Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, E

Average Accuracy: 91.3% → 96.7%

Time: 42.9s

Precision: binary64

Cost: 8452

\[ \begin{array}{c}[y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \end{array} \]

Math

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

↓

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;z \leq 5 \cdot 10^{-11}:\\ \;\;\;\;\left(c \cdot b + \left(\left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + -4 \cdot i\right) \cdot x + -4 \cdot \left(t \cdot a\right)\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(\left(z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right) - \mathsf{fma}\left(t, a \cdot 4, c \cdot \left(-b\right)\right)\right) + i \cdot \left(-4 \cdot x\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

↓

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1 (* k (* j -27.0))))
   (if (<= z 5e-11)
     (+
      (+
       (* c b)
       (+ (* (+ (* 18.0 (* y (* z t))) (* -4.0 i)) x) (* -4.0 (* t a))))
      t_1)
     (+
      t_1
      (+
       (- (* z (* t (* x (* 18.0 y)))) (fma t (* a 4.0) (* c (- b))))
       (* i (* -4.0 x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = k * (j * -27.0);
	double tmp;
	if (z <= 5e-11) {
		tmp = ((c * b) + ((((18.0 * (y * (z * t))) + (-4.0 * i)) * x) + (-4.0 * (t * a)))) + t_1;
	} else {
		tmp = t_1 + (((z * (t * (x * (18.0 * y)))) - fma(t, (a * 4.0), (c * -b))) + (i * (-4.0 * x)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

↓

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(k * Float64(j * -27.0))
	tmp = 0.0
	if (z <= 5e-11)
		tmp = Float64(Float64(Float64(c * b) + Float64(Float64(Float64(Float64(18.0 * Float64(y * Float64(z * t))) + Float64(-4.0 * i)) * x) + Float64(-4.0 * Float64(t * a)))) + t_1);
	else
		tmp = Float64(t_1 + Float64(Float64(Float64(z * Float64(t * Float64(x * Float64(18.0 * y)))) - fma(t, Float64(a * 4.0), Float64(c * Float64(-b)))) + Float64(i * Float64(-4.0 * x))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, 5e-11], N[(N[(N[(c * b), $MachinePrecision] + N[(N[(N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * i), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(N[(N[(z * N[(t * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision] + N[(c * (-b)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(-4.0 * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	91.3%
Target	97.6%
Herbie	96.7%

\[\begin{array}{l} \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \end{array} \]

Derivation

1. Split input into 2 regimes

2. if z < 5.00000000000000018e-11

   1. Initial program 91.6%

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

   2. Simplified 94.3%

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

      [Start] 91.6	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      cancel-sign-sub-inv [=>] 91.6	\[ \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-j \cdot 27\right) \cdot k} \]
      associate--l+ [=>] 91.6	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + \left(b \cdot c - \left(x \cdot 4\right) \cdot i\right)\right)} + \left(-j \cdot 27\right) \cdot k \]

   3. Taylor expanded in x around 0 96.2%

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

   if 5.00000000000000018e-11 < z

   1. Initial program 90.9%

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

   2. Taylor expanded in x around 0 83.0%

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

   3. Simplified 89.2%

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

      [Start] 83.0	\[ \left(\left(\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate-*r* [=>] 82.9	\[ \left(\left(\left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      *-commutative [=>] 82.9	\[ \left(\left(\left(\color{blue}{\left(t \cdot \left(z \cdot x\right)\right) \cdot \left(18 \cdot y\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate-*r* [=>] 83.2	\[ \left(\left(\left(\color{blue}{\left(\left(t \cdot z\right) \cdot x\right)} \cdot \left(18 \cdot y\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      *-commutative [<=] 83.2	\[ \left(\left(\left(\left(\color{blue}{\left(z \cdot t\right)} \cdot x\right) \cdot \left(18 \cdot y\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate-*l* [=>] 89.2	\[ \left(\left(\left(\color{blue}{\left(z \cdot \left(t \cdot x\right)\right)} \cdot \left(18 \cdot y\right) - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   4. Applied egg-rr 97.6%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{-11}:\\ \;\;\;\;\left(c \cdot b + \left(\left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + -4 \cdot i\right) \cdot x + -4 \cdot \left(t \cdot a\right)\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + \left(\left(z \cdot \left(t \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right) - \mathsf{fma}\left(t, a \cdot 4, c \cdot \left(-b\right)\right)\right) + i \cdot \left(-4 \cdot x\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	44.9%
Cost	2424

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a\right) + t_1\\ t_3 := -4 \cdot \left(t \cdot a + i \cdot x\right)\\ t_4 := c \cdot b + -4 \cdot \left(i \cdot x\right)\\ t_5 := c \cdot b + t_1\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+233}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+182}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+111}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{+45}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-9}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-63}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-98}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-154}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{-258}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-228}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+88}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 2
Accuracy	97.3%
Cost	2380

\[\begin{array}{l} t_1 := t \cdot \left(-4 \cdot a\right)\\ t_2 := i \cdot \left(-4 \cdot x\right)\\ t_3 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+47}:\\ \;\;\;\;\left(c \cdot b + t \cdot \left(\left(18 \cdot x\right) \cdot \left(z \cdot y\right) + -4 \cdot a\right)\right) + \left(\left(-4 \cdot i\right) \cdot x + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-136}:\\ \;\;\;\;t_3 + \left(\left(c \cdot b + \left(\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right) + t_1\right)\right) + t_2\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-68}:\\ \;\;\;\;\left(c \cdot b + \left(\left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + -4 \cdot i\right) \cdot x + -4 \cdot \left(t \cdot a\right)\right)\right) + t_3\\ \mathbf{else}:\\ \;\;\;\;t_3 + \left(\left(c \cdot b + \left(t \cdot \left(z \cdot \left(y \cdot \left(18 \cdot x\right)\right)\right) + t_1\right)\right) + t_2\right)\\ \end{array} \]

Alternative 3
Accuracy	97.4%
Cost	2252

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := \left(c \cdot b + t \cdot \left(\left(18 \cdot x\right) \cdot \left(z \cdot y\right) + -4 \cdot a\right)\right) + \left(\left(-4 \cdot i\right) \cdot x + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-136}:\\ \;\;\;\;t_1 + \left(\left(c \cdot b + \left(\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right) + t \cdot \left(-4 \cdot a\right)\right)\right) + i \cdot \left(-4 \cdot x\right)\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+44}:\\ \;\;\;\;\left(c \cdot b + \left(\left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + -4 \cdot i\right) \cdot x + -4 \cdot \left(t \cdot a\right)\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	47.0%
Cost	2161

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a\right) + t_1\\ t_3 := -4 \cdot \left(t \cdot a + i \cdot x\right)\\ t_4 := t_1 + 18 \cdot \left(\left(z \cdot x\right) \cdot \left(y \cdot t\right)\right)\\ t_5 := c \cdot b + t_1\\ \mathbf{if}\;c \leq -2.4 \cdot 10^{-99}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq -2.3 \cdot 10^{-308}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 1.75 \cdot 10^{-245}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 7 \cdot 10^{-238}:\\ \;\;\;\;t_1 + 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\\ \mathbf{elif}\;c \leq 2.9 \cdot 10^{-176}:\\ \;\;\;\;\left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;c \leq 1.12 \cdot 10^{-166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 4.8 \cdot 10^{-118}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 2.45 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 14500000000:\\ \;\;\;\;c \cdot b + -4 \cdot \left(i \cdot x\right)\\ \mathbf{elif}\;c \leq 1.32 \cdot 10^{+39} \lor \neg \left(c \leq 4.6 \cdot 10^{+83}\right) \land c \leq 2.3 \cdot 10^{+146}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 5
Accuracy	47.0%
Cost	2161

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a\right) + t_1\\ t_3 := -4 \cdot \left(t \cdot a + i \cdot x\right)\\ t_4 := t_1 + 18 \cdot \left(\left(z \cdot x\right) \cdot \left(y \cdot t\right)\right)\\ t_5 := c \cdot b + t_1\\ \mathbf{if}\;c \leq -3.3 \cdot 10^{-100}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-307}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 3.6 \cdot 10^{-246}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{-190}:\\ \;\;\;\;t_1 + x \cdot \left(y \cdot \left(18 \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;c \leq 1.9 \cdot 10^{-176}:\\ \;\;\;\;\left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-168}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.7 \cdot 10^{-118}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 6.6 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 850000000:\\ \;\;\;\;c \cdot b + -4 \cdot \left(i \cdot x\right)\\ \mathbf{elif}\;c \leq 4.4 \cdot 10^{+39} \lor \neg \left(c \leq 1.7 \cdot 10^{+84}\right) \land c \leq 1.15 \cdot 10^{+147}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 6
Accuracy	93.2%
Cost	2121

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;t \leq -3.9 \cdot 10^{-23} \lor \neg \left(t \leq 6 \cdot 10^{+60}\right):\\ \;\;\;\;t_1 + \left(c \cdot b + \left(t_2 + 18 \cdot \left(t \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot b + \left(\left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + -4 \cdot i\right) \cdot x + t_2\right)\right) + t_1\\ \end{array} \]

Alternative 7
Accuracy	97.4%
Cost	2121

\[\begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+16} \lor \neg \left(t \leq 3.6 \cdot 10^{+45}\right):\\ \;\;\;\;\left(c \cdot b + t \cdot \left(\left(18 \cdot x\right) \cdot \left(z \cdot y\right) + -4 \cdot a\right)\right) + \left(\left(-4 \cdot i\right) \cdot x + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot b + \left(\left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + -4 \cdot i\right) \cdot x + -4 \cdot \left(t \cdot a\right)\right)\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 8
Accuracy	44.1%
Cost	2028

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a + i \cdot x\right)\\ t_3 := c \cdot b + -4 \cdot \left(i \cdot x\right)\\ t_4 := c \cdot b + t_1\\ \mathbf{if}\;y \leq -9 \cdot 10^{+234}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+182}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{+33}:\\ \;\;\;\;t_1 + i \cdot \left(-4 \cdot x\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-63}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-154}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-257}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-231}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-52}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+88}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 9
Accuracy	45.5%
Cost	2020

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + i \cdot x\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ t_3 := c \cdot b + t_2\\ \mathbf{if}\;y \leq -4 \cdot 10^{+201}:\\ \;\;\;\;t_2 + 18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+33}:\\ \;\;\;\;t_2 + i \cdot \left(-4 \cdot x\right)\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-64}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-154}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-234}:\\ \;\;\;\;c \cdot b + -4 \cdot \left(i \cdot x\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-52}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;\left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + -4 \cdot i\right) \cdot x\\ \end{array} \]

Alternative 10
Accuracy	63.8%
Cost	2017

\[\begin{array}{l} t_1 := \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + -4 \cdot i\right) \cdot x\\ t_2 := k \cdot \left(j \cdot -27\right) + \left(c \cdot b + -4 \cdot \left(t \cdot a\right)\right)\\ t_3 := -4 \cdot \left(t \cdot a + i \cdot x\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{-27}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-38}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.6 \cdot 10^{-271}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.35 \cdot 10^{-301}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 10^{-252} \lor \neg \left(b \leq 2 \cdot 10^{-218}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Accuracy	62.9%
Cost	1884

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := c \cdot b + -4 \cdot \left(t \cdot a\right)\\ t_3 := t_1 + t_2\\ t_4 := \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + -4 \cdot i\right) \cdot x\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-240}:\\ \;\;\;\;c \cdot b + \left(\left(-4 \cdot i\right) \cdot x + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-38}:\\ \;\;\;\;t_2 + -27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;z \leq 1.86 \cdot 10^{+89}:\\ \;\;\;\;t_1 + \left(i \cdot \left(-4 \cdot x\right) + t \cdot \left(-4 \cdot a\right)\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+180}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+186}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+286}:\\ \;\;\;\;t_1 + 18 \cdot \left(\left(z \cdot x\right) \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Accuracy	85.8%
Cost	1865

\[\begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{-79} \lor \neg \left(t \leq 1.05 \cdot 10^{-49}\right):\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + \left(c \cdot b + \left(-4 \cdot \left(t \cdot a\right) + 18 \cdot \left(t \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot b + t \cdot \left(-4 \cdot a\right)\right) + \left(\left(-4 \cdot i\right) \cdot x + j \cdot \left(k \cdot -27\right)\right)\\ \end{array} \]

Alternative 13
Accuracy	61.9%
Cost	1753

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := t_1 + \left(c \cdot b + -4 \cdot \left(t \cdot a\right)\right)\\ t_3 := c \cdot b + \left(\left(-4 \cdot i\right) \cdot x + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{if}\;z \leq -2.15 \cdot 10^{+73}:\\ \;\;\;\;\left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-240}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 0.016:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+140} \lor \neg \left(z \leq 3.1 \cdot 10^{+288}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 + 18 \cdot \left(\left(z \cdot x\right) \cdot \left(y \cdot t\right)\right)\\ \end{array} \]

Alternative 14
Accuracy	62.0%
Cost	1752

\[\begin{array}{l} t_1 := c \cdot b + \left(\left(-4 \cdot i\right) \cdot x + j \cdot \left(k \cdot -27\right)\right)\\ t_2 := c \cdot b + -4 \cdot \left(t \cdot a\right)\\ t_3 := t_2 + -27 \cdot \left(k \cdot j\right)\\ t_4 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+62}:\\ \;\;\;\;\left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-55}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 0.009:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+142}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+287}:\\ \;\;\;\;t_4 + 18 \cdot \left(\left(z \cdot x\right) \cdot \left(y \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_4 + t_2\\ \end{array} \]

Alternative 15
Accuracy	81.5%
Cost	1741

\[\begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+73}:\\ \;\;\;\;\left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+194} \lor \neg \left(z \leq 1.65 \cdot 10^{+271}\right):\\ \;\;\;\;\left(c \cdot b + t \cdot \left(-4 \cdot a\right)\right) + \left(\left(-4 \cdot i\right) \cdot x + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + 18 \cdot \left(\left(z \cdot x\right) \cdot \left(y \cdot t\right)\right)\\ \end{array} \]

Alternative 16
Accuracy	85.8%
Cost	1737

\[\begin{array}{l} \mathbf{if}\;t \leq -5.7 \cdot 10^{-80} \lor \neg \left(t \leq 2 \cdot 10^{-50}\right):\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + \left(c \cdot b + t \cdot \left(18 \cdot \left(y \cdot \left(z \cdot x\right)\right) + -4 \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot b + t \cdot \left(-4 \cdot a\right)\right) + \left(\left(-4 \cdot i\right) \cdot x + j \cdot \left(k \cdot -27\right)\right)\\ \end{array} \]

Alternative 17
Accuracy	49.3%
Cost	1633

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := -4 \cdot \left(t \cdot a\right) + t_1\\ t_3 := c \cdot b + t_1\\ \mathbf{if}\;c \leq -1.5 \cdot 10^{-164}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-242}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3.2 \cdot 10^{-176}:\\ \;\;\;\;\left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + -4 \cdot i\right) \cdot x\\ \mathbf{elif}\;c \leq 9 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 12200000000:\\ \;\;\;\;c \cdot b + -4 \cdot \left(i \cdot x\right)\\ \mathbf{elif}\;c \leq 10^{+40} \lor \neg \left(c \leq 5.5 \cdot 10^{+81}\right) \land c \leq 1.5 \cdot 10^{+146}:\\ \;\;\;\;-4 \cdot \left(t \cdot a + i \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 18
Accuracy	40.2%
Cost	1632

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + i \cdot x\right)\\ t_2 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;j \leq -2.25 \cdot 10^{+173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -2.2 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -2.25 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3.15 \cdot 10^{-127}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;j \leq -5.1 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{-273}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;j \leq 1.42 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Accuracy	48.8%
Cost	1368

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + i \cdot x\right)\\ t_2 := c \cdot b + k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;j \leq -0.62:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -2.15 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -5.2 \cdot 10^{-210}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -7.2 \cdot 10^{-279}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;j \leq 3.6 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 20
Accuracy	50.4%
Cost	1368

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a + i \cdot x\right)\\ t_2 := c \cdot b + k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;j \leq -950:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -3.6 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -7.8 \cdot 10^{-131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.24 \cdot 10^{-278}:\\ \;\;\;\;c \cdot b + -4 \cdot \left(i \cdot x\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 21
Accuracy	29.0%
Cost	1112

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-243}:\\ \;\;\;\;\left(-4 \cdot i\right) \cdot x\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-123}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+44}:\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 22
Accuracy	26.7%
Cost	981

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;c \leq -5 \cdot 10^{-309}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 3 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 5.2 \cdot 10^{-37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.2 \cdot 10^{+84} \lor \neg \left(c \leq 1.22 \cdot 10^{+140}\right):\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 23
Accuracy	27.5%
Cost	452

\[\begin{array}{l} \mathbf{if}\;c \leq 3.6 \cdot 10^{-37}:\\ \;\;\;\;-27 \cdot \left(k \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot b\\ \end{array} \]

Alternative 24
Accuracy	23.9%
Cost	192

\[c \cdot b \]

Reproduce

herbie shell --seed 2023122 
(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) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))