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

Average Accuracy: 88.2% → 98.3%

Time: 19.6s

Precision: binary64

Cost: 8904

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{x \cdot y + t \cdot \left(z \cdot -9\right)}{a \cdot 2}\\ t_2 := \frac{z}{a} \cdot \frac{9}{\frac{2}{t}}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+297}:\\ \;\;\;\;\frac{x}{\frac{a \cdot 2}{y}} - t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right) - t_2\\ \end{array} \]

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 (/ (+ (* x y) (* t (* z -9.0))) (* a 2.0)))
        (t_2 (* (/ z a) (/ 9.0 (/ 2.0 t)))))
   (if (<= t_1 -4e+297)
     (- (/ x (/ (* a 2.0) y)) t_2)
     (if (<= t_1 2e+307)
       (/ (fma x y (* z (* t -9.0))) (* a 2.0))
       (- (* x (* y (/ 0.5 a))) t_2)))))

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 = ((x * y) + (t * (z * -9.0))) / (a * 2.0);
	double t_2 = (z / a) * (9.0 / (2.0 / t));
	double tmp;
	if (t_1 <= -4e+297) {
		tmp = (x / ((a * 2.0) / y)) - t_2;
	} else if (t_1 <= 2e+307) {
		tmp = fma(x, y, (z * (t * -9.0))) / (a * 2.0);
	} else {
		tmp = (x * (y * (0.5 / a))) - t_2;
	}
	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(Float64(Float64(x * y) + Float64(t * Float64(z * -9.0))) / Float64(a * 2.0))
	t_2 = Float64(Float64(z / a) * Float64(9.0 / Float64(2.0 / t)))
	tmp = 0.0
	if (t_1 <= -4e+297)
		tmp = Float64(Float64(x / Float64(Float64(a * 2.0) / y)) - t_2);
	elseif (t_1 <= 2e+307)
		tmp = Float64(fma(x, y, Float64(z * Float64(t * -9.0))) / Float64(a * 2.0));
	else
		tmp = Float64(Float64(x * Float64(y * Float64(0.5 / a))) - t_2);
	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[(N[(N[(x * y), $MachinePrecision] + N[(t * N[(z * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z / a), $MachinePrecision] * N[(9.0 / N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+297], N[(N[(x / N[(N[(a * 2.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[LessEqual[t$95$1, 2e+307], N[(N[(x * y + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Target

Original	88.2%
Target	91.2%
Herbie	98.3%

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2)) < -4.0000000000000001e297

   1. Initial program 13.0%

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

   2. Simplified 13.0%

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

      [Start] 13.0	\[ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
      associate-*l* [=>] 13.0	\[ \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Applied egg-rr 48.7%

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a} + \left(-\frac{z}{a} \cdot \frac{9 \cdot t}{2}\right)} \]

   4. Simplified 93.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right) - \frac{z}{a} \cdot \frac{9}{\frac{2}{t}}} \]
      Proof

      [Start] 48.7	\[ \left(x \cdot y\right) \cdot \frac{0.5}{a} + \left(-\frac{z}{a} \cdot \frac{9 \cdot t}{2}\right) \]
      sub-neg [<=] 48.7	\[ \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a} - \frac{z}{a} \cdot \frac{9 \cdot t}{2}} \]
      associate-*l* [=>] 93.8	\[ \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} - \frac{z}{a} \cdot \frac{9 \cdot t}{2} \]
      associate-/l* [=>] 93.7	\[ x \cdot \left(y \cdot \frac{0.5}{a}\right) - \frac{z}{a} \cdot \color{blue}{\frac{9}{\frac{2}{t}}} \]

   5. Applied egg-rr 93.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{a \cdot 2}{y}}} - \frac{z}{a} \cdot \frac{9}{\frac{2}{t}} \]

   if -4.0000000000000001e297 < (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2)) < 1.99999999999999997e307

   1. Initial program 98.7%

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

   2. Simplified 98.6%

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

      [Start] 98.7	\[ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
      fma-neg [=>] 98.7	\[ \frac{\color{blue}{\mathsf{fma}\left(x, y, -\left(z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]
      associate-*l* [=>] 98.6	\[ \frac{\mathsf{fma}\left(x, y, -\color{blue}{z \cdot \left(9 \cdot t\right)}\right)}{a \cdot 2} \]
      distribute-rgt-neg-in [=>] 98.6	\[ \frac{\mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(-9 \cdot t\right)}\right)}{a \cdot 2} \]
      *-commutative [=>] 98.6	\[ \frac{\mathsf{fma}\left(x, y, z \cdot \left(-\color{blue}{t \cdot 9}\right)\right)}{a \cdot 2} \]
      distribute-rgt-neg-in [=>] 98.6	\[ \frac{\mathsf{fma}\left(x, y, z \cdot \color{blue}{\left(t \cdot \left(-9\right)\right)}\right)}{a \cdot 2} \]
      metadata-eval [=>] 98.6	\[ \frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot \color{blue}{-9}\right)\right)}{a \cdot 2} \]

   if 1.99999999999999997e307 < (/.f64 (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) (*.f64 a 2))

   1. Initial program 1.3%

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

   2. Simplified 1.9%

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

      [Start] 1.3	\[ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
      associate-*l* [=>] 1.9	\[ \frac{x \cdot y - \color{blue}{z \cdot \left(9 \cdot t\right)}}{a \cdot 2} \]

   3. Applied egg-rr 46.5%

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a} + \left(-\frac{z}{a} \cdot \frac{9 \cdot t}{2}\right)} \]

   4. Simplified 98.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right) - \frac{z}{a} \cdot \frac{9}{\frac{2}{t}}} \]
      Proof

      [Start] 46.5	\[ \left(x \cdot y\right) \cdot \frac{0.5}{a} + \left(-\frac{z}{a} \cdot \frac{9 \cdot t}{2}\right) \]
      sub-neg [<=] 46.5	\[ \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a} - \frac{z}{a} \cdot \frac{9 \cdot t}{2}} \]
      associate-*l* [=>] 98.6	\[ \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} - \frac{z}{a} \cdot \frac{9 \cdot t}{2} \]
      associate-/l* [=>] 98.5	\[ x \cdot \left(y \cdot \frac{0.5}{a}\right) - \frac{z}{a} \cdot \color{blue}{\frac{9}{\frac{2}{t}}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + t \cdot \left(z \cdot -9\right)}{a \cdot 2} \leq -4 \cdot 10^{+297}:\\ \;\;\;\;\frac{x}{\frac{a \cdot 2}{y}} - \frac{z}{a} \cdot \frac{9}{\frac{2}{t}}\\ \mathbf{elif}\;\frac{x \cdot y + t \cdot \left(z \cdot -9\right)}{a \cdot 2} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right) - \frac{z}{a} \cdot \frac{9}{\frac{2}{t}}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	98.3%
Cost	2889

\[\begin{array}{l} t_1 := \frac{x \cdot y + t \cdot \left(z \cdot -9\right)}{a \cdot 2}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+297} \lor \neg \left(t_1 \leq 2 \cdot 10^{+307}\right):\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right) - \frac{z}{a} \cdot \frac{9}{\frac{2}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \end{array} \]

Alternative 2
Accuracy	98.3%
Cost	2888

\[\begin{array}{l} t_1 := \frac{x \cdot y + t \cdot \left(z \cdot -9\right)}{a \cdot 2}\\ t_2 := \frac{z}{a} \cdot \frac{9}{\frac{2}{t}}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+297}:\\ \;\;\;\;\frac{x}{\frac{a \cdot 2}{y}} - t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right) - t_2\\ \end{array} \]

Alternative 3
Accuracy	93.3%
Cost	2120

\[\begin{array}{l} t_1 := x \cdot y + t \cdot \left(z \cdot -9\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;t_1 \leq 10^{+301}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t \cdot -9\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \frac{t}{-0.2222222222222222}\\ \end{array} \]

Alternative 4
Accuracy	57.2%
Cost	1504

\[\begin{array}{l} t_1 := \frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-227}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-70}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-11}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \frac{y}{\frac{a}{0.5}}\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \frac{-4.5}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 5
Accuracy	57.1%
Cost	1504

\[\begin{array}{l} t_1 := \frac{x \cdot y}{\frac{a}{0.5}}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{-199}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-227}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-70}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-45}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-11}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \frac{-4.5}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 6
Accuracy	57.1%
Cost	1504

\[\begin{array}{l} t_1 := \frac{x \cdot y}{\frac{a}{0.5}}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{-199}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-227}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-70}:\\ \;\;\;\;\frac{z \cdot \left(t \cdot -4.5\right)}{a}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-11}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \frac{-4.5}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 7
Accuracy	58.8%
Cost	1240

\[\begin{array}{l} t_1 := -4.5 \cdot \frac{t}{\frac{a}{z}}\\ t_2 := 0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+20}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Accuracy	58.8%
Cost	1240

\[\begin{array}{l} t_1 := -4.5 \cdot \frac{t}{\frac{a}{z}}\\ t_2 := 0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+17}:\\ \;\;\;\;x \cdot \frac{y}{\frac{a}{0.5}}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	58.8%
Cost	1240

\[\begin{array}{l} t_1 := -4.5 \cdot \frac{t}{\frac{a}{z}}\\ t_2 := 0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;y \leq -4 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \frac{y}{\frac{a}{0.5}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Accuracy	58.9%
Cost	1240

\[\begin{array}{l} t_1 := t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ t_2 := 0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-45}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-11}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \frac{y}{\frac{a}{0.5}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Accuracy	58.8%
Cost	1240

\[\begin{array}{l} t_1 := 0.5 \cdot \frac{y}{\frac{a}{x}}\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{-199}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{-68}:\\ \;\;\;\;t \cdot \left(\frac{z}{a} \cdot -4.5\right)\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \frac{x \cdot 0.5}{a}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-11}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{y}{\frac{a}{0.5}}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+56}:\\ \;\;\;\;t \cdot \frac{-4.5}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Accuracy	88.2%
Cost	1229

\[\begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{+95}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+171} \lor \neg \left(t \leq 2.3 \cdot 10^{+203}\right):\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + -9 \cdot \left(z \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-4.5}{\frac{a}{z}}\\ \end{array} \]

Alternative 13
Accuracy	62.8%
Cost	713

\[\begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-59} \lor \neg \left(x \leq 1.66 \cdot 10^{-80}\right):\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 14
Accuracy	48.8%
Cost	448

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

Alternative 15
Accuracy	48.9%
Cost	448

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

Reproduce

herbie shell --seed 2023129 
(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)))