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

Average Error: 5.2 → 1.2

Time: 1.2min

Precision: binary64

Cost: 5192

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

Math

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

↓

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ t_2 := x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(\frac{x \cdot \left(\left(t \cdot z\right) \cdot \left(y \cdot 18\right)\right)}{1} + b \cdot c\right) - t_2\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\left(t \cdot \left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(\left(z \cdot x\right) \cdot \left(t \cdot 18\right)\right) + b \cdot c\right) - t_2\\ \end{array} \]

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
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
          (* (* x 4.0) i)))
        (t_2 (+ (* x (* 4.0 i)) (* j (* 27.0 k)))))
   (if (<= t_1 (- INFINITY))
     (- (+ (/ (* x (* (* t z) (* y 18.0))) 1.0) (* b c)) t_2)
     (if (<= t_1 5e+306)
       (- (+ (* t (- (* 18.0 (* (* x y) z)) (* a 4.0))) (* b c)) t_2)
       (- (+ (* y (* (* z x) (* t 18.0))) (* b c)) t_2)))))

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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double t_2 = (x * (4.0 * i)) + (j * (27.0 * k));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (((x * ((t * z) * (y * 18.0))) / 1.0) + (b * c)) - t_2;
	} else if (t_1 <= 5e+306) {
		tmp = ((t * ((18.0 * ((x * y) * z)) - (a * 4.0))) + (b * c)) - t_2;
	} else {
		tmp = ((y * ((z * x) * (t * 18.0))) + (b * c)) - t_2;
	}
	return tmp;
}

Java

public static 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);
}

↓

public static 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 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	double t_2 = (x * (4.0 * i)) + (j * (27.0 * k));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = (((x * ((t * z) * (y * 18.0))) / 1.0) + (b * c)) - t_2;
	} else if (t_1 <= 5e+306) {
		tmp = ((t * ((18.0 * ((x * y) * z)) - (a * 4.0))) + (b * c)) - t_2;
	} else {
		tmp = ((y * ((z * x) * (t * 18.0))) + (b * c)) - t_2;
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a, b, c, i, j, k):
	t_1 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)
	t_2 = (x * (4.0 * i)) + (j * (27.0 * k))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = (((x * ((t * z) * (y * 18.0))) / 1.0) + (b * c)) - t_2
	elif t_1 <= 5e+306:
		tmp = ((t * ((18.0 * ((x * y) * z)) - (a * 4.0))) + (b * c)) - t_2
	else:
		tmp = ((y * ((z * x) * (t * 18.0))) + (b * c)) - t_2
	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(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))
	t_2 = Float64(Float64(x * Float64(4.0 * i)) + Float64(j * Float64(27.0 * k)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(Float64(x * Float64(Float64(t * z) * Float64(y * 18.0))) / 1.0) + Float64(b * c)) - t_2);
	elseif (t_1 <= 5e+306)
		tmp = Float64(Float64(Float64(t * Float64(Float64(18.0 * Float64(Float64(x * y) * z)) - Float64(a * 4.0))) + Float64(b * c)) - t_2);
	else
		tmp = Float64(Float64(Float64(y * Float64(Float64(z * x) * Float64(t * 18.0))) + Float64(b * c)) - t_2);
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a, b, c, i, j, k)
	t_1 = ((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i);
	t_2 = (x * (4.0 * i)) + (j * (27.0 * k));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = (((x * ((t * z) * (y * 18.0))) / 1.0) + (b * c)) - t_2;
	elseif (t_1 <= 5e+306)
		tmp = ((t * ((18.0 * ((x * y) * z)) - (a * 4.0))) + (b * c)) - t_2;
	else
		tmp = ((y * ((z * x) * (t * 18.0))) + (b * c)) - t_2;
	end
	tmp_2 = 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[(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]}, Block[{t$95$2 = N[(N[(x * N[(4.0 * i), $MachinePrecision]), $MachinePrecision] + N[(j * N[(27.0 * k), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(N[(x * N[(N[(t * z), $MachinePrecision] * N[(y * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 1.0), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$1, 5e+306], N[(N[(N[(t * N[(N[(18.0 * N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(N[(y * N[(N[(z * x), $MachinePrecision] * N[(t * 18.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Target

Original	5.2
Target	1.5
Herbie	1.2

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

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) < -inf.0

   1. Initial program 64.0

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

   2. Simplified 40.7

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

      [Start] 64.0	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational.json-simplify-45 [=>] 64.0	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]
      rational.json-simplify-2 [=>] 64.0	\[ \left(\left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-48 [=>] 64.0	\[ \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 64.0	\[ \left(t \cdot \left(\color{blue}{z \cdot \left(\left(x \cdot 18\right) \cdot y\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-43 [<=] 41.1	\[ \left(t \cdot \left(\color{blue}{y \cdot \left(z \cdot \left(x \cdot 18\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 41.1	\[ \left(t \cdot \left(y \cdot \left(z \cdot \color{blue}{\left(18 \cdot x\right)}\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-43 [=>] 40.9	\[ \left(t \cdot \left(y \cdot \color{blue}{\left(18 \cdot \left(x \cdot z\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 40.9	\[ \left(t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{i \cdot \left(x \cdot 4\right)} + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-43 [=>] 40.6	\[ \left(t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 40.6	\[ \left(t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{k \cdot \left(j \cdot 27\right)}\right) \]
      rational.json-simplify-43 [=>] 40.7	\[ \left(t \cdot \left(y \cdot \left(18 \cdot \left(x \cdot z\right)\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Taylor expanded in y around inf 14.1

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

   4. Simplified 5.9

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

      [Start] 14.1	\[ \left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      exponential.json-simplify-11 [<=] 14.1	\[ \left(\color{blue}{{\left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)\right)}^{1}} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      exponential.json-simplify-26 [=>] 14.1	\[ \left(\color{blue}{{18}^{1} \cdot {\left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)}^{1}} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      metadata-eval [=>] 14.1	\[ \left(\color{blue}{18} \cdot {\left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)}^{1} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      exponential.json-simplify-11 [=>] 14.1	\[ \left(18 \cdot \color{blue}{\left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      rational.json-simplify-43 [=>] 7.9	\[ \left(18 \cdot \left(y \cdot \color{blue}{\left(z \cdot \left(x \cdot t\right)\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      rational.json-simplify-43 [=>] 5.9	\[ \left(18 \cdot \left(y \cdot \color{blue}{\left(x \cdot \left(t \cdot z\right)\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      rational.json-simplify-43 [=>] 5.9	\[ \left(18 \cdot \color{blue}{\left(x \cdot \left(\left(t \cdot z\right) \cdot y\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      rational.json-simplify-2 [=>] 5.9	\[ \left(18 \cdot \left(x \cdot \color{blue}{\left(y \cdot \left(t \cdot z\right)\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   5. Applied egg-rr 6.3

      \[\leadsto \left(\color{blue}{\frac{x \cdot \left(\left(t \cdot z\right) \cdot \left(y \cdot 18\right)\right)}{1}} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

   if -inf.0 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) < 4.99999999999999993e306

   1. Initial program 0.3

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

   2. Simplified 0.4

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

      [Start] 0.3	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational.json-simplify-45 [=>] 0.3	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]
      rational.json-simplify-2 [=>] 0.3	\[ \left(\left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-48 [=>] 0.3	\[ \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 0.3	\[ \left(t \cdot \left(\color{blue}{z \cdot \left(\left(x \cdot 18\right) \cdot y\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 0.3	\[ \left(t \cdot \left(z \cdot \color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 0.3	\[ \left(t \cdot \left(z \cdot \left(y \cdot \color{blue}{\left(18 \cdot x\right)}\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-43 [=>] 0.3	\[ \left(t \cdot \left(z \cdot \color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-43 [=>] 0.3	\[ \left(t \cdot \left(\color{blue}{18 \cdot \left(\left(x \cdot y\right) \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 0.3	\[ \left(t \cdot \left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{i \cdot \left(x \cdot 4\right)} + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-43 [=>] 0.4	\[ \left(t \cdot \left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 0.4	\[ \left(t \cdot \left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{k \cdot \left(j \cdot 27\right)}\right) \]
      rational.json-simplify-43 [=>] 0.4	\[ \left(t \cdot \left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   if 4.99999999999999993e306 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i))

   1. Initial program 61.7

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

   2. Simplified 60.9

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

      [Start] 61.7	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      rational.json-simplify-45 [=>] 61.7	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]
      rational.json-simplify-2 [=>] 61.7	\[ \left(\left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right)} - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-48 [=>] 61.7	\[ \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 61.7	\[ \left(t \cdot \left(\color{blue}{z \cdot \left(\left(x \cdot 18\right) \cdot y\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 61.7	\[ \left(t \cdot \left(z \cdot \color{blue}{\left(y \cdot \left(x \cdot 18\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 61.7	\[ \left(t \cdot \left(z \cdot \left(y \cdot \color{blue}{\left(18 \cdot x\right)}\right) - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-43 [=>] 61.7	\[ \left(t \cdot \left(z \cdot \color{blue}{\left(18 \cdot \left(x \cdot y\right)\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-43 [=>] 61.5	\[ \left(t \cdot \left(\color{blue}{18 \cdot \left(\left(x \cdot y\right) \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 61.5	\[ \left(t \cdot \left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{i \cdot \left(x \cdot 4\right)} + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-43 [=>] 60.9	\[ \left(t \cdot \left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]
      rational.json-simplify-2 [=>] 60.9	\[ \left(t \cdot \left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{k \cdot \left(j \cdot 27\right)}\right) \]
      rational.json-simplify-43 [=>] 60.9	\[ \left(t \cdot \left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Taylor expanded in x around inf 14.4

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

   4. Simplified 14.4

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

      [Start] 14.4	\[ \left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      rational.json-simplify-43 [=>] 14.4	\[ \left(\color{blue}{y \cdot \left(\left(t \cdot \left(z \cdot x\right)\right) \cdot 18\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      rational.json-simplify-2 [=>] 14.4	\[ \left(y \cdot \color{blue}{\left(18 \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      rational.json-simplify-2 [=>] 14.4	\[ \left(y \cdot \left(18 \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot t\right)}\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]
      rational.json-simplify-43 [=>] 14.4	\[ \left(y \cdot \color{blue}{\left(\left(z \cdot x\right) \cdot \left(t \cdot 18\right)\right)} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 1.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq -\infty:\\ \;\;\;\;\left(\frac{x \cdot \left(\left(t \cdot z\right) \cdot \left(y \cdot 18\right)\right)}{1} + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\left(t \cdot \left(18 \cdot \left(\left(x \cdot y\right) \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(\left(z \cdot x\right) \cdot \left(t \cdot 18\right)\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	22.5
Cost	2404

\[\begin{array}{l} t_1 := 27 \cdot \left(k \cdot j\right)\\ t_2 := x \cdot \left(4 \cdot i\right)\\ t_3 := 4 \cdot \left(i \cdot x\right)\\ t_4 := \left(y \cdot \left(\left(z \cdot x\right) \cdot \left(t \cdot 18\right)\right) + b \cdot c\right) - t_2\\ t_5 := t \cdot \left(a \cdot -4\right) + b \cdot c\\ t_6 := t_5 - t_1\\ t_7 := t_5 - t_2\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+131}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{+76}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{+47}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-224}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-289}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-297}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right) - t_3\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-268}:\\ \;\;\;\;\left(c \cdot b - j \cdot \left(27 \cdot k\right)\right) - t_3\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-257}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;y \leq 0.00044:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot b + \left(z \cdot \left(t \cdot x\right)\right) \cdot \left(y \cdot 18\right)\right) - t_1\\ \end{array} \]

Alternative 2
Error	36.9
Cost	2160

\[\begin{array}{l} t_1 := c \cdot b - 4 \cdot \left(i \cdot x\right)\\ t_2 := c \cdot b - 27 \cdot \left(k \cdot j\right)\\ t_3 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{+188}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+26}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-261}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-290}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-249}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+15}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(\left(z \cdot x\right) \cdot 18\right)\right)\\ \end{array} \]

Alternative 3
Error	33.3
Cost	2156

\[\begin{array}{l} t_1 := 4 \cdot \left(i \cdot x\right)\\ t_2 := c \cdot b - t_1\\ t_3 := a \cdot \left(-4 \cdot t\right) - t_1\\ t_4 := 27 \cdot \left(k \cdot j\right)\\ t_5 := c \cdot b - t_4\\ \mathbf{if}\;t \leq -1.62 \cdot 10^{+199}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{+118}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-89}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-192}:\\ \;\;\;\;\left(-t_4\right) - t_1\\ \mathbf{elif}\;t \leq -3.05 \cdot 10^{-263}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.25 \cdot 10^{-292}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 10^{-248}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-73}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	9.6
Cost	2132

\[\begin{array}{l} t_1 := x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\\ t_2 := \left(t \cdot \left(a \cdot -4\right) + b \cdot c\right) - t_1\\ \mathbf{if}\;t \leq -1.45 \cdot 10^{-88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-182}:\\ \;\;\;\;\left(18 \cdot \left(\left(z \cdot x\right) \cdot \left(y \cdot t\right)\right) + b \cdot c\right) - t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-65}:\\ \;\;\;\;\left(18 \cdot \left(x \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + b \cdot c\right) - t_1\\ \mathbf{elif}\;t \leq 570:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - 27 \cdot \left(k \cdot j\right)\\ \end{array} \]

Alternative 5
Error	8.5
Cost	2128

\[\begin{array}{l} t_1 := x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\\ t_2 := \left(t \cdot \left(a \cdot -4\right) + b \cdot c\right) - t_1\\ t_3 := \left(y \cdot \left(\left(t \cdot \left(z \cdot x\right)\right) \cdot 18\right) + b \cdot c\right) - t_1\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+164}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{+45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-171}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(18 \cdot \left(\left(z \cdot x\right) \cdot \left(y \cdot t\right)\right) + b \cdot c\right) - t_1\\ \end{array} \]

Alternative 6
Error	31.7
Cost	2020

\[\begin{array}{l} t_1 := 27 \cdot \left(k \cdot j\right)\\ t_2 := 4 \cdot \left(i \cdot x\right)\\ t_3 := c \cdot b - t_2\\ t_4 := t \cdot \left(18 \cdot \left(z \cdot \left(y \cdot x\right)\right) - 4 \cdot a\right)\\ t_5 := \left(-t_1\right) - t_2\\ t_6 := c \cdot b - t_1\\ \mathbf{if}\;t \leq -2.2 \cdot 10^{+107}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-81}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right) - t_2\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-144}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-192}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-267}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-306}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{-248}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-96}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-66}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 7
Error	33.3
Cost	1892

\[\begin{array}{l} t_1 := 4 \cdot \left(i \cdot x\right)\\ t_2 := c \cdot b - t_1\\ t_3 := c \cdot b - 27 \cdot \left(k \cdot j\right)\\ t_4 := a \cdot \left(-4 \cdot t\right) - t_1\\ \mathbf{if}\;t \leq -5 \cdot 10^{+184}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+117}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-87}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -2.85 \cdot 10^{-265}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-292}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-307}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-245}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-73}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 8
Error	10.6
Cost	1872

\[\begin{array}{l} t_1 := 27 \cdot \left(k \cdot j\right)\\ t_2 := x \cdot \left(4 \cdot i\right)\\ t_3 := \left(t \cdot \left(a \cdot -4\right) + b \cdot c\right) - \left(t_2 + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+66}:\\ \;\;\;\;\left(c \cdot b + \left(z \cdot \left(t \cdot x\right)\right) \cdot \left(y \cdot 18\right)\right) - t_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-19}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 100000:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - t_1\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+262}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot \left(\left(z \cdot x\right) \cdot \left(t \cdot 18\right)\right) + b \cdot c\right) - t_2\\ \end{array} \]

Alternative 9
Error	11.3
Cost	1740

\[\begin{array}{l} t_1 := x \cdot \left(4 \cdot i\right)\\ t_2 := \left(t \cdot \left(a \cdot -4\right) + b \cdot c\right) - \left(t_1 + j \cdot \left(27 \cdot k\right)\right)\\ t_3 := \left(y \cdot \left(\left(z \cdot x\right) \cdot \left(t \cdot 18\right)\right) + b \cdot c\right) - t_1\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+177}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	46.6
Cost	1632

\[\begin{array}{l} t_1 := \left(i \cdot x\right) \cdot -4\\ t_2 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;t \leq -6.8 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-113}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t \leq -3.7 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-183}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-92}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;18 \cdot \left(t \cdot \left(y \cdot \left(z \cdot x\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	46.5
Cost	1632

\[\begin{array}{l} t_1 := \left(i \cdot x\right) \cdot -4\\ t_2 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.55 \cdot 10^{-113}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-183}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-309}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-93}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(\left(z \cdot x\right) \cdot 18\right)\right)\\ \end{array} \]

Alternative 12
Error	18.7
Cost	1620

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right) + b \cdot c\\ t_2 := t_1 - x \cdot \left(4 \cdot i\right)\\ t_3 := t_1 - 27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;i \leq -1.5 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-63}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(y \cdot x\right)\right) - 4 \cdot a\right)\\ \mathbf{elif}\;i \leq 20.5:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+103}:\\ \;\;\;\;\left(c \cdot b - j \cdot \left(27 \cdot k\right)\right) - 4 \cdot \left(i \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	24.0
Cost	1496

\[\begin{array}{l} t_1 := 4 \cdot \left(i \cdot x\right)\\ t_2 := \left(t \cdot \left(a \cdot -4\right) + b \cdot c\right) - 27 \cdot \left(k \cdot j\right)\\ t_3 := c \cdot b - t_1\\ \mathbf{if}\;i \leq -7.5 \cdot 10^{-45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(y \cdot x\right)\right) - 4 \cdot a\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 5 \cdot 10^{+78}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+103}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-4 \cdot t\right) - t_1\\ \end{array} \]

Alternative 14
Error	18.9
Cost	1488

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right) + b \cdot c\\ t_2 := t_1 - x \cdot \left(4 \cdot i\right)\\ t_3 := t_1 - 27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;i \leq -2.85 \cdot 10^{-58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3 \cdot 10^{-63}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-34}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(z \cdot \left(y \cdot x\right)\right) - 4 \cdot a\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{+25}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	18.5
Cost	1488

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right) + b \cdot c\\ t_2 := t_1 - x \cdot \left(4 \cdot i\right)\\ \mathbf{if}\;i \leq -1.36 \cdot 10^{-58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.18 \cdot 10^{-63}:\\ \;\;\;\;t_1 - 27 \cdot \left(k \cdot j\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-9}:\\ \;\;\;\;c \cdot b + t \cdot \left(18 \cdot \left(z \cdot \left(y \cdot x\right)\right) - 4 \cdot a\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+103}:\\ \;\;\;\;\left(c \cdot b - j \cdot \left(27 \cdot k\right)\right) - 4 \cdot \left(i \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	45.9
Cost	1244

\[\begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ t_3 := \left(i \cdot x\right) \cdot -4\\ \mathbf{if}\;i \leq -5.8 \cdot 10^{-89}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq 6 \cdot 10^{-297}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;i \leq 2.7 \cdot 10^{-228}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.55 \cdot 10^{-114}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 1.45 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 17
Error	45.9
Cost	1244

\[\begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ t_2 := \left(i \cdot x\right) \cdot -4\\ \mathbf{if}\;i \leq -3 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 6.5 \cdot 10^{-296}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-226}:\\ \;\;\;\;\left(k \cdot j\right) \cdot -27\\ \mathbf{elif}\;i \leq 3.8 \cdot 10^{-114}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;i \leq 1.2 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{+103}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;i \leq 7.5 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Error	45.2
Cost	1112

\[\begin{array}{l} t_1 := j \cdot \left(k \cdot -27\right)\\ t_2 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{-86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-146}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-269}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t \leq 4.25 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-92}:\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Error	45.3
Cost	1112

\[\begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-141}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-212}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-269}:\\ \;\;\;\;c \cdot b\\ \mathbf{elif}\;t \leq 4.25 \cdot 10^{-287}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-92}:\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 20
Error	37.0
Cost	972

\[\begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-61}:\\ \;\;\;\;c \cdot b - 4 \cdot \left(i \cdot x\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(\left(z \cdot x\right) \cdot 18\right)\right)\\ \end{array} \]

Alternative 21
Error	45.1
Cost	584

\[\begin{array}{l} t_1 := -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;t \leq -2.65 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{-92}:\\ \;\;\;\;c \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 22
Error	48.0
Cost	192

\[c \cdot b \]

Reproduce

herbie shell --seed 2023077 
(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)))