Average Error: 3.5 → 0.6
Time: 7.7s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -9.22147439343650667 \cdot 10^{163} \lor \neg \left(\left(y \cdot 9\right) \cdot z \le 1.946628139104975 \cdot 10^{150}\right):\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \end{array}\]
\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 r779204 = x;
        double r779205 = 2.0;
        double r779206 = r779204 * r779205;
        double r779207 = y;
        double r779208 = 9.0;
        double r779209 = r779207 * r779208;
        double r779210 = z;
        double r779211 = r779209 * r779210;
        double r779212 = t;
        double r779213 = r779211 * r779212;
        double r779214 = r779206 - r779213;
        double r779215 = a;
        double r779216 = 27.0;
        double r779217 = r779215 * r779216;
        double r779218 = b;
        double r779219 = r779217 * r779218;
        double r779220 = r779214 + r779219;
        return r779220;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r779221 = y;
        double r779222 = 9.0;
        double r779223 = r779221 * r779222;
        double r779224 = z;
        double r779225 = r779223 * r779224;
        double r779226 = -9.221474393436507e+163;
        bool r779227 = r779225 <= r779226;
        double r779228 = 1.946628139104975e+150;
        bool r779229 = r779225 <= r779228;
        double r779230 = !r779229;
        bool r779231 = r779227 || r779230;
        double r779232 = x;
        double r779233 = 2.0;
        double r779234 = r779232 * r779233;
        double r779235 = t;
        double r779236 = r779224 * r779235;
        double r779237 = r779222 * r779236;
        double r779238 = r779221 * r779237;
        double r779239 = r779234 - r779238;
        double r779240 = a;
        double r779241 = 27.0;
        double r779242 = r779240 * r779241;
        double r779243 = b;
        double r779244 = r779242 * r779243;
        double r779245 = r779239 + r779244;
        double r779246 = r779225 * r779235;
        double r779247 = r779234 - r779246;
        double r779248 = r779241 * r779243;
        double r779249 = r779240 * r779248;
        double r779250 = r779247 + r779249;
        double r779251 = r779231 ? r779245 : r779250;
        return r779251;
}

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)))