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

Average Error: 8.27% → 3.1%

Time: 35.7s

Precision: binary64

Cost: 5320

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

Math

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

↓

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := i \cdot \left(x \cdot -4\right)\\ t_3 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t_1\right) + b \cdot c\right) + t_2\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\left(x \cdot \left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;t_3 \leq 4 \cdot 10^{+307}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right) + t_1\right) + b \cdot c\right) + t_2\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \]

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 (* t (* a -4.0)))
        (t_2 (* i (* x -4.0)))
        (t_3 (+ (+ (+ (* (* (* (* x 18.0) y) z) t) t_1) (* b c)) t_2)))
   (if (<= t_3 (- INFINITY))
     (+ (+ (* x (* t (* 18.0 (* y z)))) (* b c)) (* x (* i -4.0)))
     (if (<= t_3 4e+307)
       (+
        (+ (+ (+ (* t (* z (* x (* 18.0 y)))) t_1) (* b c)) t_2)
        (* k (* j -27.0)))
       (+ (* b c) (* x (+ (* 18.0 (* y (* z t))) (* i -4.0))))))))

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 = t * (a * -4.0);
	double t_2 = i * (x * -4.0);
	double t_3 = ((((((x * 18.0) * y) * z) * t) + t_1) + (b * c)) + t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = ((x * (t * (18.0 * (y * z)))) + (b * c)) + (x * (i * -4.0));
	} else if (t_3 <= 4e+307) {
		tmp = ((((t * (z * (x * (18.0 * y)))) + t_1) + (b * c)) + t_2) + (k * (j * -27.0));
	} else {
		tmp = (b * c) + (x * ((18.0 * (y * (z * t))) + (i * -4.0)));
	}
	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 = t * (a * -4.0);
	double t_2 = i * (x * -4.0);
	double t_3 = ((((((x * 18.0) * y) * z) * t) + t_1) + (b * c)) + t_2;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = ((x * (t * (18.0 * (y * z)))) + (b * c)) + (x * (i * -4.0));
	} else if (t_3 <= 4e+307) {
		tmp = ((((t * (z * (x * (18.0 * y)))) + t_1) + (b * c)) + t_2) + (k * (j * -27.0));
	} else {
		tmp = (b * c) + (x * ((18.0 * (y * (z * t))) + (i * -4.0)));
	}
	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 = t * (a * -4.0)
	t_2 = i * (x * -4.0)
	t_3 = ((((((x * 18.0) * y) * z) * t) + t_1) + (b * c)) + t_2
	tmp = 0
	if t_3 <= -math.inf:
		tmp = ((x * (t * (18.0 * (y * z)))) + (b * c)) + (x * (i * -4.0))
	elif t_3 <= 4e+307:
		tmp = ((((t * (z * (x * (18.0 * y)))) + t_1) + (b * c)) + t_2) + (k * (j * -27.0))
	else:
		tmp = (b * c) + (x * ((18.0 * (y * (z * t))) + (i * -4.0)))
	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(t * Float64(a * -4.0))
	t_2 = Float64(i * Float64(x * -4.0))
	t_3 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) + t_1) + Float64(b * c)) + t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(x * Float64(t * Float64(18.0 * Float64(y * z)))) + Float64(b * c)) + Float64(x * Float64(i * -4.0)));
	elseif (t_3 <= 4e+307)
		tmp = Float64(Float64(Float64(Float64(Float64(t * Float64(z * Float64(x * Float64(18.0 * y)))) + t_1) + Float64(b * c)) + t_2) + Float64(k * Float64(j * -27.0)));
	else
		tmp = Float64(Float64(b * c) + Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) + Float64(i * -4.0))));
	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 = t * (a * -4.0);
	t_2 = i * (x * -4.0);
	t_3 = ((((((x * 18.0) * y) * z) * t) + t_1) + (b * c)) + t_2;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = ((x * (t * (18.0 * (y * z)))) + (b * c)) + (x * (i * -4.0));
	elseif (t_3 <= 4e+307)
		tmp = ((((t * (z * (x * (18.0 * y)))) + t_1) + (b * c)) + t_2) + (k * (j * -27.0));
	else
		tmp = (b * c) + (x * ((18.0 * (y * (z * t))) + (i * -4.0)));
	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[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(N[(x * N[(t * N[(18.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] + N[(x * N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 4e+307], N[(N[(N[(N[(N[(t * N[(z * N[(x * N[(18.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	8.27%
Target	2.33%
Herbie	3.1%

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

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 100

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

   2. Simplified 64.8

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

      [Start] 100	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate--l- [=>] 100	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]
      associate-+l- [=>] 100	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-+l- [<=] 100	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      distribute-rgt-out-- [=>] 100	\[ \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 64.83	\[ \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 64.83	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 64.8	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Taylor expanded in x around inf 68.44

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

   4. Simplified 68.44

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

      [Start] 68.44	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right) \]
      associate-*r* [=>] 68.44	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(4 \cdot i\right) \cdot x} \]
      *-commutative [<=] 68.44	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   5. Taylor expanded in x around inf 27.89

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

   6. Simplified 40.8

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

      [Start] 27.89	\[ \left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]
      associate-*r* [=>] 28.83	\[ \left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]
      associate-*r* [=>] 19.47	\[ \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)} + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]
      associate-*r* [=>] 20.78	\[ \left(\color{blue}{\left(\left(18 \cdot y\right) \cdot \left(t \cdot z\right)\right) \cdot x} + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]
      *-commutative [=>] 20.78	\[ \left(\left(\left(18 \cdot y\right) \cdot \color{blue}{\left(z \cdot t\right)}\right) \cdot x + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]
      associate-*l* [<=] 41.14	\[ \left(\color{blue}{\left(\left(\left(18 \cdot y\right) \cdot z\right) \cdot t\right)} \cdot x + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]
      associate-*r* [<=] 40.8	\[ \left(\left(\color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)} \cdot t\right) \cdot x + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]
      *-commutative [<=] 40.8	\[ \left(\color{blue}{x \cdot \left(\left(18 \cdot \left(y \cdot z\right)\right) \cdot t\right)} + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]
      *-commutative [=>] 40.8	\[ \left(x \cdot \color{blue}{\left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)} + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]

   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)) < 3.99999999999999994e307

   1. Initial program 0.54

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

   2. Taylor expanded in x around 0 0.54

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

   3. Simplified 0.66

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

      [Start] 0.54	\[ \left(\left(\left(\left(\left(18 \cdot \left(y \cdot x\right)\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate-*r* [=>] 0.66	\[ \left(\left(\left(\left(\color{blue}{\left(\left(18 \cdot y\right) \cdot x\right)} \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      *-commutative [<=] 0.66	\[ \left(\left(\left(\left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   if 3.99999999999999994e307 < (-.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 98.43

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

   2. Simplified 59.23

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

      [Start] 98.43	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      associate--l- [=>] 98.43	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)} \]
      associate-+l- [=>] 98.43	\[ \color{blue}{\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(\left(a \cdot 4\right) \cdot t - b \cdot c\right)\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-+l- [<=] 98.43	\[ \color{blue}{\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right)} - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      distribute-rgt-out-- [=>] 98.43	\[ \left(\color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right)} + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 59.23	\[ \left(t \cdot \left(\color{blue}{\left(x \cdot 18\right) \cdot \left(y \cdot z\right)} - a \cdot 4\right) + b \cdot c\right) - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 59.23	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(\color{blue}{x \cdot \left(4 \cdot i\right)} + \left(j \cdot 27\right) \cdot k\right) \]
      associate-*l* [=>] 59.23	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + \color{blue}{j \cdot \left(27 \cdot k\right)}\right) \]

   3. Taylor expanded in x around inf 63.95

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

   4. Simplified 63.95

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

      [Start] 63.95	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - 4 \cdot \left(i \cdot x\right) \]
      associate-*r* [=>] 63.95	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{\left(4 \cdot i\right) \cdot x} \]
      *-commutative [<=] 63.95	\[ \left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \color{blue}{x \cdot \left(4 \cdot i\right)} \]

   5. Taylor expanded in x around inf 33.85

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

   6. Simplified 37.35

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

      [Start] 33.85	\[ \left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]
      associate-*r* [=>] 34.46	\[ \left(\color{blue}{\left(18 \cdot y\right) \cdot \left(t \cdot \left(z \cdot x\right)\right)} + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]
      associate-*r* [=>] 21.77	\[ \left(\left(18 \cdot y\right) \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot x\right)} + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]
      associate-*r* [=>] 23.62	\[ \left(\color{blue}{\left(\left(18 \cdot y\right) \cdot \left(t \cdot z\right)\right) \cdot x} + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]
      *-commutative [=>] 23.62	\[ \left(\left(\left(18 \cdot y\right) \cdot \color{blue}{\left(z \cdot t\right)}\right) \cdot x + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]
      associate-*l* [<=] 37.61	\[ \left(\color{blue}{\left(\left(\left(18 \cdot y\right) \cdot z\right) \cdot t\right)} \cdot x + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]
      associate-*r* [<=] 37.35	\[ \left(\left(\color{blue}{\left(18 \cdot \left(y \cdot z\right)\right)} \cdot t\right) \cdot x + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]
      *-commutative [<=] 37.35	\[ \left(\color{blue}{x \cdot \left(\left(18 \cdot \left(y \cdot z\right)\right) \cdot t\right)} + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]
      *-commutative [=>] 37.35	\[ \left(x \cdot \color{blue}{\left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right)} + b \cdot c\right) - x \cdot \left(4 \cdot i\right) \]

   7. Taylor expanded in x around 0 23.04

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

4. Final simplification 3.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq -\infty:\\ \;\;\;\;\left(x \cdot \left(t \cdot \left(18 \cdot \left(y \cdot z\right)\right)\right) + b \cdot c\right) + x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq 4 \cdot 10^{+307}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(z \cdot \left(x \cdot \left(18 \cdot y\right)\right)\right) + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(j \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	49.88%
Cost	2289

\[\begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := b \cdot c - t_2\\ t_4 := x \cdot \left(i \cdot -4\right)\\ t_5 := b \cdot c + t_4\\ t_6 := t_4 - t_2\\ \mathbf{if}\;k \leq -1.42 \cdot 10^{-68}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;k \leq 1.68 \cdot 10^{-245}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 6.5 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.32 \cdot 10^{-134}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 5.1 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{-81}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 1.55 \cdot 10^{-20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 5.8 \cdot 10^{-6}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.5 \cdot 10^{+51} \lor \neg \left(k \leq 1.8 \cdot 10^{+130}\right) \land k \leq 7 \cdot 10^{+217}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 2
Error	49.84%
Cost	2289

\[\begin{array}{l} t_1 := t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ t_2 := \left(j \cdot 27\right) \cdot k\\ t_3 := x \cdot \left(i \cdot -4\right)\\ t_4 := b \cdot c + t_3\\ t_5 := t_3 - t_2\\ t_6 := b \cdot c - t_2\\ \mathbf{if}\;k \leq -3.4 \cdot 10^{-60}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 3.9 \cdot 10^{-251}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 1.9 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 4.4 \cdot 10^{-140}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 3.9 \cdot 10^{-120}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;k \leq 3.4 \cdot 10^{-81}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 2.35 \cdot 10^{-20}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{-7}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.05 \cdot 10^{+51} \lor \neg \left(k \leq 2.35 \cdot 10^{+131}\right) \land k \leq 6.8 \cdot 10^{+217}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 3
Error	49.84%
Cost	2289

\[\begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := x \cdot \left(i \cdot -4\right)\\ t_3 := b \cdot c + t_2\\ t_4 := t_2 - t_1\\ t_5 := b \cdot c - t_1\\ \mathbf{if}\;k \leq -5.3 \cdot 10^{-67}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 7.6 \cdot 10^{-246}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 2.6 \cdot 10^{-171}:\\ \;\;\;\;t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right)\right) + t \cdot \left(a \cdot -4\right)\\ \mathbf{elif}\;k \leq 1.42 \cdot 10^{-130}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 5.5 \cdot 10^{-120}:\\ \;\;\;\;t \cdot \left(a \cdot -4 + 18 \cdot \left(z \cdot \left(x \cdot y\right)\right)\right)\\ \mathbf{elif}\;k \leq 9.5 \cdot 10^{-81}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 1.14 \cdot 10^{-20}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 0.00035:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 6.8 \cdot 10^{+21}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;k \leq 5.2 \cdot 10^{+51} \lor \neg \left(k \leq 1.05 \cdot 10^{+131}\right) \land k \leq 2.7 \cdot 10^{+218}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 4
Error	51.72%
Cost	2156

\[\begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := b \cdot c - t_1\\ t_3 := k \cdot \left(j \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ t_4 := b \cdot c + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ t_5 := x \cdot \left(i \cdot -4\right)\\ t_6 := t_5 - t_1\\ t_7 := b \cdot c + t_5\\ \mathbf{if}\;a \leq -2.9 \cdot 10^{+22}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -9.8 \cdot 10^{-71}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-163}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{-265}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-305}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{-282}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-75}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{elif}\;a \leq 205000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.85 \cdot 10^{+152}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_7\\ \end{array} \]

Alternative 5
Error	7.05%
Cost	2121

\[\begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{-114} \lor \neg \left(t \leq 2.25 \cdot 10^{-179}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) + a \cdot -4\right)\right) + \left(x \cdot \left(i \cdot -4\right) + j \cdot \left(k \cdot -27\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]

Alternative 6
Error	14.17%
Cost	1737

\[\begin{array}{l} \mathbf{if}\;k \leq -2.1 \cdot 10^{-205} \lor \neg \left(k \leq 4 \cdot 10^{-82}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \end{array} \]

Alternative 7
Error	47.78%
Cost	1628

\[\begin{array}{l} t_1 := b \cdot c + x \cdot \left(i \cdot -4\right)\\ t_2 := k \cdot \left(j \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ t_3 := b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -0.5:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-271}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-303}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-110}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 0.00063:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	15.36%
Cost	1609

\[\begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+278} \lor \neg \left(y \leq -4.1 \cdot 10^{+251}\right):\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(18 \cdot y\right) \cdot \left(t \cdot \left(x \cdot z\right)\right) + x \cdot \left(i \cdot -4\right)\\ \end{array} \]

Alternative 9
Error	46.76%
Cost	1496

\[\begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := b \cdot c - t_1\\ t_3 := k \cdot \left(j \cdot -27\right) + t \cdot \left(a \cdot -4\right)\\ t_4 := x \cdot \left(i \cdot -4\right)\\ t_5 := t_4 - t_1\\ \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-95}:\\ \;\;\;\;b \cdot c + t_4\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-271}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-303}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 0.000196:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 10
Error	31.43%
Cost	1360

\[\begin{array}{l} t_1 := \left(j \cdot 27\right) \cdot k\\ t_2 := x \cdot \left(i \cdot -4\right) - t_1\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 0.00033:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+119}:\\ \;\;\;\;b \cdot c - t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \end{array} \]

Alternative 11
Error	68.33%
Cost	1244

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;j \leq -2.15 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -5.4 \cdot 10^{-166}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -1.38 \cdot 10^{-201}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -4.5 \cdot 10^{-272}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -1.25 \cdot 10^{-288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4 \cdot 10^{-167}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	68.38%
Cost	1244

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{-13}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right)\\ \mathbf{elif}\;j \leq -2.7 \cdot 10^{-165}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -6.8 \cdot 10^{-205}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -3.9 \cdot 10^{-272}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-165}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \end{array} \]

Alternative 13
Error	25.45%
Cost	1225

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{-91} \lor \neg \left(x \leq 0.00091\right):\\ \;\;\;\;\left(b \cdot c + -4 \cdot \left(x \cdot i\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(b \cdot c + -4 \cdot \left(t \cdot a\right)\right)\\ \end{array} \]

Alternative 14
Error	54.12%
Cost	1106

\[\begin{array}{l} \mathbf{if}\;j \leq -1.6 \cdot 10^{-165} \lor \neg \left(j \leq -3.8 \cdot 10^{-209} \lor \neg \left(j \leq -2.9 \cdot 10^{-273}\right) \land j \leq 9.5 \cdot 10^{-139}\right):\\ \;\;\;\;b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(x \cdot i\right)\\ \end{array} \]

Alternative 15
Error	50.97%
Cost	1104

\[\begin{array}{l} t_1 := b \cdot c + x \cdot \left(i \cdot -4\right)\\ t_2 := b \cdot c - \left(j \cdot 27\right) \cdot k\\ \mathbf{if}\;j \leq -0.006:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -9 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-165}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	68.47%
Cost	716

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-285}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{-146}:\\ \;\;\;\;-4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	66.32%
Cost	585

\[\begin{array}{l} \mathbf{if}\;k \leq -7 \cdot 10^{-53} \lor \neg \left(k \leq 3.6 \cdot 10^{-64}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 18
Error	74.99%
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2023090 
(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)))