Average Error: 3.6 → 2.1
Time: 12.2s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le 3.109405208337589429613705910964062865937 \cdot 10^{-73}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(z \cdot 9\right)\right) \cdot t\right) + 27 \cdot \left(a \cdot b\right)\\ \end{array}\]
\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}\;t \le 3.109405208337589429613705910964062865937 \cdot 10^{-73}:\\
\;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(z \cdot 9\right)\right) \cdot t\right) + 27 \cdot \left(a \cdot b\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r509214 = x;
        double r509215 = 2.0;
        double r509216 = r509214 * r509215;
        double r509217 = y;
        double r509218 = 9.0;
        double r509219 = r509217 * r509218;
        double r509220 = z;
        double r509221 = r509219 * r509220;
        double r509222 = t;
        double r509223 = r509221 * r509222;
        double r509224 = r509216 - r509223;
        double r509225 = a;
        double r509226 = 27.0;
        double r509227 = r509225 * r509226;
        double r509228 = b;
        double r509229 = r509227 * r509228;
        double r509230 = r509224 + r509229;
        return r509230;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r509231 = t;
        double r509232 = 3.1094052083375894e-73;
        bool r509233 = r509231 <= r509232;
        double r509234 = x;
        double r509235 = 2.0;
        double r509236 = r509234 * r509235;
        double r509237 = y;
        double r509238 = z;
        double r509239 = 9.0;
        double r509240 = r509238 * r509239;
        double r509241 = r509240 * r509231;
        double r509242 = r509237 * r509241;
        double r509243 = r509236 - r509242;
        double r509244 = a;
        double r509245 = 27.0;
        double r509246 = r509244 * r509245;
        double r509247 = b;
        double r509248 = r509246 * r509247;
        double r509249 = r509243 + r509248;
        double r509250 = r509237 * r509240;
        double r509251 = r509250 * r509231;
        double r509252 = r509236 - r509251;
        double r509253 = r509244 * r509247;
        double r509254 = r509245 * r509253;
        double r509255 = r509252 + r509254;
        double r509256 = r509233 ? r509249 : r509255;
        return r509256;
}

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
Herbie2.1
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811188954625810696587370427881 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if t < 3.1094052083375894e-73

    1. Initial program 4.6

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

    3. Applied associate-*l*4.6

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

    4. Simplified4.6

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

    6. Applied associate-*l*2.5

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

    if 3.1094052083375894e-73 < t

    1. Initial program 1.1

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

    3. Applied associate-*l*1.1

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

    4. Simplified1.1

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

    5. Taylor expanded around 0 1.0

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

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le 3.109405208337589429613705910964062865937 \cdot 10^{-73}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(z \cdot 9\right)\right) \cdot t\right) + 27 \cdot \left(a \cdot b\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(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)))