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

Average Error: 3.2 → 1.5

Time: 22.1s

Precision: binary64

Cost: 3400

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

Math

\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

↓

\[\begin{array}{l} t_1 := \left(a \cdot 27\right) \cdot b\\ t_2 := \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + t_1\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{+304}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+142}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + t_1\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))

↓

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* a 27.0) b))
        (t_2 (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) t_1)))
   (if (<= t_2 -4e+304)
     (+ (- (* x 2.0) (* y (* 9.0 (* z t)))) (* a (* 27.0 b)))
     (if (<= t_2 5e+142) t_2 (+ (- (* x 2.0) (* y (* (* 9.0 z) t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

↓

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = ((x * 2.0) - (((y * 9.0) * z) * t)) + t_1;
	double tmp;
	if (t_2 <= -4e+304) {
		tmp = ((x * 2.0) - (y * (9.0 * (z * t)))) + (a * (27.0 * b));
	} else if (t_2 <= 5e+142) {
		tmp = t_2;
	} else {
		tmp = ((x * 2.0) - (y * ((9.0 * z) * t))) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    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
    code = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + ((a * 27.0d0) * b)
end function

↓

real(8) function code(x, y, z, t, a, b)
    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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (a * 27.0d0) * b
    t_2 = ((x * 2.0d0) - (((y * 9.0d0) * z) * t)) + t_1
    if (t_2 <= (-4d+304)) then
        tmp = ((x * 2.0d0) - (y * (9.0d0 * (z * t)))) + (a * (27.0d0 * b))
    else if (t_2 <= 5d+142) then
        tmp = t_2
    else
        tmp = ((x * 2.0d0) - (y * ((9.0d0 * z) * t))) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
}

↓

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (a * 27.0) * b;
	double t_2 = ((x * 2.0) - (((y * 9.0) * z) * t)) + t_1;
	double tmp;
	if (t_2 <= -4e+304) {
		tmp = ((x * 2.0) - (y * (9.0 * (z * t)))) + (a * (27.0 * b));
	} else if (t_2 <= 5e+142) {
		tmp = t_2;
	} else {
		tmp = ((x * 2.0) - (y * ((9.0 * z) * t))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	return ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b)

↓

def code(x, y, z, t, a, b):
	t_1 = (a * 27.0) * b
	t_2 = ((x * 2.0) - (((y * 9.0) * z) * t)) + t_1
	tmp = 0
	if t_2 <= -4e+304:
		tmp = ((x * 2.0) - (y * (9.0 * (z * t)))) + (a * (27.0 * b))
	elif t_2 <= 5e+142:
		tmp = t_2
	else:
		tmp = ((x * 2.0) - (y * ((9.0 * z) * t))) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + Float64(Float64(a * 27.0) * b))
end

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(a * 27.0) * b)
	t_2 = Float64(Float64(Float64(x * 2.0) - Float64(Float64(Float64(y * 9.0) * z) * t)) + t_1)
	tmp = 0.0
	if (t_2 <= -4e+304)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(y * Float64(9.0 * Float64(z * t)))) + Float64(a * Float64(27.0 * b)));
	elseif (t_2 <= 5e+142)
		tmp = t_2;
	else
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(y * Float64(Float64(9.0 * z) * t))) + t_1);
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x * 2.0) - (((y * 9.0) * z) * t)) + ((a * 27.0) * b);
end

↓

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (a * 27.0) * b;
	t_2 = ((x * 2.0) - (((y * 9.0) * z) * t)) + t_1;
	tmp = 0.0;
	if (t_2 <= -4e+304)
		tmp = ((x * 2.0) - (y * (9.0 * (z * t)))) + (a * (27.0 * b));
	elseif (t_2 <= 5e+142)
		tmp = t_2;
	else
		tmp = ((x * 2.0) - (y * ((9.0 * z) * t))) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * 2.0), $MachinePrecision] - N[(N[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, -4e+304], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(9.0 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(27.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+142], t$95$2, N[(N[(N[(x * 2.0), $MachinePrecision] - N[(y * N[(N[(9.0 * z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]

Target

Original	3.2
Target	3.6
Herbie	1.5

\[\begin{array}{l} \mathbf{if}\;y < 7.590524218811189 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b)) < -3.9999999999999998e304

   1. Initial program 52.3

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Simplified 0.6

      \[\leadsto \color{blue}{\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + a \cdot \left(27 \cdot b\right)} \]
      Proof

      [Start] 52.3	\[ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
      rational.json-simplify-2 [=>] 52.3	\[ \left(x \cdot 2 - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b \]
      rational.json-simplify-43 [=>] 1.4	\[ \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]
      rational.json-simplify-2 [=>] 1.4	\[ \left(x \cdot 2 - \color{blue}{\left(z \cdot t\right) \cdot \left(y \cdot 9\right)}\right) + \left(a \cdot 27\right) \cdot b \]
      rational.json-simplify-43 [=>] 1.2	\[ \left(x \cdot 2 - \color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]
      rational.json-simplify-2 [=>] 1.2	\[ \left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + \color{blue}{b \cdot \left(a \cdot 27\right)} \]
      rational.json-simplify-43 [=>] 0.6	\[ \left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + \color{blue}{a \cdot \left(27 \cdot b\right)} \]

   if -3.9999999999999998e304 < (+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b)) < 5.0000000000000001e142

   1. Initial program 0.6

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   if 5.0000000000000001e142 < (+.f64 (-.f64 (*.f64 x 2) (*.f64 (*.f64 (*.f64 y 9) z) t)) (*.f64 (*.f64 a 27) b))

   1. Initial program 4.7

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]

   2. Simplified 3.9

      \[\leadsto \color{blue}{\left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b} \]
      Proof

      [Start] 4.7	\[ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
      rational.json-simplify-2 [=>] 4.7	\[ \left(x \cdot 2 - \color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b \]
      rational.json-simplify-2 [=>] 4.7	\[ \left(x \cdot 2 - t \cdot \color{blue}{\left(z \cdot \left(y \cdot 9\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]
      rational.json-simplify-43 [=>] 4.7	\[ \left(x \cdot 2 - t \cdot \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]
      rational.json-simplify-43 [=>] 3.9	\[ \left(x \cdot 2 - \color{blue}{y \cdot \left(\left(9 \cdot z\right) \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b \]

3. Recombined 3 regimes into one program.

4. Final simplification 1.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \leq -4 \cdot 10^{+304}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \leq 5 \cdot 10^{+142}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \]

Alternatives

Alternative 1
Error	22.3
Cost	1368

\[\begin{array}{l} t_1 := \left(x + \left(a \cdot 13.5\right) \cdot b\right) \cdot 2\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.38 \cdot 10^{-102}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-201}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-67}:\\ \;\;\;\;\left(z \cdot \left(t \cdot -9\right)\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Error	22.4
Cost	1368

\[\begin{array}{l} t_1 := 2 \cdot x + a \cdot \left(27 \cdot b\right)\\ t_2 := \left(x + \left(a \cdot 13.5\right) \cdot b\right) \cdot 2\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-102}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-272}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-200}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \mathbf{elif}\;x \leq 7.7 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{-71}:\\ \;\;\;\;\left(z \cdot \left(t \cdot -9\right)\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	22.4
Cost	1368

\[\begin{array}{l} t_1 := 2 \cdot x + a \cdot \left(27 \cdot b\right)\\ t_2 := \left(x + \left(a \cdot 13.5\right) \cdot b\right) \cdot 2\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-102}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(z \cdot -9\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-271}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-196}:\\ \;\;\;\;\frac{\left(y \cdot z\right) \cdot \left(t \cdot -18\right)}{2}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-70}:\\ \;\;\;\;\left(z \cdot \left(t \cdot -9\right)\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	30.5
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ t_2 := a \cdot \left(27 \cdot b\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{+63}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-220}:\\ \;\;\;\;y \cdot \left(\left(t \cdot z\right) \cdot -9\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-269}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-177}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]

Alternative 5
Error	30.4
Cost	1240

\[\begin{array}{l} t_1 := a \cdot \left(27 \cdot b\right)\\ t_2 := \left(t \cdot z\right) \cdot \left(y \cdot -9\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+63}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-217}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{-197}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]

Alternative 6
Error	30.5
Cost	1240

\[\begin{array}{l} t_1 := \left(t \cdot z\right) \cdot \left(y \cdot -9\right)\\ \mathbf{if}\;x \leq -5.5 \cdot 10^{+62}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \leq -3.15 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-267}:\\ \;\;\;\;\frac{b \cdot \left(a \cdot 54\right)}{2}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-197}:\\ \;\;\;\;t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-173}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]

Alternative 7
Error	1.6
Cost	1220

\[\begin{array}{l} \mathbf{if}\;z \leq 7 \cdot 10^{+88}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - t \cdot \left(\left(y \cdot z\right) \cdot 9\right)\\ \end{array} \]

Alternative 8
Error	1.6
Cost	1220

\[\begin{array}{l} \mathbf{if}\;z \leq 4.4 \cdot 10^{+72}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(\left(9 \cdot z\right) \cdot t\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - t \cdot \left(\left(y \cdot z\right) \cdot 9\right)\\ \end{array} \]

Alternative 9
Error	13.6
Cost	1096

\[\begin{array}{l} t_1 := t \cdot \left(\left(y \cdot z\right) \cdot 9\right)\\ \mathbf{if}\;x \leq -8 \cdot 10^{-103}:\\ \;\;\;\;2 \cdot x - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+23}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x - t_1\\ \end{array} \]

Alternative 10
Error	31.0
Cost	976

\[\begin{array}{l} t_1 := t \cdot \left(\left(y \cdot z\right) \cdot -9\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+62}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-174}:\\ \;\;\;\;a \cdot \left(27 \cdot b\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]

Alternative 11
Error	13.7
Cost	968

\[\begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+101}:\\ \;\;\;\;2 \cdot x - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-135}:\\ \;\;\;\;2 \cdot x + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x - t \cdot \left(\left(y \cdot z\right) \cdot 9\right)\\ \end{array} \]

Alternative 12
Error	14.4
Cost	836

\[\begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+101}:\\ \;\;\;\;2 \cdot x - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x + a \cdot \left(27 \cdot b\right)\\ \end{array} \]

Alternative 13
Error	28.9
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-93}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+24}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]

Alternative 14
Error	38.0
Cost	192

\[2 \cdot x \]

Reproduce

herbie shell --seed 2023074 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"
  :precision binary64

  :herbie-target
  (if (< y 7.590524218811189e-161) (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b))) (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b)))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))