Average Error: 5.7 → 4.2
Time: 31.1s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -6.023016971486713978695466466448444890718 \cdot 10^{129} \lor \neg \left(z \le 4.983042576879064654649325286831293190518 \cdot 10^{-72}\right):\\ \;\;\;\;\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(x \cdot \left(\left(y \cdot 18\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\\ \end{array}\]
\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k
↓
\begin{array}{l}
\mathbf{if}\;z \le -6.023016971486713978695466466448444890718 \cdot 10^{129} \lor \neg \left(z \le 4.983042576879064654649325286831293190518 \cdot 10^{-72}\right):\\
\;\;\;\;\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(t \cdot \left(x \cdot \left(\left(y \cdot 18\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r463114 = x;
        double r463115 = 18.0;
        double r463116 = r463114 * r463115;
        double r463117 = y;
        double r463118 = r463116 * r463117;
        double r463119 = z;
        double r463120 = r463118 * r463119;
        double r463121 = t;
        double r463122 = r463120 * r463121;
        double r463123 = a;
        double r463124 = 4.0;
        double r463125 = r463123 * r463124;
        double r463126 = r463125 * r463121;
        double r463127 = r463122 - r463126;
        double r463128 = b;
        double r463129 = c;
        double r463130 = r463128 * r463129;
        double r463131 = r463127 + r463130;
        double r463132 = r463114 * r463124;
        double r463133 = i;
        double r463134 = r463132 * r463133;
        double r463135 = r463131 - r463134;
        double r463136 = j;
        double r463137 = 27.0;
        double r463138 = r463136 * r463137;
        double r463139 = k;
        double r463140 = r463138 * r463139;
        double r463141 = r463135 - r463140;
        return r463141;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r463142 = z;
        double r463143 = -6.023016971486714e+129;
        bool r463144 = r463142 <= r463143;
        double r463145 = 4.983042576879065e-72;
        bool r463146 = r463142 <= r463145;
        double r463147 = !r463146;
        bool r463148 = r463144 || r463147;
        double r463149 = t;
        double r463150 = x;
        double r463151 = 18.0;
        double r463152 = r463150 * r463151;
        double r463153 = y;
        double r463154 = r463152 * r463153;
        double r463155 = r463154 * r463142;
        double r463156 = a;
        double r463157 = 4.0;
        double r463158 = r463156 * r463157;
        double r463159 = r463155 - r463158;
        double r463160 = r463149 * r463159;
        double r463161 = b;
        double r463162 = c;
        double r463163 = r463161 * r463162;
        double r463164 = r463160 + r463163;
        double r463165 = r463150 * r463157;
        double r463166 = i;
        double r463167 = r463165 * r463166;
        double r463168 = j;
        double r463169 = 27.0;
        double r463170 = k;
        double r463171 = r463169 * r463170;
        double r463172 = r463168 * r463171;
        double r463173 = r463167 + r463172;
        double r463174 = r463164 - r463173;
        double r463175 = r463153 * r463151;
        double r463176 = r463175 * r463142;
        double r463177 = r463150 * r463176;
        double r463178 = r463177 - r463158;
        double r463179 = r463149 * r463178;
        double r463180 = r463179 + r463163;
        double r463181 = r463168 * r463169;
        double r463182 = r463181 * r463170;
        double r463183 = r463167 + r463182;
        double r463184 = r463180 - r463183;
        double r463185 = r463148 ? r463174 : r463184;
        return r463185;
}

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

Bits error versus j

Bits error versus k

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.7
Target1.6
Herbie4.2
\[\begin{array}{l} \mathbf{if}\;t \lt -1.62108153975413982700795070153457058168 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{elif}\;t \lt 165.6802794380522243500308832153677940369:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -6.023016971486714e+129 or 4.983042576879065e-72 < z

    1. Initial program 6.7

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    2. Simplified6.7

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)}\]
    3. Using strategy rm

    4. Applied associate-*l*6.7

      \[\leadsto \left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \color{blue}{j \cdot \left(27 \cdot k\right)}\right)\]

    if -6.023016971486714e+129 < z < 4.983042576879065e-72

    1. Initial program 5.1

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    2. Simplified5.1

      \[\leadsto \color{blue}{\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)}\]
    3. Using strategy rm

    4. Applied associate-*l*5.1

      \[\leadsto \left(t \cdot \left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\]

    5. Simplified5.1

      \[\leadsto \left(t \cdot \left(\left(x \cdot \color{blue}{\left(y \cdot 18\right)}\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\]
    6. Using strategy rm

    7. Applied associate-*l*2.5

      \[\leadsto \left(t \cdot \left(\color{blue}{x \cdot \left(\left(y \cdot 18\right) \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification4.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.023016971486713978695466466448444890718 \cdot 10^{129} \lor \neg \left(z \le 4.983042576879064654649325286831293190518 \cdot 10^{-72}\right):\\ \;\;\;\;\left(t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(x \cdot \left(\left(y \cdot 18\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18) y) z) t) (* (* a 4) t)) (* b c)) (* (* x 4) i)) (* (* j 27) k)))