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

Average Accuracy: 95.3% → 98.7%

Time: 24.0s

Precision: binary64

Cost: 21572

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

Math

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

↓

\[\begin{array}{l} t_1 := \mathsf{fma}\left(b \cdot -27, a, a \cdot \left(b \cdot 27\right)\right)\\ \mathbf{if}\;z \leq -1.25 \cdot 10^{+50}:\\ \;\;\;\;x \cdot 2 - \left(\mathsf{fma}\left(y, \left(z \cdot 9\right) \cdot t, a \cdot \left(b \cdot -27\right)\right) + \left(t_1 + t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, b \cdot 27, x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \end{array} \]

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 (fma (* b -27.0) a (* a (* b 27.0)))))
   (if (<= z -1.25e+50)
     (- (* x 2.0) (+ (fma y (* (* z 9.0) t) (* a (* b -27.0))) (+ t_1 t_1)))
     (fma a (* b 27.0) (- (* x 2.0) (* 9.0 (* t (* z y))))))))

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 = fma((b * -27.0), a, (a * (b * 27.0)));
	double tmp;
	if (z <= -1.25e+50) {
		tmp = (x * 2.0) - (fma(y, ((z * 9.0) * t), (a * (b * -27.0))) + (t_1 + t_1));
	} else {
		tmp = fma(a, (b * 27.0), ((x * 2.0) - (9.0 * (t * (z * y)))));
	}
	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 = fma(Float64(b * -27.0), a, Float64(a * Float64(b * 27.0)))
	tmp = 0.0
	if (z <= -1.25e+50)
		tmp = Float64(Float64(x * 2.0) - Float64(fma(y, Float64(Float64(z * 9.0) * t), Float64(a * Float64(b * -27.0))) + Float64(t_1 + t_1)));
	else
		tmp = fma(a, Float64(b * 27.0), Float64(Float64(x * 2.0) - Float64(9.0 * Float64(t * Float64(z * y)))));
	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[(b * -27.0), $MachinePrecision] * a + N[(a * N[(b * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.25e+50], N[(N[(x * 2.0), $MachinePrecision] - N[(N[(y * N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision] + N[(a * N[(b * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$1 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * 27.0), $MachinePrecision] + N[(N[(x * 2.0), $MachinePrecision] - N[(9.0 * N[(t * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	95.3%
Target	94.6%
Herbie	98.7%

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

Derivation

1. Split input into 2 regimes

2. if z < -1.25e50

   1. Initial program 46.8%

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

   2. Simplified 99.0%

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

      [Start] 46.8	\[ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
      associate-+l- [=>] 46.8	\[ \color{blue}{x \cdot 2 - \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]
      sub-neg [=>] 46.8	\[ \color{blue}{x \cdot 2 + \left(-\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)\right)} \]
      neg-mul-1 [=>] 46.8	\[ x \cdot 2 + \color{blue}{-1 \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]
      metadata-eval [<=] 46.8	\[ x \cdot 2 + \color{blue}{\left(-1\right)} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]
      metadata-eval [<=] 46.8	\[ x \cdot 2 + \left(-\color{blue}{\left(--1\right)}\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]
      cancel-sign-sub-inv [<=] 46.8	\[ \color{blue}{x \cdot 2 - \left(--1\right) \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]
      metadata-eval [=>] 46.8	\[ x \cdot 2 - \color{blue}{1} \cdot \left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right) \]
      *-lft-identity [=>] 46.8	\[ x \cdot 2 - \color{blue}{\left(\left(\left(y \cdot 9\right) \cdot z\right) \cdot t - \left(a \cdot 27\right) \cdot b\right)} \]
      associate-*l* [=>] 99.0	\[ x \cdot 2 - \left(\color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)} - \left(a \cdot 27\right) \cdot b\right) \]
      associate-*l* [=>] 99.0	\[ x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - \color{blue}{a \cdot \left(27 \cdot b\right)}\right) \]

   3. Applied egg-rr 99.4%

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

      [Start] 99.0	\[ x \cdot 2 - \left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right) \]
      prod-diff [=>] 99.0	\[ x \cdot 2 - \color{blue}{\left(\mathsf{fma}\left(y \cdot 9, z \cdot t, -\left(27 \cdot b\right) \cdot a\right) + \mathsf{fma}\left(-27 \cdot b, a, \left(27 \cdot b\right) \cdot a\right)\right)} \]
      *-commutative [<=] 99.0	\[ x \cdot 2 - \left(\mathsf{fma}\left(y \cdot 9, z \cdot t, -\color{blue}{a \cdot \left(27 \cdot b\right)}\right) + \mathsf{fma}\left(-27 \cdot b, a, \left(27 \cdot b\right) \cdot a\right)\right) \]
      fma-neg [<=] 99.0	\[ x \cdot 2 - \left(\color{blue}{\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)} + \mathsf{fma}\left(-27 \cdot b, a, \left(27 \cdot b\right) \cdot a\right)\right) \]
      prod-diff [=>] 99.0	\[ x \cdot 2 - \left(\color{blue}{\left(\mathsf{fma}\left(y \cdot 9, z \cdot t, -\left(27 \cdot b\right) \cdot a\right) + \mathsf{fma}\left(-27 \cdot b, a, \left(27 \cdot b\right) \cdot a\right)\right)} + \mathsf{fma}\left(-27 \cdot b, a, \left(27 \cdot b\right) \cdot a\right)\right) \]
      *-commutative [<=] 99.0	\[ x \cdot 2 - \left(\left(\mathsf{fma}\left(y \cdot 9, z \cdot t, -\color{blue}{a \cdot \left(27 \cdot b\right)}\right) + \mathsf{fma}\left(-27 \cdot b, a, \left(27 \cdot b\right) \cdot a\right)\right) + \mathsf{fma}\left(-27 \cdot b, a, \left(27 \cdot b\right) \cdot a\right)\right) \]
      fma-neg [<=] 99.0	\[ x \cdot 2 - \left(\left(\color{blue}{\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right)} + \mathsf{fma}\left(-27 \cdot b, a, \left(27 \cdot b\right) \cdot a\right)\right) + \mathsf{fma}\left(-27 \cdot b, a, \left(27 \cdot b\right) \cdot a\right)\right) \]
      associate-+l+ [=>] 98.9	\[ x \cdot 2 - \color{blue}{\left(\left(\left(y \cdot 9\right) \cdot \left(z \cdot t\right) - a \cdot \left(27 \cdot b\right)\right) + \left(\mathsf{fma}\left(-27 \cdot b, a, \left(27 \cdot b\right) \cdot a\right) + \mathsf{fma}\left(-27 \cdot b, a, \left(27 \cdot b\right) \cdot a\right)\right)\right)} \]

   if -1.25e50 < z

   1. Initial program 98.5%

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

   2. Simplified 95.3%

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

      [Start] 98.5	\[ \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b \]
      +-commutative [=>] 98.5	\[ \color{blue}{\left(a \cdot 27\right) \cdot b + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]
      associate-*l* [=>] 98.4	\[ \color{blue}{a \cdot \left(27 \cdot b\right)} + \left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) \]
      fma-def [=>] 98.4	\[ \color{blue}{\mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right)} \]
      associate-*l* [=>] 95.1	\[ \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) \]
      *-commutative [=>] 95.1	\[ \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{\left(9 \cdot y\right)} \cdot \left(z \cdot t\right)\right) \]
      associate-*l* [=>] 95.3	\[ \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - \color{blue}{9 \cdot \left(y \cdot \left(z \cdot t\right)\right)}\right) \]

   3. Taylor expanded in y around 0 95.3%

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

   4. Simplified 98.6%

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

      [Start] 95.3	\[ \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) \]
      *-commutative [=>] 95.3	\[ \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \color{blue}{\left(\left(t \cdot z\right) \cdot y\right)}\right) \]
      associate-*l* [=>] 98.6	\[ \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \color{blue}{\left(t \cdot \left(z \cdot y\right)\right)}\right) \]
      *-commutative [<=] 98.6	\[ \mathsf{fma}\left(a, 27 \cdot b, x \cdot 2 - 9 \cdot \left(t \cdot \color{blue}{\left(y \cdot z\right)}\right)\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+50}:\\ \;\;\;\;x \cdot 2 - \left(\mathsf{fma}\left(y, \left(z \cdot 9\right) \cdot t, a \cdot \left(b \cdot -27\right)\right) + \left(\mathsf{fma}\left(b \cdot -27, a, a \cdot \left(b \cdot 27\right)\right) + \mathsf{fma}\left(b \cdot -27, a, a \cdot \left(b \cdot 27\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, b \cdot 27, x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	98.7%
Cost	7492

\[\begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+51}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(z \cdot \left(9 \cdot t\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, b \cdot 27, x \cdot 2 - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	83.0%
Cost	2384

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ t_2 := x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{+30}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{+220}:\\ \;\;\;\;t_1 + y \cdot \left(t \cdot \left(z \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x + x\right)\\ \end{array} \]

Alternative 3
Accuracy	67.3%
Cost	2137

\[\begin{array}{l} t_1 := t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ t_2 := x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{if}\;x \cdot 2 \leq 5 \cdot 10^{-282}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot 2 \leq 5 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot 2 \leq 2 \cdot 10^{-94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot 2 \leq 2 \cdot 10^{-50}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;x \cdot 2 \leq 2 \cdot 10^{+19} \lor \neg \left(x \cdot 2 \leq 2 \cdot 10^{+58}\right):\\ \;\;\;\;b \cdot \left(a \cdot 27\right) + \left(x + x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	52.7%
Cost	1636

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot 27\right)\\ t_2 := t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ t_3 := -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+53}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-99}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-161}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{+18}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+57}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \]

Alternative 5
Accuracy	52.9%
Cost	1636

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot 27\right)\\ t_2 := t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ \mathbf{if}\;x \leq -3.15 \cdot 10^{+53}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-96}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-163}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-47}:\\ \;\;\;\;t \cdot \left(y \cdot \left(z \cdot -9\right)\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+19}:\\ \;\;\;\;b \cdot \left(a \cdot 27\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \]

Alternative 6
Accuracy	83.7%
Cost	1480

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-14}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{elif}\;t_1 \leq 10^{+30}:\\ \;\;\;\;x \cdot 2 - 9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x + x\right)\\ \end{array} \]

Alternative 7
Accuracy	83.7%
Cost	1480

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-14}:\\ \;\;\;\;x \cdot 2 - a \cdot \left(b \cdot -27\right)\\ \mathbf{elif}\;t_1 \leq 10^{+30}:\\ \;\;\;\;x \cdot 2 - y \cdot \left(\left(z \cdot 9\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x + x\right)\\ \end{array} \]

Alternative 8
Accuracy	52.9%
Cost	1372

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot 27\right)\\ t_2 := -9 \cdot \left(y \cdot \left(z \cdot t\right)\right)\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-92}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-163}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.35 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \]

Alternative 9
Accuracy	53.0%
Cost	1372

\[\begin{array}{l} t_1 := a \cdot \left(b \cdot 27\right)\\ t_2 := -9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{+53}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-93}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \]

Alternative 10
Accuracy	67.5%
Cost	1369

\[\begin{array}{l} t_1 := t \cdot \left(z \cdot \left(y \cdot -9\right)\right)\\ t_2 := b \cdot \left(a \cdot 27\right) + \left(x + x\right)\\ \mathbf{if}\;x \leq 2 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-51}:\\ \;\;\;\;-9 \cdot \left(z \cdot \left(y \cdot t\right)\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+19} \lor \neg \left(x \leq 7.2 \cdot 10^{+57}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Accuracy	96.7%
Cost	1220

\[\begin{array}{l} \mathbf{if}\;z \leq 8.7 \cdot 10^{+135}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(z \cdot \left(9 \cdot t\right)\right)\right) + b \cdot \left(a \cdot 27\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot y\right) \cdot \left(t \cdot -9\right)\\ \end{array} \]

Alternative 12
Accuracy	98.9%
Cost	1220

\[\begin{array}{l} t_1 := b \cdot \left(a \cdot 27\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+35}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(z \cdot \left(9 \cdot t\right)\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(x \cdot 2 - t \cdot \left(9 \cdot \left(z \cdot y\right)\right)\right)\\ \end{array} \]

Alternative 13
Accuracy	55.5%
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -3.15 \cdot 10^{+53}:\\ \;\;\;\;x + x\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+41}:\\ \;\;\;\;27 \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x + x\\ \end{array} \]

Alternative 14
Accuracy	40.7%
Cost	192

\[x + x \]

Alternative 15
Accuracy	3.2%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023151 
(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)))