Average Error: 3.7 → 1.3
Time: 8.7s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot 9 \le -8.63828739859890366 \cdot 10^{64} \lor \neg \left(y \cdot 9 \le 4.26640526336584695 \cdot 10^{171}\right):\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 + \left(-9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]
\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 r784208 = x;
        double r784209 = 2.0;
        double r784210 = r784208 * r784209;
        double r784211 = y;
        double r784212 = 9.0;
        double r784213 = r784211 * r784212;
        double r784214 = z;
        double r784215 = r784213 * r784214;
        double r784216 = t;
        double r784217 = r784215 * r784216;
        double r784218 = r784210 - r784217;
        double r784219 = a;
        double r784220 = 27.0;
        double r784221 = r784219 * r784220;
        double r784222 = b;
        double r784223 = r784221 * r784222;
        double r784224 = r784218 + r784223;
        return r784224;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r784225 = y;
        double r784226 = 9.0;
        double r784227 = r784225 * r784226;
        double r784228 = -8.638287398598904e+64;
        bool r784229 = r784227 <= r784228;
        double r784230 = 4.266405263365847e+171;
        bool r784231 = r784227 <= r784230;
        double r784232 = !r784231;
        bool r784233 = r784229 || r784232;
        double r784234 = x;
        double r784235 = 2.0;
        double r784236 = r784234 * r784235;
        double r784237 = z;
        double r784238 = t;
        double r784239 = r784237 * r784238;
        double r784240 = r784227 * r784239;
        double r784241 = r784236 - r784240;
        double r784242 = a;
        double r784243 = 27.0;
        double r784244 = r784242 * r784243;
        double r784245 = b;
        double r784246 = r784244 * r784245;
        double r784247 = r784241 + r784246;
        double r784248 = r784237 * r784225;
        double r784249 = r784238 * r784248;
        double r784250 = r784226 * r784249;
        double r784251 = -r784250;
        double r784252 = r784236 + r784251;
        double r784253 = r784252 + r784246;
        double r784254 = r784233 ? r784247 : r784253;
        return r784254;
}

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)))