Average Error: 6.3 → 1.2
Time: 31.1s
Precision: 64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(a + b \cdot c\right) \cdot c \le -3.366177053613654395798675960966992222011 \cdot 10^{198} \lor \neg \left(\left(a + b \cdot c\right) \cdot c \le 4.788215598584803852236065219824838534122 \cdot 10^{299}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot i\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \end{array}\]
2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)
↓
\begin{array}{l}
\mathbf{if}\;\left(a + b \cdot c\right) \cdot c \le -3.366177053613654395798675960966992222011 \cdot 10^{198} \lor \neg \left(\left(a + b \cdot c\right) \cdot c \le 4.788215598584803852236065219824838534122 \cdot 10^{299}\right):\\
\;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot i\right) \cdot c\right)\\

\mathbf{else}:\\
\;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r404615 = 2.0;
        double r404616 = x;
        double r404617 = y;
        double r404618 = r404616 * r404617;
        double r404619 = z;
        double r404620 = t;
        double r404621 = r404619 * r404620;
        double r404622 = r404618 + r404621;
        double r404623 = a;
        double r404624 = b;
        double r404625 = c;
        double r404626 = r404624 * r404625;
        double r404627 = r404623 + r404626;
        double r404628 = r404627 * r404625;
        double r404629 = i;
        double r404630 = r404628 * r404629;
        double r404631 = r404622 - r404630;
        double r404632 = r404615 * r404631;
        return r404632;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r404633 = a;
        double r404634 = b;
        double r404635 = c;
        double r404636 = r404634 * r404635;
        double r404637 = r404633 + r404636;
        double r404638 = r404637 * r404635;
        double r404639 = -3.3661770536136544e+198;
        bool r404640 = r404638 <= r404639;
        double r404641 = 4.788215598584804e+299;
        bool r404642 = r404638 <= r404641;
        double r404643 = !r404642;
        bool r404644 = r404640 || r404643;
        double r404645 = 2.0;
        double r404646 = x;
        double r404647 = y;
        double r404648 = r404646 * r404647;
        double r404649 = z;
        double r404650 = t;
        double r404651 = r404649 * r404650;
        double r404652 = r404648 + r404651;
        double r404653 = i;
        double r404654 = r404637 * r404653;
        double r404655 = r404654 * r404635;
        double r404656 = r404652 - r404655;
        double r404657 = r404645 * r404656;
        double r404658 = r404638 * r404653;
        double r404659 = r404652 - r404658;
        double r404660 = r404645 * r404659;
        double r404661 = r404644 ? r404657 : r404660;
        return r404661;
}

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

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.3
Target1.7
Herbie1.2
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* (+ a (* b c)) c) < -3.3661770536136544e+198 or 4.788215598584804e+299 < (* (+ a (* b c)) c)

    1. Initial program 41.2

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

    3. Applied associate-*l*6.2

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

    4. Simplified6.2

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

    6. Applied associate-*r*6.3

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

    if -3.3661770536136544e+198 < (* (+ a (* b c)) c) < 4.788215598584804e+299

    1. Initial program 0.3

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a + b \cdot c\right) \cdot c \le -3.366177053613654395798675960966992222011 \cdot 10^{198} \lor \neg \left(\left(a + b \cdot c\right) \cdot c \le 4.788215598584803852236065219824838534122 \cdot 10^{299}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot i\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* 2 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))