Average Error: 3.6 → 0.6
Time: 16.7s
Precision: 64
\[\left(x \cdot 2.0 - \left(\left(y \cdot 9.0\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27.0\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -0.007343319779592058:\\ \;\;\;\;\left(x \cdot 2.0 - t \cdot \left(\left(z \cdot y\right) \cdot 9.0\right)\right) + 27.0 \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;t \le 6.659586950487052 \cdot 10^{+19}:\\ \;\;\;\;x \cdot 2.0 + \left(a \cdot \left(27.0 \cdot b\right) - \left(\left(9.0 \cdot y\right) \cdot t\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2.0 - t \cdot \left(\left(z \cdot y\right) \cdot 9.0\right)\right) + 27.0 \cdot \left(b \cdot a\right)\\ \end{array}\]
\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}\;t \le -0.007343319779592058:\\
\;\;\;\;\left(x \cdot 2.0 - t \cdot \left(\left(z \cdot y\right) \cdot 9.0\right)\right) + 27.0 \cdot \left(b \cdot a\right)\\

\mathbf{elif}\;t \le 6.659586950487052 \cdot 10^{+19}:\\
\;\;\;\;x \cdot 2.0 + \left(a \cdot \left(27.0 \cdot b\right) - \left(\left(9.0 \cdot y\right) \cdot t\right) \cdot z\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r39531395 = x;
        double r39531396 = 2.0;
        double r39531397 = r39531395 * r39531396;
        double r39531398 = y;
        double r39531399 = 9.0;
        double r39531400 = r39531398 * r39531399;
        double r39531401 = z;
        double r39531402 = r39531400 * r39531401;
        double r39531403 = t;
        double r39531404 = r39531402 * r39531403;
        double r39531405 = r39531397 - r39531404;
        double r39531406 = a;
        double r39531407 = 27.0;
        double r39531408 = r39531406 * r39531407;
        double r39531409 = b;
        double r39531410 = r39531408 * r39531409;
        double r39531411 = r39531405 + r39531410;
        return r39531411;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r39531412 = t;
        double r39531413 = -0.007343319779592058;
        bool r39531414 = r39531412 <= r39531413;
        double r39531415 = x;
        double r39531416 = 2.0;
        double r39531417 = r39531415 * r39531416;
        double r39531418 = z;
        double r39531419 = y;
        double r39531420 = r39531418 * r39531419;
        double r39531421 = 9.0;
        double r39531422 = r39531420 * r39531421;
        double r39531423 = r39531412 * r39531422;
        double r39531424 = r39531417 - r39531423;
        double r39531425 = 27.0;
        double r39531426 = b;
        double r39531427 = a;
        double r39531428 = r39531426 * r39531427;
        double r39531429 = r39531425 * r39531428;
        double r39531430 = r39531424 + r39531429;
        double r39531431 = 6.659586950487052e+19;
        bool r39531432 = r39531412 <= r39531431;
        double r39531433 = r39531425 * r39531426;
        double r39531434 = r39531427 * r39531433;
        double r39531435 = r39531421 * r39531419;
        double r39531436 = r39531435 * r39531412;
        double r39531437 = r39531436 * r39531418;
        double r39531438 = r39531434 - r39531437;
        double r39531439 = r39531417 + r39531438;
        double r39531440 = r39531432 ? r39531439 : r39531430;
        double r39531441 = r39531414 ? r39531430 : r39531440;
        return r39531441;
}

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

Original3.6
Target2.6
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2.0 - \left(\left(y \cdot 9.0\right) \cdot z\right) \cdot t\right) + a \cdot \left(27.0 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2.0 - 9.0 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27.0\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < -0.007343319779592058 or 6.659586950487052e+19 < t

    1. Initial program 0.9

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

    2. Taylor expanded around 0 0.9

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

    3. Taylor expanded around 0 0.8

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

    if -0.007343319779592058 < t < 6.659586950487052e+19

    1. Initial program 5.5

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

    3. Applied sub-neg5.5

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

    4. Applied associate-+l+5.5

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

    5. Simplified0.5

      \[\leadsto x \cdot 2.0 + \color{blue}{\left(a \cdot \left(27.0 \cdot b\right) - \left(t \cdot \left(y \cdot 9.0\right)\right) \cdot z\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -0.007343319779592058:\\ \;\;\;\;\left(x \cdot 2.0 - t \cdot \left(\left(z \cdot y\right) \cdot 9.0\right)\right) + 27.0 \cdot \left(b \cdot a\right)\\ \mathbf{elif}\;t \le 6.659586950487052 \cdot 10^{+19}:\\ \;\;\;\;x \cdot 2.0 + \left(a \cdot \left(27.0 \cdot b\right) - \left(\left(9.0 \cdot y\right) \cdot t\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2.0 - t \cdot \left(\left(z \cdot y\right) \cdot 9.0\right)\right) + 27.0 \cdot \left(b \cdot a\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019164 
(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)))