;
        double r1364314 = r1364312 * r1364313;
        double r1364315 = b;
        double r1364316 = r1364314 * r1364315;
        double r1364317 = r1364311 + r1364316;
        double r1364318 = r1364307 * r1364295;
        double r1364319 = r1364308 * r1364318;
        double r1364320 = r1364296 * r1364319;
        double r1364321 = -r1364320;
        double r1364322 = r1364306 + r1364321;
        double r1364323 = r1364322 + r1364316;
        double r1364324 = r1364303 ? r1364317 : r1364323;
        return r1364324;
}

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)))