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

Percentage Accurate: 91.1% → 96.8%

Time: 14.4s

Precision: binary64

Cost: 8520

• Unsound rule application detected in e-graph. Results may not be sound.

• 28.1% of points produce a very large (infinite) output. You may want to add a precondition.

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

Math

\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

↓

\[\begin{array}{l} t_1 := -4.5 \cdot \frac{t}{a}\\ t_2 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(t_1, z, 0.5 \cdot \left(y \cdot \frac{-1}{\frac{-a}{x}}\right)\right)\\ \mathbf{elif}\;t_2 \leq 10^{+136}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t_1, z, 0.5 \cdot \frac{y}{\frac{a}{x}}\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))

↓

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* -4.5 (/ t a))) (t_2 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_2 (- INFINITY))
     (fma t_1 z (* 0.5 (* y (/ -1.0 (/ (- a) x)))))
     (if (<= t_2 1e+136)
       (/ (fma z (* t -9.0) (* x y)) (* a 2.0))
       (fma t_1 z (* 0.5 (/ y (/ a x))))))))

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double t_1 = -4.5 * (t / a);
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma(t_1, z, (0.5 * (y * (-1.0 / (-a / x)))));
	} else if (t_2 <= 1e+136) {
		tmp = fma(z, (t * -9.0), (x * y)) / (a * 2.0);
	} else {
		tmp = fma(t_1, z, (0.5 * (y / (a / x))));
	}
	return tmp;
}

Julia

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

↓

function code(x, y, z, t, a)
	t_1 = Float64(-4.5 * Float64(t / a))
	t_2 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = fma(t_1, z, Float64(0.5 * Float64(y * Float64(-1.0 / Float64(Float64(-a) / x)))));
	elseif (t_2 <= 1e+136)
		tmp = Float64(fma(z, Float64(t * -9.0), Float64(x * y)) / Float64(a * 2.0));
	else
		tmp = fma(t_1, z, Float64(0.5 * Float64(y / Float64(a / x))));
	end
	return tmp
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(-4.5 * N[(t / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(t$95$1 * z + N[(0.5 * N[(y * N[(-1.0 / N[((-a) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+136], N[(N[(z * N[(t * -9.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * z + N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Target

Original	91.1%
Target	93.8%
Herbie	96.8%

\[\begin{array}{l} \mathbf{if}\;a < -2.090464557976709 \cdot 10^{+86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a < 2.144030707833976 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array} \]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 67.8%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Simplified 67.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}} \]
      Step-by-step derivation

      [Start] 67.8%	\[ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
      sub-neg [=>] 67.8%	\[ \frac{\color{blue}{x \cdot y + \left(-\left(z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]
      +-commutative [=>] 67.8%	\[ \frac{\color{blue}{\left(-\left(z \cdot 9\right) \cdot t\right) + x \cdot y}}{a \cdot 2} \]
      neg-sub0 [=>] 67.8%	\[ \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]
      associate-+l- [=>] 67.8%	\[ \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]
      sub0-neg [=>] 67.8%	\[ \frac{\color{blue}{-\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]
      neg-mul-1 [=>] 67.8%	\[ \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]
      associate-/l* [=>] 67.8%	\[ \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]
      associate-/r/ [=>] 67.8%	\[ \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]
      *-commutative [=>] 67.8%	\[ \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]
      sub-neg [=>] 67.8%	\[ \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]
      +-commutative [=>] 67.8%	\[ \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]
      neg-sub0 [=>] 67.8%	\[ \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]
      associate-+l- [=>] 67.8%	\[ \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]
      sub0-neg [=>] 67.8%	\[ \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]
      distribute-lft-neg-out [=>] 67.8%	\[ \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]
      distribute-rgt-neg-in [=>] 67.8%	\[ \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Taylor expanded in x around 0 67.8%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{y \cdot x}{a}} \]

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5 \cdot \frac{t}{a}, z, 0.5 \cdot \frac{y}{\frac{a}{x}}\right)} \]
      Step-by-step derivation

      [Start] 67.8%	\[ -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{y \cdot x}{a} \]
      associate-*l/ [<=] 83.9%	\[ -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} + 0.5 \cdot \frac{y \cdot x}{a} \]
      associate-*r* [=>] 84.1%	\[ \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right) \cdot z} + 0.5 \cdot \frac{y \cdot x}{a} \]
      fma-def [=>] 84.1%	\[ \color{blue}{\mathsf{fma}\left(-4.5 \cdot \frac{t}{a}, z, 0.5 \cdot \frac{y \cdot x}{a}\right)} \]
      associate-/l* [=>] 99.8%	\[ \mathsf{fma}\left(-4.5 \cdot \frac{t}{a}, z, 0.5 \cdot \color{blue}{\frac{y}{\frac{a}{x}}}\right) \]

   5. Applied egg-rr 99.9%

      \[\leadsto \mathsf{fma}\left(-4.5 \cdot \frac{t}{a}, z, 0.5 \cdot \color{blue}{\left(\left(-y\right) \cdot \frac{1}{\frac{-a}{x}}\right)}\right) \]
      Step-by-step derivation

      [Start] 99.8%	\[ \mathsf{fma}\left(-4.5 \cdot \frac{t}{a}, z, 0.5 \cdot \frac{y}{\frac{a}{x}}\right) \]
      frac-2neg [=>] 99.8%	\[ \mathsf{fma}\left(-4.5 \cdot \frac{t}{a}, z, 0.5 \cdot \color{blue}{\frac{-y}{-\frac{a}{x}}}\right) \]
      div-inv [=>] 99.9%	\[ \mathsf{fma}\left(-4.5 \cdot \frac{t}{a}, z, 0.5 \cdot \color{blue}{\left(\left(-y\right) \cdot \frac{1}{-\frac{a}{x}}\right)}\right) \]
      distribute-neg-frac [=>] 99.9%	\[ \mathsf{fma}\left(-4.5 \cdot \frac{t}{a}, z, 0.5 \cdot \left(\left(-y\right) \cdot \frac{1}{\color{blue}{\frac{-a}{x}}}\right)\right) \]

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 1.00000000000000006e136

   1. Initial program 97.9%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Simplified 97.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}{a \cdot 2}} \]
      Step-by-step derivation

      [Start] 97.9%	\[ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
      sub-neg [=>] 97.9%	\[ \frac{\color{blue}{x \cdot y + \left(-\left(z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]
      +-commutative [=>] 97.9%	\[ \frac{\color{blue}{\left(-\left(z \cdot 9\right) \cdot t\right) + x \cdot y}}{a \cdot 2} \]
      associate-*l* [=>] 97.9%	\[ \frac{\left(-\color{blue}{z \cdot \left(9 \cdot t\right)}\right) + x \cdot y}{a \cdot 2} \]
      distribute-rgt-neg-in [=>] 97.9%	\[ \frac{\color{blue}{z \cdot \left(-9 \cdot t\right)} + x \cdot y}{a \cdot 2} \]
      fma-def [=>] 97.9%	\[ \frac{\color{blue}{\mathsf{fma}\left(z, -9 \cdot t, x \cdot y\right)}}{a \cdot 2} \]
      *-commutative [=>] 97.9%	\[ \frac{\mathsf{fma}\left(z, -\color{blue}{t \cdot 9}, x \cdot y\right)}{a \cdot 2} \]
      distribute-rgt-neg-in [=>] 97.9%	\[ \frac{\mathsf{fma}\left(z, \color{blue}{t \cdot \left(-9\right)}, x \cdot y\right)}{a \cdot 2} \]
      metadata-eval [=>] 97.9%	\[ \frac{\mathsf{fma}\left(z, t \cdot \color{blue}{-9}, x \cdot y\right)}{a \cdot 2} \]

   if 1.00000000000000006e136 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 83.0%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]

   2. Simplified 84.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}} \]
      Step-by-step derivation

      [Start] 83.0%	\[ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
      sub-neg [=>] 83.0%	\[ \frac{\color{blue}{x \cdot y + \left(-\left(z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]
      +-commutative [=>] 83.0%	\[ \frac{\color{blue}{\left(-\left(z \cdot 9\right) \cdot t\right) + x \cdot y}}{a \cdot 2} \]
      neg-sub0 [=>] 83.0%	\[ \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]
      associate-+l- [=>] 83.0%	\[ \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]
      sub0-neg [=>] 83.0%	\[ \frac{\color{blue}{-\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]
      neg-mul-1 [=>] 83.0%	\[ \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]
      associate-/l* [=>] 83.0%	\[ \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]
      associate-/r/ [=>] 83.0%	\[ \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]
      *-commutative [=>] 83.0%	\[ \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]
      sub-neg [=>] 83.0%	\[ \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]
      +-commutative [=>] 83.0%	\[ \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]
      neg-sub0 [=>] 83.0%	\[ \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]
      associate-+l- [=>] 83.0%	\[ \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]
      sub0-neg [=>] 83.0%	\[ \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]
      distribute-lft-neg-out [=>] 83.0%	\[ \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]
      distribute-rgt-neg-in [=>] 83.0%	\[ \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Taylor expanded in x around 0 84.6%

      \[\leadsto \color{blue}{-4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{y \cdot x}{a}} \]

   4. Applied egg-rr 93.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-4.5 \cdot \frac{t}{a}, z, 0.5 \cdot \frac{y}{\frac{a}{x}}\right)} \]
      Step-by-step derivation

      [Start] 84.6%	\[ -4.5 \cdot \frac{t \cdot z}{a} + 0.5 \cdot \frac{y \cdot x}{a} \]
      associate-*l/ [<=] 84.6%	\[ -4.5 \cdot \color{blue}{\left(\frac{t}{a} \cdot z\right)} + 0.5 \cdot \frac{y \cdot x}{a} \]
      associate-*r* [=>] 84.6%	\[ \color{blue}{\left(-4.5 \cdot \frac{t}{a}\right) \cdot z} + 0.5 \cdot \frac{y \cdot x}{a} \]
      fma-def [=>] 86.2%	\[ \color{blue}{\mathsf{fma}\left(-4.5 \cdot \frac{t}{a}, z, 0.5 \cdot \frac{y \cdot x}{a}\right)} \]
      associate-/l* [=>] 93.4%	\[ \mathsf{fma}\left(-4.5 \cdot \frac{t}{a}, z, 0.5 \cdot \color{blue}{\frac{y}{\frac{a}{x}}}\right) \]

3. Recombined 3 regimes into one program.

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(-4.5 \cdot \frac{t}{a}, z, 0.5 \cdot \left(y \cdot \frac{-1}{\frac{-a}{x}}\right)\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 10^{+136}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-4.5 \cdot \frac{t}{a}, z, 0.5 \cdot \frac{y}{\frac{a}{x}}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	96.8%
Cost	8520

\[\begin{array}{l} t_1 := -4.5 \cdot \frac{t}{a}\\ t_2 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(t_1, z, 0.5 \cdot \left(y \cdot \frac{-1}{\frac{-a}{x}}\right)\right)\\ \mathbf{elif}\;t_2 \leq 10^{+136}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t_1, z, 0.5 \cdot \frac{y}{\frac{a}{x}}\right)\\ \end{array} \]

Alternative 2
Accuracy	96.7%
Cost	8520

\[\begin{array}{l} t_1 := -4.5 \cdot \frac{t}{a}\\ t_2 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;z \cdot t_1 - 0.5 \cdot \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;t_2 \leq 10^{+136}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t_1, z, 0.5 \cdot \frac{y}{\frac{a}{x}}\right)\\ \end{array} \]

Alternative 3
Accuracy	97.0%
Cost	8392

\[\begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right) - 0.5 \cdot \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;t_1 \leq 10^{+244}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, t \cdot -9, x \cdot y\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right) + \frac{y}{a} \cdot \left(x \cdot 0.5\right)\\ \end{array} \]

Alternative 4
Accuracy	97.0%
Cost	2249

\[\begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+244}\right):\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right) + \frac{y}{a} \cdot \left(x \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \]

Alternative 5
Accuracy	97.0%
Cost	2248

\[\begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right) - 0.5 \cdot \frac{y}{\frac{-a}{x}}\\ \mathbf{elif}\;t_1 \leq 10^{+244}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot -4.5\right) + \frac{y}{a} \cdot \left(x \cdot 0.5\right)\\ \end{array} \]

Alternative 6
Accuracy	94.8%
Cost	1609

\[\begin{array}{l} t_1 := \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+256}\right):\\ \;\;\;\;\left(t \cdot -4.5\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \]

Alternative 7
Accuracy	93.0%
Cost	1092

\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+280}:\\ \;\;\;\;\frac{\frac{x}{a}}{\frac{2}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot y + z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a}\\ \end{array} \]

Alternative 8
Accuracy	64.1%
Cost	977

\[\begin{array}{l} t_1 := 0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+96}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \leq -0.008 \lor \neg \left(x \leq 2.9 \cdot 10^{-47}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 9
Accuracy	65.4%
Cost	976

\[\begin{array}{l} t_1 := x \cdot \frac{y \cdot 0.5}{a}\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+96}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;x \leq -0.0078:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-47}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Accuracy	74.2%
Cost	968

\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+60}:\\ \;\;\;\;\frac{x}{a} \cdot \frac{y}{2}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-34}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y \cdot 0.5}{a}\\ \end{array} \]

Alternative 11
Accuracy	51.3%
Cost	448

\[-4.5 \cdot \left(z \cdot \frac{t}{a}\right) \]

Alternative 12
Accuracy	50.7%
Cost	448

\[-4.5 \cdot \left(t \cdot \frac{z}{a}\right) \]

Alternative 13
Accuracy	50.7%
Cost	448

\[-4.5 \cdot \frac{t}{\frac{a}{z}} \]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :herbie-target
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9.0 t))) (* a 2.0)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9.0) t)) (* a 2.0)))