Average Error: 3.5 → 0.6
Time: 10.1s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -9.22147439343650667 \cdot 10^{163} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 1.946628139104975 \cdot 10^{150}\right):\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \end{array}\]
\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 -9.22147439343650667 \cdot 10^{163} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 1.946628139104975 \cdot 10^{150}\right):\\
\;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\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) + a \cdot \left(27 \cdot b\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r707264 = x;
        double r707265 = 2.0;
        double r707266 = r707264 * r707265;
        double r707267 = y;
        double r707268 = 9.0;
        double r707269 = r707267 * r707268;
        double r707270 = z;
        double r707271 = r707269 * r707270;
        double r707272 = t;
        double r707273 = r707271 * r707272;
        double r707274 = r707266 - r707273;
        double r707275 = a;
        double r707276 = 27.0;
        double r707277 = r707275 * r707276;
        double r707278 = b;
        double r707279 = r707277 * r707278;
        double r707280 = r707274 + r707279;
        return r707280;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r707281 = y;
        double r707282 = 9.0;
        double r707283 = r707281 * r707282;
        double r707284 = z;
        double r707285 = r707283 * r707284;
        double r707286 = -9.221474393436507e+163;
        bool r707287 = r707285 <= r707286;
        double r707288 = 1.946628139104975e+150;
        bool r707289 = r707285 <= r707288;
        double r707290 = !r707289;
        bool r707291 = r707287 || r707290;
        double r707292 = x;
        double r707293 = 2.0;
        double r707294 = r707292 * r707293;
        double r707295 = t;
        double r707296 = r707284 * r707295;
        double r707297 = r707282 * r707296;
        double r707298 = r707281 * r707297;
        double r707299 = r707294 - r707298;
        double r707300 = a;
        double r707301 = 27.0;
        double r707302 = r707300 * r707301;
        double r707303 = b;
        double r707304 = r707302 * r707303;
        double r707305 = r707299 + r707304;
        double r707306 = r707285 * r707295;
        double r707307 = r707294 - r707306;
        double r707308 = r707301 * r707303;
        double r707309 = r707300 * r707308;
        double r707310 = r707307 + r707309;
        double r707311 = r707291 ? r707305 : r707310;
        return r707311;
}

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

Original3.5
Target2.6
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) < -9.221474393436507e+163 or 1.946628139104975e+150 < (* (* y 9.0) z)

    1. Initial program 18.6

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

    3. Applied associate-*l*1.8

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

    5. Applied associate-*l*1.5

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

    if -9.221474393436507e+163 < (* (* y 9.0) z) < 1.946628139104975e+150

    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*0.5

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -9.22147439343650667 \cdot 10^{163} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 1.946628139104975 \cdot 10^{150}\right):\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(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)))