Average Error: 3.7 → 0.4
Time: 4.4s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -1.54938897895284943 \cdot 10^{217}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(\sqrt[3]{9} \cdot \left(z \cdot t\right)\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 1.15944334374810585 \cdot 10^{190}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + {\left(27 \cdot \left(a \cdot b\right)\right)}^{1}\\ \end{array}\]
\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 -1.54938897895284943 \cdot 10^{217}:\\
\;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(\sqrt[3]{9} \cdot \left(z \cdot t\right)\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\

\mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 1.15944334374810585 \cdot 10^{190}:\\
\;\;\;\;\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 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + {\left(27 \cdot \left(a \cdot b\right)\right)}^{1}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r585083 = x;
        double r585084 = 2.0;
        double r585085 = r585083 * r585084;
        double r585086 = y;
        double r585087 = 9.0;
        double r585088 = r585086 * r585087;
        double r585089 = z;
        double r585090 = r585088 * r585089;
        double r585091 = t;
        double r585092 = r585090 * r585091;
        double r585093 = r585085 - r585092;
        double r585094 = a;
        double r585095 = 27.0;
        double r585096 = r585094 * r585095;
        double r585097 = b;
        double r585098 = r585096 * r585097;
        double r585099 = r585093 + r585098;
        return r585099;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r585100 = y;
        double r585101 = 9.0;
        double r585102 = r585100 * r585101;
        double r585103 = z;
        double r585104 = r585102 * r585103;
        double r585105 = -1.5493889789528494e+217;
        bool r585106 = r585104 <= r585105;
        double r585107 = x;
        double r585108 = 2.0;
        double r585109 = r585107 * r585108;
        double r585110 = cbrt(r585101);
        double r585111 = r585110 * r585110;
        double r585112 = t;
        double r585113 = r585103 * r585112;
        double r585114 = r585110 * r585113;
        double r585115 = r585111 * r585114;
        double r585116 = r585100 * r585115;
        double r585117 = r585109 - r585116;
        double r585118 = a;
        double r585119 = 27.0;
        double r585120 = r585118 * r585119;
        double r585121 = b;
        double r585122 = r585120 * r585121;
        double r585123 = r585117 + r585122;
        double r585124 = 1.1594433437481059e+190;
        bool r585125 = r585104 <= r585124;
        double r585126 = r585104 * r585112;
        double r585127 = r585109 - r585126;
        double r585128 = r585119 * r585121;
        double r585129 = r585118 * r585128;
        double r585130 = r585127 + r585129;
        double r585131 = r585101 * r585103;
        double r585132 = r585131 * r585112;
        double r585133 = r585100 * r585132;
        double r585134 = r585109 - r585133;
        double r585135 = r585118 * r585121;
        double r585136 = r585119 * r585135;
        double r585137 = 1.0;
        double r585138 = pow(r585136, r585137);
        double r585139 = r585134 + r585138;
        double r585140 = r585125 ? r585130 : r585139;
        double r585141 = r585106 ? r585123 : r585140;
        return r585141;
}

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
Target3.0
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (* y 9.0) z) < -1.5493889789528494e+217

    1. Initial program 31.1

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

    3. Applied associate-*l*1.9

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

    5. Applied associate-*l*0.9

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

    7. Applied add-cube-cbrt0.9

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

    8. Applied associate-*l*1.0

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

    if -1.5493889789528494e+217 < (* (* y 9.0) z) < 1.1594433437481059e+190

    1. Initial program 0.4

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

    3. Applied associate-*l*0.4

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

    if 1.1594433437481059e+190 < (* (* y 9.0) z)

    1. Initial program 24.0

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

    3. Applied associate-*l*1.4

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

    5. Applied associate-*l*0.8

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

    7. Applied associate-*r*0.8

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

    9. Applied pow10.8

      \[\leadsto \left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot \color{blue}{{b}^{1}}\]

    10. Applied pow10.8

      \[\leadsto \left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + \left(a \cdot \color{blue}{{27}^{1}}\right) \cdot {b}^{1}\]

    11. Applied pow10.8

      \[\leadsto \left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + \left(\color{blue}{{a}^{1}} \cdot {27}^{1}\right) \cdot {b}^{1}\]

    12. Applied pow-prod-down0.8

      \[\leadsto \left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + \color{blue}{{\left(a \cdot 27\right)}^{1}} \cdot {b}^{1}\]

    13. Applied pow-prod-down0.8

      \[\leadsto \left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + \color{blue}{{\left(\left(a \cdot 27\right) \cdot b\right)}^{1}}\]

    14. Simplified0.7

      \[\leadsto \left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + {\color{blue}{\left(27 \cdot \left(a \cdot b\right)\right)}}^{1}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -1.54938897895284943 \cdot 10^{217}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(\sqrt[3]{9} \cdot \sqrt[3]{9}\right) \cdot \left(\sqrt[3]{9} \cdot \left(z \cdot t\right)\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 1.15944334374810585 \cdot 10^{190}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + {\left(27 \cdot \left(a \cdot b\right)\right)}^{1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020089 
(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)))