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

Average Error: 3.2 → 0.7

Time: 19.0s

Precision: binary64

Cost: 14664

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

Math

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

↓

\[\begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ t_2 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(x \cdot 2 + \left(z \cdot \left(y \cdot t\right)\right) \cdot -9\right) + t_2\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+268}:\\ \;\;\;\;\mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \mathsf{fma}\left(x, 2, 27 \cdot \left(a \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, t \cdot \left(z \cdot -9\right), t_2\right)\right)\\ \end{array} \]

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) t)) (t_2 (* (* a 27.0) b)))
   (if (<= t_1 (- INFINITY))
     (+ (+ (* x 2.0) (* (* z (* y t)) -9.0)) t_2)
     (if (<= t_1 5e+268)
       (fma t (* (* y z) -9.0) (fma x 2.0 (* 27.0 (* a b))))
       (fma x 2.0 (fma y (* t (* z -9.0)) t_2))))))

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) * t;
	double t_2 = (a * 27.0) * b;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = ((x * 2.0) + ((z * (y * t)) * -9.0)) + t_2;
	} else if (t_1 <= 5e+268) {
		tmp = fma(t, ((y * z) * -9.0), fma(x, 2.0, (27.0 * (a * b))));
	} else {
		tmp = fma(x, 2.0, fma(y, (t * (z * -9.0)), t_2));
	}
	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(Float64(y * 9.0) * z) * t)
	t_2 = Float64(Float64(a * 27.0) * b)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(x * 2.0) + Float64(Float64(z * Float64(y * t)) * -9.0)) + t_2);
	elseif (t_1 <= 5e+268)
		tmp = fma(t, Float64(Float64(y * z) * -9.0), fma(x, 2.0, Float64(27.0 * Float64(a * b))));
	else
		tmp = fma(x, 2.0, fma(y, Float64(t * Float64(z * -9.0)), t_2));
	end
	return 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[(N[(y * 9.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * 27.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(N[(x * 2.0), $MachinePrecision] + N[(N[(z * N[(y * t), $MachinePrecision]), $MachinePrecision] * -9.0), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[t$95$1, 5e+268], N[(t * N[(N[(y * z), $MachinePrecision] * -9.0), $MachinePrecision] + N[(x * 2.0 + N[(27.0 * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * 2.0 + N[(y * N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	3.2
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 3 regimes

2. if (*.f64 (*.f64 (*.f64 y 9) z) t) < -inf.0

   1. Initial program 64.0

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

   2. Taylor expanded in y around 0 0.3

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

   3. Simplified 1.0

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

      [Start] 0.3	\[ \left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b \]
      associate-*r* [=>] 1.0	\[ \left(x \cdot 2 - 9 \cdot \color{blue}{\left(\left(y \cdot t\right) \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b \]
      *-commutative [=>] 1.0	\[ \left(x \cdot 2 - 9 \cdot \color{blue}{\left(z \cdot \left(y \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b \]

   if -inf.0 < (*.f64 (*.f64 (*.f64 y 9) z) t) < 5.0000000000000002e268

   1. Initial program 0.5

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

   2. Simplified 0.4

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

      [Start] 0.5	\[ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
      sub-neg [=>] 0.5	\[ \color{blue}{\left(x \cdot 2 + \left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)\right)} + \left(a \cdot 27\right) \cdot b \]
      +-commutative [=>] 0.5	\[ \color{blue}{\left(\left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + x \cdot 2\right)} + \left(a \cdot 27\right) \cdot b \]
      associate-+l+ [=>] 0.5	\[ \color{blue}{\left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right)} \]
      distribute-lft-neg-in [=>] 0.5	\[ \color{blue}{\left(-\left(y \cdot 9\right) \cdot z\right) \cdot t} + \left(x \cdot 2 + \left(a \cdot 27\right) \cdot b\right) \]
      +-commutative [<=] 0.5	\[ \left(-\left(y \cdot 9\right) \cdot z\right) \cdot t + \color{blue}{\left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]
      *-commutative [=>] 0.5	\[ \color{blue}{t \cdot \left(-\left(y \cdot 9\right) \cdot z\right)} + \left(\left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]
      fma-def [=>] 0.5	\[ \color{blue}{\mathsf{fma}\left(t, -\left(y \cdot 9\right) \cdot z, \left(a \cdot 27\right) \cdot b + x \cdot 2\right)} \]
      *-commutative [=>] 0.5	\[ \mathsf{fma}\left(t, -\color{blue}{\left(9 \cdot y\right)} \cdot z, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]
      associate-*l* [=>] 0.5	\[ \mathsf{fma}\left(t, -\color{blue}{9 \cdot \left(y \cdot z\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]
      *-commutative [=>] 0.5	\[ \mathsf{fma}\left(t, -\color{blue}{\left(y \cdot z\right) \cdot 9}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]
      distribute-rgt-neg-in [=>] 0.5	\[ \mathsf{fma}\left(t, \color{blue}{\left(y \cdot z\right) \cdot \left(-9\right)}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]
      metadata-eval [=>] 0.5	\[ \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot \color{blue}{-9}, \left(a \cdot 27\right) \cdot b + x \cdot 2\right) \]
      +-commutative [=>] 0.5	\[ \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \color{blue}{x \cdot 2 + \left(a \cdot 27\right) \cdot b}\right) \]
      fma-def [=>] 0.5	\[ \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \color{blue}{\mathsf{fma}\left(x, 2, \left(a \cdot 27\right) \cdot b\right)}\right) \]
      *-commutative [=>] 0.5	\[ \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \mathsf{fma}\left(x, 2, \color{blue}{\left(27 \cdot a\right)} \cdot b\right)\right) \]
      associate-*l* [=>] 0.4	\[ \mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \mathsf{fma}\left(x, 2, \color{blue}{27 \cdot \left(a \cdot b\right)}\right)\right) \]

   if 5.0000000000000002e268 < (*.f64 (*.f64 (*.f64 y 9) z) t)

   1. Initial program 35.5

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

   2. Simplified 7.7

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

      [Start] 35.5	\[ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
      associate-+l- [=>] 35.5	\[ \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]
      fma-neg [=>] 35.5	\[ \color{blue}{\mathsf{fma}\left(x, 2, -\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]
      neg-sub0 [=>] 35.5	\[ \mathsf{fma}\left(x, 2, \color{blue}{0 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)}\right) \]
      associate-+l- [<=] 35.5	\[ \mathsf{fma}\left(x, 2, \color{blue}{\left(0 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b}\right) \]
      neg-sub0 [<=] 35.5	\[ \mathsf{fma}\left(x, 2, \color{blue}{\left(-\left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} + \left(a \cdot 27\right) \cdot b\right) \]
      *-commutative [=>] 35.5	\[ \mathsf{fma}\left(x, 2, \left(-\color{blue}{t \cdot \left(\left(y \cdot 9\right) \cdot z\right)}\right) + \left(a \cdot 27\right) \cdot b\right) \]
      distribute-lft-neg-in [=>] 35.5	\[ \mathsf{fma}\left(x, 2, \color{blue}{\left(-t\right) \cdot \left(\left(y \cdot 9\right) \cdot z\right)} + \left(a \cdot 27\right) \cdot b\right) \]
      associate-*l* [=>] 34.8	\[ \mathsf{fma}\left(x, 2, \left(-t\right) \cdot \color{blue}{\left(y \cdot \left(9 \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b\right) \]
      *-commutative [=>] 34.8	\[ \mathsf{fma}\left(x, 2, \left(-t\right) \cdot \color{blue}{\left(\left(9 \cdot z\right) \cdot y\right)} + \left(a \cdot 27\right) \cdot b\right) \]
      associate-*r* [=>] 7.7	\[ \mathsf{fma}\left(x, 2, \color{blue}{\left(\left(-t\right) \cdot \left(9 \cdot z\right)\right) \cdot y} + \left(a \cdot 27\right) \cdot b\right) \]
      *-commutative [=>] 7.7	\[ \mathsf{fma}\left(x, 2, \color{blue}{y \cdot \left(\left(-t\right) \cdot \left(9 \cdot z\right)\right)} + \left(a \cdot 27\right) \cdot b\right) \]
      fma-def [=>] 7.7	\[ \mathsf{fma}\left(x, 2, \color{blue}{\mathsf{fma}\left(y, \left(-t\right) \cdot \left(9 \cdot z\right), \left(a \cdot 27\right) \cdot b\right)}\right) \]
      distribute-lft-neg-in [<=] 7.7	\[ \mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, \color{blue}{-t \cdot \left(9 \cdot z\right)}, \left(a \cdot 27\right) \cdot b\right)\right) \]
      distribute-rgt-neg-in [=>] 7.7	\[ \mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, \color{blue}{t \cdot \left(-9 \cdot z\right)}, \left(a \cdot 27\right) \cdot b\right)\right) \]
      *-commutative [=>] 7.7	\[ \mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, t \cdot \left(-\color{blue}{z \cdot 9}\right), \left(a \cdot 27\right) \cdot b\right)\right) \]
      distribute-rgt-neg-in [=>] 7.7	\[ \mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, t \cdot \color{blue}{\left(z \cdot \left(-9\right)\right)}, \left(a \cdot 27\right) \cdot b\right)\right) \]
      metadata-eval [=>] 7.7	\[ \mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, t \cdot \left(z \cdot \color{blue}{-9}\right), \left(a \cdot 27\right) \cdot b\right)\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq -\infty:\\ \;\;\;\;\left(x \cdot 2 + \left(z \cdot \left(y \cdot t\right)\right) \cdot -9\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;\left(\left(y \cdot 9\right) \cdot z\right) \cdot t \leq 5 \cdot 10^{+268}:\\ \;\;\;\;\mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \mathsf{fma}\left(x, 2, 27 \cdot \left(a \cdot b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(y, t \cdot \left(z \cdot -9\right), \left(a \cdot 27\right) \cdot b\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	1.1
Cost	14664

\[\begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ t_2 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(x \cdot 2 + \left(z \cdot \left(y \cdot t\right)\right) \cdot -9\right) + t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+270}:\\ \;\;\;\;\mathsf{fma}\left(x, 2, \mathsf{fma}\left(t, y \cdot \left(z \cdot -9\right), t_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 2
Error	0.9
Cost	14020

\[\begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;\left(y \cdot 9\right) \cdot z \leq 5 \cdot 10^{+303}:\\ \;\;\;\;\mathsf{fma}\left(t, \left(y \cdot z\right) \cdot -9, \mathsf{fma}\left(x, 2, t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 3
Error	1.1
Cost	2120

\[\begin{array}{l} t_1 := \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\\ t_2 := \left(a \cdot 27\right) \cdot b\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(x \cdot 2 + \left(z \cdot \left(y \cdot t\right)\right) \cdot -9\right) + t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+270}:\\ \;\;\;\;t_2 + \left(x \cdot 2 + t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 4
Error	21.3
Cost	1369

\[\begin{array}{l} t_1 := t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ t_2 := 27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{if}\;x \leq -4.1 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.52 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-108} \lor \neg \left(x \leq 4 \cdot 10^{-17}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 5
Error	0.6
Cost	1220

\[\begin{array}{l} \mathbf{if}\;z \leq 0.5:\\ \;\;\;\;a \cdot \left(27 \cdot b\right) + \left(x \cdot 2 + \left(z \cdot t\right) \cdot \left(y \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 + \left(z \cdot \left(y \cdot t\right)\right) \cdot -9\right) + \left(a \cdot 27\right) \cdot b\\ \end{array} \]

Alternative 6
Error	11.8
Cost	1097

\[\begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{+27} \lor \neg \left(x \leq 1.22 \cdot 10^{-14}\right):\\ \;\;\;\;t_1 + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;t_1 + -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 7
Error	5.0
Cost	1088

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

Alternative 8
Error	29.6
Cost	980

\[\begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := y \cdot \left(z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+27}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 9
Error	29.6
Cost	980

\[\begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ t_2 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+27}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 10
Error	29.5
Cost	980

\[\begin{array}{l} t_1 := 27 \cdot \left(a \cdot b\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+27}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-112}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.65 \cdot 10^{-14}:\\ \;\;\;\;-9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 11
Error	14.4
Cost	969

\[\begin{array}{l} \mathbf{if}\;a \leq -2.3 \cdot 10^{-9} \lor \neg \left(a \leq 6.5 \cdot 10^{-148}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \end{array} \]

Alternative 12
Error	14.6
Cost	969

\[\begin{array}{l} \mathbf{if}\;a \leq -2.5 \cdot 10^{-9} \lor \neg \left(a \leq 2.4 \cdot 10^{-156}\right):\\ \;\;\;\;27 \cdot \left(a \cdot b\right) + x \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2 + \left(z \cdot t\right) \cdot \left(y \cdot -9\right)\\ \end{array} \]

Alternative 13
Error	28.9
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+27}:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+103}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]

Alternative 14
Error	37.4
Cost	192

\[x \cdot 2 \]

Reproduce

herbie shell --seed 2023060 
(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)))