Average Error: 3.6 → 0.9
Time: 4.2s
Precision: 64
\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -8.136617691166394293958905321873276745445 \cdot 10^{112}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 1.92464941334376671587030199770510870782 \cdot 10^{175}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]
\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 \le -8.136617691166394293958905321873276745445 \cdot 10^{112}:\\
\;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\

\mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 1.92464941334376671587030199770510870782 \cdot 10^{175}:\\
\;\;\;\;\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 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r776146 = x;
        double r776147 = 2.0;
        double r776148 = r776146 * r776147;
        double r776149 = y;
        double r776150 = 9.0;
        double r776151 = r776149 * r776150;
        double r776152 = z;
        double r776153 = r776151 * r776152;
        double r776154 = t;
        double r776155 = r776153 * r776154;
        double r776156 = r776148 - r776155;
        double r776157 = a;
        double r776158 = 27.0;
        double r776159 = r776157 * r776158;
        double r776160 = b;
        double r776161 = r776159 * r776160;
        double r776162 = r776156 + r776161;
        return r776162;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r776163 = y;
        double r776164 = 9.0;
        double r776165 = r776163 * r776164;
        double r776166 = z;
        double r776167 = r776165 * r776166;
        double r776168 = -8.136617691166394e+112;
        bool r776169 = r776167 <= r776168;
        double r776170 = x;
        double r776171 = 2.0;
        double r776172 = r776170 * r776171;
        double r776173 = t;
        double r776174 = r776166 * r776173;
        double r776175 = r776165 * r776174;
        double r776176 = r776172 - r776175;
        double r776177 = a;
        double r776178 = 27.0;
        double r776179 = b;
        double r776180 = r776178 * r776179;
        double r776181 = r776177 * r776180;
        double r776182 = r776176 + r776181;
        double r776183 = 1.9246494133437667e+175;
        bool r776184 = r776167 <= r776183;
        double r776185 = r776164 * r776166;
        double r776186 = r776163 * r776185;
        double r776187 = r776186 * r776173;
        double r776188 = r776172 - r776187;
        double r776189 = r776177 * r776178;
        double r776190 = r776189 * r776179;
        double r776191 = r776188 + r776190;
        double r776192 = r776164 * r776174;
        double r776193 = r776163 * r776192;
        double r776194 = r776172 - r776193;
        double r776195 = r776194 + r776190;
        double r776196 = r776184 ? r776191 : r776195;
        double r776197 = r776169 ? r776182 : r776196;
        return r776197;
}

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
Target2.7
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811188954625810696587370427881 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (* y 9.0) z) < -8.136617691166394e+112

    1. Initial program 15.0

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

    3. Applied associate-*l*3.3

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

    5. Applied associate-*l*3.3

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

    if -8.136617691166394e+112 < (* (* y 9.0) z) < 1.9246494133437667e+175

    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*0.6

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

    if 1.9246494133437667e+175 < (* (* y 9.0) z)

    1. Initial program 20.3

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

    3. Applied associate-*l*1.7

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

    5. Applied associate-*l*1.4

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \le -8.136617691166394293958905321873276745445 \cdot 10^{112}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot 9\right) \cdot \left(z \cdot t\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 1.92464941334376671587030199770510870782 \cdot 10^{175}:\\ \;\;\;\;\left(x \cdot 2 - \left(y \cdot \left(9 \cdot z\right)\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Reproduce

herbie shell --seed 2019354 
(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)))