Average Error: 5.8 → 1.1
Time: 25.9s
Precision: 64
\[2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(c \cdot b + a\right) \cdot c \le -7.711821572914459 \cdot 10^{+111}:\\ \;\;\;\;2.0 \cdot \left(\left(x \cdot y + t \cdot z\right) + \left(-c\right) \cdot \left(a \cdot i + \left(i \cdot c\right) \cdot b\right)\right)\\ \mathbf{elif}\;\left(c \cdot b + a\right) \cdot c \le 5.793851923347976 \cdot 10^{+108}:\\ \;\;\;\;\left(\left(x \cdot y + t \cdot z\right) - \left(\left(c \cdot b + a\right) \cdot c\right) \cdot i\right) \cdot 2.0\\ \mathbf{else}:\\ \;\;\;\;2.0 \cdot \left(\left(x \cdot y + t \cdot z\right) - \left(c \cdot b + a\right) \cdot \left(i \cdot c\right)\right)\\ \end{array}\]
2.0 \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(c \cdot b + a\right) \cdot c \le -7.711821572914459 \cdot 10^{+111}:\\
\;\;\;\;2.0 \cdot \left(\left(x \cdot y + t \cdot z\right) + \left(-c\right) \cdot \left(a \cdot i + \left(i \cdot c\right) \cdot b\right)\right)\\

\mathbf{elif}\;\left(c \cdot b + a\right) \cdot c \le 5.793851923347976 \cdot 10^{+108}:\\
\;\;\;\;\left(\left(x \cdot y + t \cdot z\right) - \left(\left(c \cdot b + a\right) \cdot c\right) \cdot i\right) \cdot 2.0\\

\mathbf{else}:\\
\;\;\;\;2.0 \cdot \left(\left(x \cdot y + t \cdot z\right) - \left(c \cdot b + a\right) \cdot \left(i \cdot c\right)\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r33306695 = 2.0;
        double r33306696 = x;
        double r33306697 = y;
        double r33306698 = r33306696 * r33306697;
        double r33306699 = z;
        double r33306700 = t;
        double r33306701 = r33306699 * r33306700;
        double r33306702 = r33306698 + r33306701;
        double r33306703 = a;
        double r33306704 = b;
        double r33306705 = c;
        double r33306706 = r33306704 * r33306705;
        double r33306707 = r33306703 + r33306706;
        double r33306708 = r33306707 * r33306705;
        double r33306709 = i;
        double r33306710 = r33306708 * r33306709;
        double r33306711 = r33306702 - r33306710;
        double r33306712 = r33306695 * r33306711;
        return r33306712;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r33306713 = c;
        double r33306714 = b;
        double r33306715 = r33306713 * r33306714;
        double r33306716 = a;
        double r33306717 = r33306715 + r33306716;
        double r33306718 = r33306717 * r33306713;
        double r33306719 = -7.711821572914459e+111;
        bool r33306720 = r33306718 <= r33306719;
        double r33306721 = 2.0;
        double r33306722 = x;
        double r33306723 = y;
        double r33306724 = r33306722 * r33306723;
        double r33306725 = t;
        double r33306726 = z;
        double r33306727 = r33306725 * r33306726;
        double r33306728 = r33306724 + r33306727;
        double r33306729 = -r33306713;
        double r33306730 = i;
        double r33306731 = r33306716 * r33306730;
        double r33306732 = r33306730 * r33306713;
        double r33306733 = r33306732 * r33306714;
        double r33306734 = r33306731 + r33306733;
        double r33306735 = r33306729 * r33306734;
        double r33306736 = r33306728 + r33306735;
        double r33306737 = r33306721 * r33306736;
        double r33306738 = 5.793851923347976e+108;
        bool r33306739 = r33306718 <= r33306738;
        double r33306740 = r33306718 * r33306730;
        double r33306741 = r33306728 - r33306740;
        double r33306742 = r33306741 * r33306721;
        double r33306743 = r33306717 * r33306732;
        double r33306744 = r33306728 - r33306743;
        double r33306745 = r33306721 * r33306744;
        double r33306746 = r33306739 ? r33306742 : r33306745;
        double r33306747 = r33306720 ? r33306737 : r33306746;
        return r33306747;
}

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

Original5.8
Target1.9
Herbie1.1
\[2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Split input into 3 regimes

  2. if (* (+ a (* b c)) c) < -7.711821572914459e+111

    1. Initial program 19.0

      \[2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
    2. Using strategy rm

    3. Applied associate-*l*4.4

      \[\leadsto 2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\]

    4. Taylor expanded around inf 24.6

      \[\leadsto 2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(i \cdot \left(b \cdot {c}^{2}\right) + a \cdot \left(i \cdot c\right)\right)}\right)\]

    5. Simplified19.0

      \[\leadsto 2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(\left(c \cdot c\right) \cdot \left(i \cdot b\right) + \left(c \cdot i\right) \cdot a\right)}\right)\]
    6. Using strategy rm

    7. Applied sub-neg19.0

      \[\leadsto 2.0 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) + \left(-\left(\left(c \cdot c\right) \cdot \left(i \cdot b\right) + \left(c \cdot i\right) \cdot a\right)\right)\right)}\]

    8. Simplified2.6

      \[\leadsto 2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(-c\right) \cdot \left(i \cdot a + \left(c \cdot i\right) \cdot b\right)}\right)\]

    if -7.711821572914459e+111 < (* (+ a (* b c)) c) < 5.793851923347976e+108

    1. Initial program 0.3

      \[2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]

    if 5.793851923347976e+108 < (* (+ a (* b c)) c)

    1. Initial program 19.2

      \[2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
    2. Using strategy rm

    3. Applied associate-*l*3.5

      \[\leadsto 2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot b + a\right) \cdot c \le -7.711821572914459 \cdot 10^{+111}:\\ \;\;\;\;2.0 \cdot \left(\left(x \cdot y + t \cdot z\right) + \left(-c\right) \cdot \left(a \cdot i + \left(i \cdot c\right) \cdot b\right)\right)\\ \mathbf{elif}\;\left(c \cdot b + a\right) \cdot c \le 5.793851923347976 \cdot 10^{+108}:\\ \;\;\;\;\left(\left(x \cdot y + t \cdot z\right) - \left(\left(c \cdot b + a\right) \cdot c\right) \cdot i\right) \cdot 2.0\\ \mathbf{else}:\\ \;\;\;\;2.0 \cdot \left(\left(x \cdot y + t \cdot z\right) - \left(c \cdot b + a\right) \cdot \left(i \cdot c\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"

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

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