Average Error: 6.3 → 0.8
Time: 34.8s
Precision: 64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(a + b \cdot c\right) \cdot c \le -7.325317889675971913133681007644511818637 \cdot 10^{166} \lor \neg \left(\left(a + b \cdot c\right) \cdot c \le 2.227380694343007122238278526287058546545 \cdot 10^{113}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a \cdot i + \left(i \cdot c\right) \cdot b\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \end{array}\]
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 -7.325317889675971913133681007644511818637 \cdot 10^{166} \lor \neg \left(\left(a + b \cdot c\right) \cdot c \le 2.227380694343007122238278526287058546545 \cdot 10^{113}\right):\\
\;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a \cdot i + \left(i \cdot c\right) \cdot b\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 r543113 = 2.0;
        double r543114 = x;
        double r543115 = y;
        double r543116 = r543114 * r543115;
        double r543117 = z;
        double r543118 = t;
        double r543119 = r543117 * r543118;
        double r543120 = r543116 + r543119;
        double r543121 = a;
        double r543122 = b;
        double r543123 = c;
        double r543124 = r543122 * r543123;
        double r543125 = r543121 + r543124;
        double r543126 = r543125 * r543123;
        double r543127 = i;
        double r543128 = r543126 * r543127;
        double r543129 = r543120 - r543128;
        double r543130 = r543113 * r543129;
        return r543130;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r543131 = a;
        double r543132 = b;
        double r543133 = c;
        double r543134 = r543132 * r543133;
        double r543135 = r543131 + r543134;
        double r543136 = r543135 * r543133;
        double r543137 = -7.325317889675972e+166;
        bool r543138 = r543136 <= r543137;
        double r543139 = 2.227380694343007e+113;
        bool r543140 = r543136 <= r543139;
        double r543141 = !r543140;
        bool r543142 = r543138 || r543141;
        double r543143 = 2.0;
        double r543144 = x;
        double r543145 = y;
        double r543146 = r543144 * r543145;
        double r543147 = z;
        double r543148 = t;
        double r543149 = r543147 * r543148;
        double r543150 = r543146 + r543149;
        double r543151 = i;
        double r543152 = r543131 * r543151;
        double r543153 = r543151 * r543133;
        double r543154 = r543153 * r543132;
        double r543155 = r543152 + r543154;
        double r543156 = r543155 * r543133;
        double r543157 = r543150 - r543156;
        double r543158 = r543143 * r543157;
        double r543159 = r543136 * r543151;
        double r543160 = r543150 - r543159;
        double r543161 = r543143 * r543160;
        double r543162 = r543142 ? r543158 : r543161;
        return r543162;
}

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
Target1.9
Herbie0.8
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* (+ a (* b c)) c) < -7.325317889675972e+166 or 2.227380694343007e+113 < (* (+ a (* b c)) c)

    1. Initial program 23.3

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

    3. Applied associate-*l*4.4

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

    4. Simplified4.4

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

    6. Applied add-cube-cbrt5.0

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(\left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \sqrt[3]{a + b \cdot c}\right)} \cdot \left(i \cdot c\right)\right)\]
    7. Using strategy rm

    8. Applied associate-*r*6.4

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

    9. Simplified5.9

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

    11. Applied distribute-lft-in5.9

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

    12. Simplified5.9

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

    13. Simplified2.2

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

    if -7.325317889675972e+166 < (* (+ a (* b c)) c) < 2.227380694343007e+113

    1. Initial program 0.4

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

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a + b \cdot c\right) \cdot c \le -7.325317889675971913133681007644511818637 \cdot 10^{166} \lor \neg \left(\left(a + b \cdot c\right) \cdot c \le 2.227380694343007122238278526287058546545 \cdot 10^{113}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a \cdot i + \left(i \cdot c\right) \cdot b\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019322 
(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))))