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

Average Error: 3.1 → 0.7

Time: 19.1s

Precision: binary64

Cost: 1476

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

Math

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

↓

\[\begin{array}{l} t_1 := \left(y \cdot 9\right) \cdot z\\ \mathbf{if}\;t_1 \leq 10^{+180}:\\ \;\;\;\;\left(x \cdot 2 - t_1 \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-9 \cdot z\right)\right) + \left(x + \left(x - b \cdot \left(a \cdot -27\right)\right)\right)\\ \end{array} \]

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 (* (* y 9.0) z)))
   (if (<= t_1 1e+180)
     (+ (- (* x 2.0) (* t_1 t)) (* (* a 27.0) b))
     (+ (* y (* t (* -9.0 z))) (+ x (- x (* b (* a -27.0))))))))

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 = (y * 9.0) * z;
	double tmp;
	if (t_1 <= 1e+180) {
		tmp = ((x * 2.0) - (t_1 * t)) + ((a * 27.0) * b);
	} else {
		tmp = (y * (t * (-9.0 * z))) + (x + (x - (b * (a * -27.0))));
	}
	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) :: tmp
    t_1 = (y * 9.0d0) * z
    if (t_1 <= 1d+180) then
        tmp = ((x * 2.0d0) - (t_1 * t)) + ((a * 27.0d0) * b)
    else
        tmp = (y * (t * ((-9.0d0) * z))) + (x + (x - (b * (a * (-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) {
	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 = (y * 9.0) * z;
	double tmp;
	if (t_1 <= 1e+180) {
		tmp = ((x * 2.0) - (t_1 * t)) + ((a * 27.0) * b);
	} else {
		tmp = (y * (t * (-9.0 * z))) + (x + (x - (b * (a * -27.0))));
	}
	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 = (y * 9.0) * z
	tmp = 0
	if t_1 <= 1e+180:
		tmp = ((x * 2.0) - (t_1 * t)) + ((a * 27.0) * b)
	else:
		tmp = (y * (t * (-9.0 * z))) + (x + (x - (b * (a * -27.0))))
	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(y * 9.0) * z)
	tmp = 0.0
	if (t_1 <= 1e+180)
		tmp = Float64(Float64(Float64(x * 2.0) - Float64(t_1 * t)) + Float64(Float64(a * 27.0) * b));
	else
		tmp = Float64(Float64(y * Float64(t * Float64(-9.0 * z))) + Float64(x + Float64(x - Float64(b * Float64(a * -27.0)))));
	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 = (y * 9.0) * z;
	tmp = 0.0;
	if (t_1 <= 1e+180)
		tmp = ((x * 2.0) - (t_1 * t)) + ((a * 27.0) * b);
	else
		tmp = (y * (t * (-9.0 * z))) + (x + (x - (b * (a * -27.0))));
	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[(y * 9.0), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+180], N[(N[(N[(x * 2.0), $MachinePrecision] - N[(t$95$1 * t), $MachinePrecision]), $MachinePrecision] + N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(t * N[(-9.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x + N[(x - N[(b * N[(a * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	3.1
Target	3.5
Herbie	0.7

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y 9) z) < 1e180

   1. Initial program 0.7

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

   if 1e180 < (*.f64 (*.f64 y 9) z)

   1. Initial program 25.2

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

   2. Applied egg-rr 25.2

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

   3. Simplified 0.6

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

      [Start] 25.2	\[ \left(\left(x + x\right) + \left(\left(-9 \cdot y\right) \cdot z\right) \cdot t\right) - \left(-27 \cdot a\right) \cdot b \]
      rational_best_oopsla_all_46_json_45_simplify-107 [=>] 25.2	\[ \color{blue}{\left(\left(-9 \cdot y\right) \cdot z\right) \cdot t + \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 25.2	\[ \color{blue}{t \cdot \left(\left(-9 \cdot y\right) \cdot z\right)} + \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 25.2	\[ t \cdot \color{blue}{\left(z \cdot \left(-9 \cdot y\right)\right)} + \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 25.0	\[ t \cdot \color{blue}{\left(-9 \cdot \left(z \cdot y\right)\right)} + \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [<=] 25.0	\[ t \cdot \left(-9 \cdot \color{blue}{\left(y \cdot z\right)}\right) + \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 24.7	\[ \color{blue}{-9 \cdot \left(t \cdot \left(y \cdot z\right)\right)} + \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) \]
      rational_best_oopsla_all_46_json_45_simplify-7 [<=] 0.6	\[ -9 \cdot \color{blue}{\left(y \cdot \left(t \cdot z\right)\right)} + \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 0.6	\[ \color{blue}{y \cdot \left(-9 \cdot \left(t \cdot z\right)\right)} + \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) \]
      rational_best_oopsla_all_46_json_45_simplify-7 [=>] 0.6	\[ y \cdot \color{blue}{\left(t \cdot \left(-9 \cdot z\right)\right)} + \left(\left(x + x\right) - \left(-27 \cdot a\right) \cdot b\right) \]
      rational_best_oopsla_all_46_json_45_simplify-107 [=>] 0.6	\[ y \cdot \left(t \cdot \left(-9 \cdot z\right)\right) + \color{blue}{\left(x + \left(x - \left(-27 \cdot a\right) \cdot b\right)\right)} \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.6	\[ y \cdot \left(t \cdot \left(-9 \cdot z\right)\right) + \left(x + \left(x - \color{blue}{b \cdot \left(-27 \cdot a\right)}\right)\right) \]
      rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.6	\[ y \cdot \left(t \cdot \left(-9 \cdot z\right)\right) + \left(x + \left(x - b \cdot \color{blue}{\left(a \cdot -27\right)}\right)\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 10^{+180}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-9 \cdot z\right)\right) + \left(x + \left(x - b \cdot \left(a \cdot -27\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	29.5
Cost	1772

\[\begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+37}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \leq -4.05 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-87}:\\ \;\;\;\;-z \cdot \left(y \cdot \left(t \cdot 9\right)\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-110}:\\ \;\;\;\;a \cdot \left(b \cdot 27\right)\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-198}:\\ \;\;\;\;y \cdot \left(-9 \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{-214}:\\ \;\;\;\;t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-285}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-209}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-84}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]

Alternative 2
Error	29.1
Cost	1376

\[\begin{array}{l} t_1 := -9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+37}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]

Alternative 3
Error	29.7
Cost	1376

\[\begin{array}{l} t_1 := t \cdot \left(-9 \cdot \left(y \cdot z\right)\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+37}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-267}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-284}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]

Alternative 4
Error	29.6
Cost	1376

\[\begin{array}{l} t_1 := t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+37}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-266}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.35 \cdot 10^{-284}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]

Alternative 5
Error	29.6
Cost	1376

\[\begin{array}{l} t_1 := t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{+37}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-258}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.62 \cdot 10^{-285}:\\ \;\;\;\;\left(t \cdot z\right) \cdot \left(y \cdot -9\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-210}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]

Alternative 6
Error	13.9
Cost	1364

\[\begin{array}{l} t_1 := 2 \cdot x - \left(9 \cdot z\right) \cdot \left(y \cdot t\right)\\ t_2 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;z \leq -1.85 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-84}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-9 \cdot z\right)\right) + t_2\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-181}:\\ \;\;\;\;\left(x + x\right) - a \cdot \left(b \cdot -27\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-219}:\\ \;\;\;\;2 \cdot x - \left(y \cdot 9\right) \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-44}:\\ \;\;\;\;2 \cdot x + t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	13.4
Cost	1232

\[\begin{array}{l} t_1 := 2 \cdot x - \left(9 \cdot z\right) \cdot \left(y \cdot t\right)\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-181}:\\ \;\;\;\;\left(x + x\right) - a \cdot \left(b \cdot -27\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-219}:\\ \;\;\;\;2 \cdot x - \left(y \cdot 9\right) \cdot \left(t \cdot z\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-47}:\\ \;\;\;\;2 \cdot x + 27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	1.4
Cost	1220

\[\begin{array}{l} \mathbf{if}\;z \leq 1.9 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-9 \cdot z\right)\right) + \left(x + \left(x - b \cdot \left(a \cdot -27\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x - \left(9 \cdot z\right) \cdot \left(y \cdot t\right)\\ \end{array} \]

Alternative 9
Error	16.3
Cost	1104

\[\begin{array}{l} t_1 := x + \left(x - b \cdot \left(-27 \cdot a\right)\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-9 \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-12}:\\ \;\;\;\;-z \cdot \left(y \cdot \left(t \cdot 9\right)\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\\ \end{array} \]

Alternative 10
Error	16.4
Cost	1104

\[\begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+26}:\\ \;\;\;\;y \cdot \left(t \cdot \left(-9 \cdot z\right)\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+14}:\\ \;\;\;\;x + \left(x - b \cdot \left(-27 \cdot a\right)\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-12}:\\ \;\;\;\;-z \cdot \left(y \cdot \left(t \cdot 9\right)\right)\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+79}:\\ \;\;\;\;\left(x + x\right) - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(y \cdot \left(-9 \cdot z\right)\right)\\ \end{array} \]

Alternative 11
Error	12.8
Cost	968

\[\begin{array}{l} t_1 := 2 \cdot x - \left(9 \cdot z\right) \cdot \left(y \cdot t\right)\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-52}:\\ \;\;\;\;\left(x + x\right) - a \cdot \left(b \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	28.0
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+37}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-26}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]

Alternative 13
Error	28.1
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+37}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-26}:\\ \;\;\;\;a \cdot \left(b \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]

Alternative 14
Error	37.4
Cost	192

\[2 \cdot x \]

Reproduce

herbie shell --seed 2023090 
(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)))