Average Error: 3.7 → 0.5
Time: 5.6s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z = -\infty:\\ \;\;\;\;\left(x \cdot 2 - \left(\sqrt[3]{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)} \cdot \sqrt[3]{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \cdot \sqrt[3]{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 3.08499988077266071 \cdot 10^{296}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(\left(a \cdot 27\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{b}\\ \end{array}\]
\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}\;\left(y \cdot 9\right) \cdot z = -\infty:\\
\;\;\;\;\left(x \cdot 2 - \left(\sqrt[3]{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)} \cdot \sqrt[3]{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \cdot \sqrt[3]{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b\\

\mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 3.08499988077266071 \cdot 10^{296}:\\
\;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(\left(a \cdot 27\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{b}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r748101 = x;
        double r748102 = 2.0;
        double r748103 = r748101 * r748102;
        double r748104 = y;
        double r748105 = 9.0;
        double r748106 = r748104 * r748105;
        double r748107 = z;
        double r748108 = r748106 * r748107;
        double r748109 = t;
        double r748110 = r748108 * r748109;
        double r748111 = r748103 - r748110;
        double r748112 = a;
        double r748113 = 27.0;
        double r748114 = r748112 * r748113;
        double r748115 = b;
        double r748116 = r748114 * r748115;
        double r748117 = r748111 + r748116;
        return r748117;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r748118 = y;
        double r748119 = 9.0;
        double r748120 = r748118 * r748119;
        double r748121 = z;
        double r748122 = r748120 * r748121;
        double r748123 = -inf.0;
        bool r748124 = r748122 <= r748123;
        double r748125 = x;
        double r748126 = 2.0;
        double r748127 = r748125 * r748126;
        double r748128 = t;
        double r748129 = r748121 * r748128;
        double r748130 = r748120 * r748129;
        double r748131 = cbrt(r748130);
        double r748132 = r748131 * r748131;
        double r748133 = r748132 * r748131;
        double r748134 = r748127 - r748133;
        double r748135 = a;
        double r748136 = 27.0;
        double r748137 = r748135 * r748136;
        double r748138 = b;
        double r748139 = r748137 * r748138;
        double r748140 = r748134 + r748139;
        double r748141 = 3.0849998807726607e+296;
        bool r748142 = r748122 <= r748141;
        double r748143 = r748119 * r748121;
        double r748144 = r748118 * r748143;
        double r748145 = r748144 * r748128;
        double r748146 = r748127 - r748145;
        double r748147 = r748146 + r748139;
        double r748148 = r748127 - r748130;
        double r748149 = cbrt(r748138);
        double r748150 = r748149 * r748149;
        double r748151 = r748137 * r748150;
        double r748152 = r748151 * r748149;
        double r748153 = r748148 + r748152;
        double r748154 = r748142 ? r748147 : r748153;
        double r748155 = r748124 ? r748140 : r748154;
        return r748155;
}

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
Target2.7
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (* y 9.0) z) < -inf.0

    1. Initial program 64.0

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

    3. Applied associate-*l*1.0

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

    5. Applied add-cube-cbrt1.6

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

    if -inf.0 < (* (* y 9.0) z) < 3.0849998807726607e+296

    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

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

    if 3.0849998807726607e+296 < (* (* y 9.0) z)

    1. Initial program 58.3

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

    3. Applied associate-*l*0.9

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

    5. Applied add-cube-cbrt1.0

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

    6. Applied associate-*r*1.0

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z = -\infty:\\ \;\;\;\;\left(x \cdot 2 - \left(\sqrt[3]{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)} \cdot \sqrt[3]{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \cdot \sqrt[3]{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 3.08499988077266071 \cdot 10^{296}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + \left(\left(a \cdot 27\right) \cdot \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right)\right) \cdot \sqrt[3]{b}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(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)))