Average Error: 3.8 → 0.6
Time: 12.2s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot 9 \le -3.338893372507656821369864426932132802203 \cdot 10^{-32}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\sqrt{9} \cdot \left(\sqrt{9} \cdot \left(z \cdot t\right)\right)\right)\right) + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \cdot 9 \le 2.413987217248999323243296963509637530176 \cdot 10^{-42}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \sqrt{27} \cdot \left(\sqrt{27} \cdot \left(a \cdot b\right)\right)\\ \end{array}\]
\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}\;y \cdot 9 \le -3.338893372507656821369864426932132802203 \cdot 10^{-32}:\\
\;\;\;\;\left(x \cdot 2 - y \cdot \left(\sqrt{9} \cdot \left(\sqrt{9} \cdot \left(z \cdot t\right)\right)\right)\right) + 27 \cdot \left(a \cdot b\right)\\

\mathbf{elif}\;y \cdot 9 \le 2.413987217248999323243296963509637530176 \cdot 10^{-42}:\\
\;\;\;\;\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 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \sqrt{27} \cdot \left(\sqrt{27} \cdot \left(a \cdot b\right)\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r438068 = x;
        double r438069 = 2.0;
        double r438070 = r438068 * r438069;
        double r438071 = y;
        double r438072 = 9.0;
        double r438073 = r438071 * r438072;
        double r438074 = z;
        double r438075 = r438073 * r438074;
        double r438076 = t;
        double r438077 = r438075 * r438076;
        double r438078 = r438070 - r438077;
        double r438079 = a;
        double r438080 = 27.0;
        double r438081 = r438079 * r438080;
        double r438082 = b;
        double r438083 = r438081 * r438082;
        double r438084 = r438078 + r438083;
        return r438084;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r438085 = y;
        double r438086 = 9.0;
        double r438087 = r438085 * r438086;
        double r438088 = -3.338893372507657e-32;
        bool r438089 = r438087 <= r438088;
        double r438090 = x;
        double r438091 = 2.0;
        double r438092 = r438090 * r438091;
        double r438093 = sqrt(r438086);
        double r438094 = z;
        double r438095 = t;
        double r438096 = r438094 * r438095;
        double r438097 = r438093 * r438096;
        double r438098 = r438093 * r438097;
        double r438099 = r438085 * r438098;
        double r438100 = r438092 - r438099;
        double r438101 = 27.0;
        double r438102 = a;
        double r438103 = b;
        double r438104 = r438102 * r438103;
        double r438105 = r438101 * r438104;
        double r438106 = r438100 + r438105;
        double r438107 = 2.4139872172489993e-42;
        bool r438108 = r438087 <= r438107;
        double r438109 = r438087 * r438094;
        double r438110 = r438109 * r438095;
        double r438111 = r438092 - r438110;
        double r438112 = r438101 * r438103;
        double r438113 = r438102 * r438112;
        double r438114 = r438111 + r438113;
        double r438115 = r438087 * r438096;
        double r438116 = r438092 - r438115;
        double r438117 = sqrt(r438101);
        double r438118 = r438117 * r438104;
        double r438119 = r438117 * r438118;
        double r438120 = r438116 + r438119;
        double r438121 = r438108 ? r438114 : r438120;
        double r438122 = r438089 ? r438106 : r438121;
        return r438122;
}

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

Original3.8
Target2.6
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811188954625810696587370427881 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* y 9.0) < -3.338893372507657e-32

    1. Initial program 7.1

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

    3. Applied associate-*l*0.8

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

    4. Taylor expanded around 0 0.8

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

    6. Applied associate-*l*0.7

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

    8. Applied add-sqr-sqrt0.7

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

    9. Applied associate-*l*0.8

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

    if -3.338893372507657e-32 < (* y 9.0) < 2.4139872172489993e-42

    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

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

    if 2.4139872172489993e-42 < (* y 9.0)

    1. Initial program 7.2

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

    3. Applied associate-*l*0.7

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

    4. Taylor expanded around 0 0.7

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

    6. Applied add-sqr-sqrt0.7

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

    7. Applied associate-*l*0.8

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot 9 \le -3.338893372507656821369864426932132802203 \cdot 10^{-32}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\sqrt{9} \cdot \left(\sqrt{9} \cdot \left(z \cdot t\right)\right)\right)\right) + 27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;y \cdot 9 \le 2.413987217248999323243296963509637530176 \cdot 10^{-42}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \sqrt{27} \cdot \left(\sqrt{27} \cdot \left(a \cdot b\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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)))