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

Average Accuracy: 91.1% → 92.2%

Time: 46.1s

Precision: binary64

Cost: 3652

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

Math

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

↓

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{if}\;t_1 \leq 10^{+288}:\\ \;\;\;\;t_1 - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

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
         (-
          (+ (- (* (* (* (* x 18.0) y) z) t) (* t (* a 4.0))) (* b c))
          (* (* x 4.0) i))))
   (if (<= t_1 1e+288)
     (- t_1 (* (* j 27.0) k))
     (+ (* x (+ (* 18.0 (* y (* z t))) (* i -4.0))) (* k (* j -27.0))))))

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 = ((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= 1e+288) {
		tmp = t_1 - ((j * 27.0) * k);
	} else {
		tmp = (x * ((18.0 * (y * (z * t))) + (i * -4.0))) + (k * (j * -27.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    code = (((((((x * 18.0d0) * y) * z) * t) - ((a * 4.0d0) * t)) + (b * c)) - ((x * 4.0d0) * i)) - ((j * 27.0d0) * k)
end function

↓

real(8) function code(x, y, z, t, a, b, c, i, j, k)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8), intent (in) :: k
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((((((x * 18.0d0) * y) * z) * t) - (t * (a * 4.0d0))) + (b * c)) - ((x * 4.0d0) * i)
    if (t_1 <= 1d+288) then
        tmp = t_1 - ((j * 27.0d0) * k)
    else
        tmp = (x * ((18.0d0 * (y * (z * t))) + (i * (-4.0d0)))) + (k * (j * (-27.0d0)))
    end if
    code = tmp
end function

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) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i);
	double tmp;
	if (t_1 <= 1e+288) {
		tmp = t_1 - ((j * 27.0) * k);
	} else {
		tmp = (x * ((18.0 * (y * (z * t))) + (i * -4.0))) + (k * (j * -27.0));
	}
	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 = ((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i)
	tmp = 0
	if t_1 <= 1e+288:
		tmp = t_1 - ((j * 27.0) * k)
	else:
		tmp = (x * ((18.0 * (y * (z * t))) + (i * -4.0))) + (k * (j * -27.0))
	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(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(t * Float64(a * 4.0))) + Float64(b * c)) - Float64(Float64(x * 4.0) * i))
	tmp = 0.0
	if (t_1 <= 1e+288)
		tmp = Float64(t_1 - Float64(Float64(j * 27.0) * k));
	else
		tmp = Float64(Float64(x * Float64(Float64(18.0 * Float64(y * Float64(z * t))) + Float64(i * -4.0))) + Float64(k * Float64(j * -27.0)));
	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 = ((((((x * 18.0) * y) * z) * t) - (t * (a * 4.0))) + (b * c)) - ((x * 4.0) * i);
	tmp = 0.0;
	if (t_1 <= 1e+288)
		tmp = t_1 - ((j * 27.0) * k);
	else
		tmp = (x * ((18.0 * (y * (z * t))) + (i * -4.0))) + (k * (j * -27.0));
	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[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(t * N[(a * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+288], N[(t$95$1 - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(18.0 * N[(y * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(k * N[(j * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	91.1%
Target	97.3%
Herbie	92.2%

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

Derivation

1. Split input into 2 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)) < 1e288

   1. Initial program 95.1%

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

   if 1e288 < (-.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 39.7%

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

   2. Simplified 56.9%

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

      [Start] 39.7	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]
      sub-neg [=>] 39.7	\[ \color{blue}{\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\left(j \cdot 27\right) \cdot k\right)} \]
      *-commutative [=>] 39.7	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \left(-\color{blue}{k \cdot \left(j \cdot 27\right)}\right) \]
      distribute-rgt-neg-in [=>] 39.7	\[ \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) + \color{blue}{k \cdot \left(-j \cdot 27\right)} \]

   3. Taylor expanded in x around inf 55.6%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i \leq 10^{+288}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - t \cdot \left(a \cdot 4\right)\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	46.4%
Cost	2684

\[\begin{array}{l} t_1 := k \cdot \left(j \cdot -27\right)\\ t_2 := t_1 + 18 \cdot \left(t \cdot \left(y \cdot \left(x \cdot z\right)\right)\right)\\ t_3 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_4 := -4 \cdot \left(x \cdot i + t \cdot a\right)\\ t_5 := t_1 + i \cdot \left(x \cdot -4\right)\\ t_6 := -4 \cdot \left(t \cdot a\right)\\ t_7 := b \cdot c + t_6\\ \mathbf{if}\;a \leq -2.35 \cdot 10^{+40}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -0.013:\\ \;\;\;\;b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-26}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-126}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-172}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -6.3 \cdot 10^{-246}:\\ \;\;\;\;t_1 + b \cdot c\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-220}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-140}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-49}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-20}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+22}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{+39}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+118}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_6\\ \end{array} \]

Alternative 2
Accuracy	64.7%
Cost	2280

\[\begin{array}{l} t_1 := -27 \cdot \left(j \cdot k\right)\\ t_2 := b \cdot c + \left(-4 \cdot \left(x \cdot i\right) + t_1\right)\\ t_3 := b \cdot c + \left(t_1 + -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{-83}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + 18 \cdot \left(y \cdot \left(x \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-264}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-94}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-93}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{+210}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+227}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	59.5%
Cost	2148

\[\begin{array}{l} t_1 := x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ t_2 := b \cdot c + \left(-27 \cdot \left(j \cdot k\right) + -4 \cdot \left(t \cdot a\right)\right)\\ t_3 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;k \leq -2 \cdot 10^{-200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -3.05 \cdot 10^{-226}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 2.25 \cdot 10^{-258}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 4.8 \cdot 10^{-207}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 5.4 \cdot 10^{-78}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;k \leq 1.3 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 5.2 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{+49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.75 \cdot 10^{+99}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \end{array} \]

Alternative 4
Accuracy	89.3%
Cost	1988

\[\begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+274}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t \cdot \left(\left(x \cdot 18\right) \cdot \left(y \cdot z\right) - a \cdot 4\right) + b \cdot c\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ \end{array} \]

Alternative 5
Accuracy	46.6%
Cost	1899

\[\begin{array}{l} t_1 := b \cdot c + -27 \cdot \left(j \cdot k\right)\\ t_2 := -4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{if}\;a \leq -6.8 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -0.0085:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.15 \cdot 10^{-114}:\\ \;\;\;\;18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-172} \lor \neg \left(a \leq -4.2 \cdot 10^{-271}\right) \land \left(a \leq 1.7 \cdot 10^{-294} \lor \neg \left(a \leq 2.45 \cdot 10^{+22}\right) \land \left(a \leq 2.55 \cdot 10^{+39} \lor \neg \left(a \leq 6.8 \cdot 10^{+114}\right)\right)\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	82.2%
Cost	1872

\[\begin{array}{l} t_1 := \left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) - \left(x \cdot \left(4 \cdot i\right) + j \cdot \left(27 \cdot k\right)\right)\\ t_2 := 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{+275}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.1 \cdot 10^{+229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{+225}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{+168}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	50.6%
Cost	1760

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := b \cdot c + t_1\\ t_3 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_4 := k \cdot \left(j \cdot -27\right)\\ t_5 := -4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{if}\;k \leq -5 \cdot 10^{-5}:\\ \;\;\;\;b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq -2.85 \cdot 10^{-229}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 2.1 \cdot 10^{-297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{-210}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 1.08 \cdot 10^{-72}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 6.8 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{+111}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;k \leq 2.8 \cdot 10^{+153}:\\ \;\;\;\;t_4 + b \cdot c\\ \mathbf{else}:\\ \;\;\;\;t_4 + t_1\\ \end{array} \]

Alternative 8
Accuracy	48.4%
Cost	1760

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := k \cdot \left(j \cdot -27\right)\\ t_3 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;k \leq -0.000112:\\ \;\;\;\;t_2 + 18 \cdot \left(y \cdot \left(x \cdot \left(z \cdot t\right)\right)\right)\\ \mathbf{elif}\;k \leq -7.8 \cdot 10^{-226}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.5 \cdot 10^{-209}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq 1.28 \cdot 10^{-76}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;k \leq 3.2 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.9 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;k \leq 1.4 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 + i \cdot \left(x \cdot -4\right)\\ \end{array} \]

Alternative 9
Accuracy	50.9%
Cost	1500

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := b \cdot c - 4 \cdot \left(x \cdot i\right)\\ t_3 := b \cdot c + -27 \cdot \left(j \cdot k\right)\\ t_4 := -4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{if}\;k \leq -5 \cdot 10^{-7}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq -5.1 \cdot 10^{-227}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.8 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 4.6 \cdot 10^{-73}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;k \leq 6.5 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 9 \cdot 10^{+110}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Accuracy	50.0%
Cost	1496

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;k \leq -1.08 \cdot 10^{-7}:\\ \;\;\;\;b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq -2.45 \cdot 10^{-235}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 6.1 \cdot 10^{-77}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;k \leq 2.2 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 3.15 \cdot 10^{+50}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right)\\ \mathbf{elif}\;k \leq 9.2 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \end{array} \]

Alternative 11
Accuracy	69.0%
Cost	1480

\[\begin{array}{l} \mathbf{if}\;k \leq -9.5 \cdot 10^{-5}:\\ \;\;\;\;b \cdot c + \left(-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{+98}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) - \left(x \cdot 4\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(18 \cdot \left(y \cdot \left(z \cdot t\right)\right) + i \cdot -4\right) + k \cdot \left(j \cdot -27\right)\\ \end{array} \]

Alternative 12
Accuracy	49.8%
Cost	1236

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i + t \cdot a\right)\\ t_2 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_3 := b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -0.000112:\\ \;\;\;\;t_3\\ \mathbf{elif}\;k \leq -1.6 \cdot 10^{-259}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 3 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 2.4 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq 1.02 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 13
Accuracy	50.2%
Cost	1232

\[\begin{array}{l} \mathbf{if}\;k \leq -3.95 \cdot 10^{-10}:\\ \;\;\;\;b \cdot c + -27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq -2.95 \cdot 10^{-235}:\\ \;\;\;\;b \cdot c - 4 \cdot \left(x \cdot i\right)\\ \mathbf{elif}\;k \leq 4.3 \cdot 10^{-76}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{elif}\;k \leq 5.5 \cdot 10^{+96}:\\ \;\;\;\;b \cdot c + -4 \cdot \left(t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;k \cdot \left(j \cdot -27\right) + i \cdot \left(x \cdot -4\right)\\ \end{array} \]

Alternative 14
Accuracy	70.7%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;k \leq -9 \cdot 10^{-6} \lor \neg \left(k \leq 7.2 \cdot 10^{+96}\right):\\ \;\;\;\;b \cdot c + \left(-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(j \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot c + t \cdot \left(a \cdot -4\right)\right) - \left(x \cdot 4\right) \cdot i\\ \end{array} \]

Alternative 15
Accuracy	30.8%
Cost	980

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -1.32 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -2.8 \cdot 10^{-235}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 1.35 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 1.9 \cdot 10^{-163}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 2.7 \cdot 10^{+97}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Accuracy	30.0%
Cost	980

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := -27 \cdot \left(j \cdot k\right)\\ \mathbf{if}\;k \leq -9 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;k \leq -2 \cdot 10^{-235}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 2.2 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 4.5 \cdot 10^{-210}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;k \leq 1.3 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Accuracy	29.9%
Cost	980

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;k \leq -1.05 \cdot 10^{-6}:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq -3.3 \cdot 10^{-235}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;k \leq 6.5 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;k \leq 5.2 \cdot 10^{-208}:\\ \;\;\;\;x \cdot \left(i \cdot -4\right)\\ \mathbf{elif}\;k \leq 1.15 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 18
Accuracy	43.0%
Cost	840

\[\begin{array}{l} \mathbf{if}\;k \leq -0.000118:\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{elif}\;k \leq 1.2 \cdot 10^{+116}:\\ \;\;\;\;-4 \cdot \left(x \cdot i + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \end{array} \]

Alternative 19
Accuracy	31.9%
Cost	585

\[\begin{array}{l} \mathbf{if}\;k \leq -1 \cdot 10^{-6} \lor \neg \left(k \leq 3.5 \cdot 10^{+84}\right):\\ \;\;\;\;-27 \cdot \left(j \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 20
Accuracy	24.5%
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2023146 
(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)))