Average Error: 3.5 → 1.4
Time: 14.2s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -5.676106603176618479833130858551602850216 \cdot 10^{-187}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t \le 6.09835887199337102189769286793387544193 \cdot 10^{-79}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(z \cdot 9\right)\right) \cdot t\right) + \sqrt{27} \cdot \left(\left(\sqrt{27} \cdot a\right) \cdot b\right)\\ \end{array}\]
\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 -5.676106603176618479833130858551602850216 \cdot 10^{-187}:\\
\;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\

\mathbf{elif}\;t \le 6.09835887199337102189769286793387544193 \cdot 10^{-79}:\\
\;\;\;\;\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) + \sqrt{27} \cdot \left(\left(\sqrt{27} \cdot a\right) \cdot b\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r533076 = x;
        double r533077 = 2.0;
        double r533078 = r533076 * r533077;
        double r533079 = y;
        double r533080 = 9.0;
        double r533081 = r533079 * r533080;
        double r533082 = z;
        double r533083 = r533081 * r533082;
        double r533084 = t;
        double r533085 = r533083 * r533084;
        double r533086 = r533078 - r533085;
        double r533087 = a;
        double r533088 = 27.0;
        double r533089 = r533087 * r533088;
        double r533090 = b;
        double r533091 = r533089 * r533090;
        double r533092 = r533086 + r533091;
        return r533092;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r533093 = t;
        double r533094 = -5.676106603176618e-187;
        bool r533095 = r533093 <= r533094;
        double r533096 = x;
        double r533097 = 2.0;
        double r533098 = r533096 * r533097;
        double r533099 = y;
        double r533100 = 9.0;
        double r533101 = r533099 * r533100;
        double r533102 = z;
        double r533103 = r533101 * r533102;
        double r533104 = r533103 * r533093;
        double r533105 = r533098 - r533104;
        double r533106 = a;
        double r533107 = 27.0;
        double r533108 = b;
        double r533109 = r533107 * r533108;
        double r533110 = r533106 * r533109;
        double r533111 = r533105 + r533110;
        double r533112 = 6.098358871993371e-79;
        bool r533113 = r533093 <= r533112;
        double r533114 = r533102 * r533100;
        double r533115 = r533114 * r533093;
        double r533116 = r533099 * r533115;
        double r533117 = r533098 - r533116;
        double r533118 = r533106 * r533107;
        double r533119 = r533118 * r533108;
        double r533120 = r533117 + r533119;
        double r533121 = r533099 * r533114;
        double r533122 = r533121 * r533093;
        double r533123 = r533098 - r533122;
        double r533124 = sqrt(r533107);
        double r533125 = r533124 * r533106;
        double r533126 = r533125 * r533108;
        double r533127 = r533124 * r533126;
        double r533128 = r533123 + r533127;
        double r533129 = r533113 ? r533120 : r533128;
        double r533130 = r533095 ? r533111 : r533129;
        return r533130;
}

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

Original3.5
Target2.6
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811188954625810696587370427881 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -5.676106603176618e-187

    1. Initial program 2.0

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

    3. Applied associate-*l*2.0

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

    if -5.676106603176618e-187 < t < 6.098358871993371e-79

    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*7.0

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

    4. Simplified7.0

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

    6. Applied associate-*l*0.8

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

    if 6.098358871993371e-79 < t

    1. Initial program 1.2

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

    3. Applied associate-*l*1.2

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

    4. Simplified1.2

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

    5. Taylor expanded around 0 1.2

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

    7. Applied add-sqr-sqrt1.2

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

    8. Applied associate-*l*1.2

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

    10. Applied associate-*r*1.3

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

  4. Final simplification1.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -5.676106603176618479833130858551602850216 \cdot 10^{-187}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t \le 6.09835887199337102189769286793387544193 \cdot 10^{-79}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(z \cdot 9\right)\right) \cdot t\right) + \sqrt{27} \cdot \left(\left(\sqrt{27} \cdot a\right) \cdot b\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 
(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)))