Average Error: 3.4 → 0.4
Time: 16.0s
Precision: 64
\[\left(x \cdot 2.0 - \left(\left(y \cdot 9.0\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27.0\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9.0\right) \cdot z \le -6.169830986569156 \cdot 10^{+244}:\\ \;\;\;\;\left(b \cdot \left(a \cdot 27.0\right) - z \cdot \left(y \cdot \left(t \cdot 9.0\right)\right)\right) + x \cdot 2.0\\ \mathbf{elif}\;\left(y \cdot 9.0\right) \cdot z \le 6.348735557462148 \cdot 10^{+226}:\\ \;\;\;\;\left(x \cdot 2.0 - \left(\left(y \cdot 9.0\right) \cdot z\right) \cdot t\right) + 27.0 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2.0 - \left(9.0 \cdot \left(t \cdot z\right)\right) \cdot y\right) + a \cdot \left(27.0 \cdot b\right)\\ \end{array}\]
\left(x \cdot 2.0 - \left(\left(y \cdot 9.0\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27.0\right) \cdot b
↓
\begin{array}{l}
\mathbf{if}\;\left(y \cdot 9.0\right) \cdot z \le -6.169830986569156 \cdot 10^{+244}:\\
\;\;\;\;\left(b \cdot \left(a \cdot 27.0\right) - z \cdot \left(y \cdot \left(t \cdot 9.0\right)\right)\right) + x \cdot 2.0\\

\mathbf{elif}\;\left(y \cdot 9.0\right) \cdot z \le 6.348735557462148 \cdot 10^{+226}:\\
\;\;\;\;\left(x \cdot 2.0 - \left(\left(y \cdot 9.0\right) \cdot z\right) \cdot t\right) + 27.0 \cdot \left(a \cdot b\right)\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot 2.0 - \left(9.0 \cdot \left(t \cdot z\right)\right) \cdot y\right) + a \cdot \left(27.0 \cdot b\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r38448277 = x;
        double r38448278 = 2.0;
        double r38448279 = r38448277 * r38448278;
        double r38448280 = y;
        double r38448281 = 9.0;
        double r38448282 = r38448280 * r38448281;
        double r38448283 = z;
        double r38448284 = r38448282 * r38448283;
        double r38448285 = t;
        double r38448286 = r38448284 * r38448285;
        double r38448287 = r38448279 - r38448286;
        double r38448288 = a;
        double r38448289 = 27.0;
        double r38448290 = r38448288 * r38448289;
        double r38448291 = b;
        double r38448292 = r38448290 * r38448291;
        double r38448293 = r38448287 + r38448292;
        return r38448293;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r38448294 = y;
        double r38448295 = 9.0;
        double r38448296 = r38448294 * r38448295;
        double r38448297 = z;
        double r38448298 = r38448296 * r38448297;
        double r38448299 = -6.169830986569156e+244;
        bool r38448300 = r38448298 <= r38448299;
        double r38448301 = b;
        double r38448302 = a;
        double r38448303 = 27.0;
        double r38448304 = r38448302 * r38448303;
        double r38448305 = r38448301 * r38448304;
        double r38448306 = t;
        double r38448307 = r38448306 * r38448295;
        double r38448308 = r38448294 * r38448307;
        double r38448309 = r38448297 * r38448308;
        double r38448310 = r38448305 - r38448309;
        double r38448311 = x;
        double r38448312 = 2.0;
        double r38448313 = r38448311 * r38448312;
        double r38448314 = r38448310 + r38448313;
        double r38448315 = 6.348735557462148e+226;
        bool r38448316 = r38448298 <= r38448315;
        double r38448317 = r38448298 * r38448306;
        double r38448318 = r38448313 - r38448317;
        double r38448319 = r38448302 * r38448301;
        double r38448320 = r38448303 * r38448319;
        double r38448321 = r38448318 + r38448320;
        double r38448322 = r38448306 * r38448297;
        double r38448323 = r38448295 * r38448322;
        double r38448324 = r38448323 * r38448294;
        double r38448325 = r38448313 - r38448324;
        double r38448326 = r38448303 * r38448301;
        double r38448327 = r38448302 * r38448326;
        double r38448328 = r38448325 + r38448327;
        double r38448329 = r38448316 ? r38448321 : r38448328;
        double r38448330 = r38448300 ? r38448314 : r38448329;
        return r38448330;
}

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

Original3.4
Target2.5
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2.0 - \left(\left(y \cdot 9.0\right) \cdot z\right) \cdot t\right) + a \cdot \left(27.0 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2.0 - 9.0 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27.0\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (* y 9.0) z) < -6.169830986569156e+244

    1. Initial program 35.4

      \[\left(x \cdot 2.0 - \left(\left(y \cdot 9.0\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27.0\right) \cdot b\]
    2. Using strategy rm

    3. Applied associate-*l*1.1

      \[\leadsto \left(x \cdot 2.0 - \color{blue}{\left(y \cdot 9.0\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27.0\right) \cdot b\]
    4. Using strategy rm

    5. Applied associate-*l*0.5

      \[\leadsto \left(x \cdot 2.0 - \color{blue}{y \cdot \left(9.0 \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27.0\right) \cdot b\]
    6. Using strategy rm

    7. Applied sub-neg0.5

      \[\leadsto \color{blue}{\left(x \cdot 2.0 + \left(-y \cdot \left(9.0 \cdot \left(z \cdot t\right)\right)\right)\right)} + \left(a \cdot 27.0\right) \cdot b\]

    8. Applied associate-+l+0.5

      \[\leadsto \color{blue}{x \cdot 2.0 + \left(\left(-y \cdot \left(9.0 \cdot \left(z \cdot t\right)\right)\right) + \left(a \cdot 27.0\right) \cdot b\right)}\]

    9. Simplified0.6

      \[\leadsto x \cdot 2.0 + \color{blue}{\left(\left(a \cdot 27.0\right) \cdot b - \left(y \cdot \left(t \cdot 9.0\right)\right) \cdot z\right)}\]

    if -6.169830986569156e+244 < (* (* y 9.0) z) < 6.348735557462148e+226

    1. Initial program 0.4

      \[\left(x \cdot 2.0 - \left(\left(y \cdot 9.0\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27.0\right) \cdot b\]

    2. Taylor expanded around 0 0.3

      \[\leadsto \left(x \cdot 2.0 - \left(\left(y \cdot 9.0\right) \cdot z\right) \cdot t\right) + \color{blue}{27.0 \cdot \left(a \cdot b\right)}\]

    if 6.348735557462148e+226 < (* (* y 9.0) z)

    1. Initial program 29.3

      \[\left(x \cdot 2.0 - \left(\left(y \cdot 9.0\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27.0\right) \cdot b\]
    2. Using strategy rm

    3. Applied associate-*l*1.5

      \[\leadsto \left(x \cdot 2.0 - \color{blue}{\left(y \cdot 9.0\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27.0\right) \cdot b\]
    4. Using strategy rm

    5. Applied associate-*l*0.4

      \[\leadsto \left(x \cdot 2.0 - \color{blue}{y \cdot \left(9.0 \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27.0\right) \cdot b\]
    6. Using strategy rm

    7. Applied associate-*l*0.6

      \[\leadsto \left(x \cdot 2.0 - y \cdot \left(9.0 \cdot \left(z \cdot t\right)\right)\right) + \color{blue}{a \cdot \left(27.0 \cdot b\right)}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9.0\right) \cdot z \le -6.169830986569156 \cdot 10^{+244}:\\ \;\;\;\;\left(b \cdot \left(a \cdot 27.0\right) - z \cdot \left(y \cdot \left(t \cdot 9.0\right)\right)\right) + x \cdot 2.0\\ \mathbf{elif}\;\left(y \cdot 9.0\right) \cdot z \le 6.348735557462148 \cdot 10^{+226}:\\ \;\;\;\;\left(x \cdot 2.0 - \left(\left(y \cdot 9.0\right) \cdot z\right) \cdot t\right) + 27.0 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2.0 - \left(9.0 \cdot \left(t \cdot z\right)\right) \cdot y\right) + a \cdot \left(27.0 \cdot b\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"

  :herbie-target
  (if (< y 7.590524218811189e-161) (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b))) (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b)))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))