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

Average Accuracy: 88.3% → 98.4%

Time: 16.8s

Precision: binary64

Cost: 2249

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

Math

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

↓

\[\begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+221} \lor \neg \left(t_1 \leq 2 \cdot 10^{+202}\right):\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}} - t \cdot \left(z \cdot \frac{4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a \cdot 2}\\ \end{array} \]

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) (* (* z 9.0) t))))
   (if (or (<= t_1 -1e+221) (not (<= t_1 2e+202)))
     (- (* 0.5 (/ y (/ a x))) (* t (* z (/ 4.5 a))))
     (/ t_1 (* a 2.0)))))

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) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -1e+221) || !(t_1 <= 2e+202)) {
		tmp = (0.5 * (y / (a / x))) - (t * (z * (4.5 / a)));
	} else {
		tmp = t_1 / (a * 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    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
    code = ((x * y) - ((z * 9.0d0) * t)) / (a * 2.0d0)
end function

↓

real(8) function code(x, y, z, t, a)
    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) :: t_1
    real(8) :: tmp
    t_1 = (x * y) - ((z * 9.0d0) * t)
    if ((t_1 <= (-1d+221)) .or. (.not. (t_1 <= 2d+202))) then
        tmp = (0.5d0 * (y / (a / x))) - (t * (z * (4.5d0 / a)))
    else
        tmp = t_1 / (a * 2.0d0)
    end if
    code = tmp
end function

Java

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

↓

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if ((t_1 <= -1e+221) || !(t_1 <= 2e+202)) {
		tmp = (0.5 * (y / (a / x))) - (t * (z * (4.5 / a)));
	} else {
		tmp = t_1 / (a * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	return ((x * y) - ((z * 9.0) * t)) / (a * 2.0)

↓

def code(x, y, z, t, a):
	t_1 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if (t_1 <= -1e+221) or not (t_1 <= 2e+202):
		tmp = (0.5 * (y / (a / x))) - (t * (z * (4.5 / a)))
	else:
		tmp = t_1 / (a * 2.0)
	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(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if ((t_1 <= -1e+221) || !(t_1 <= 2e+202))
		tmp = Float64(Float64(0.5 * Float64(y / Float64(a / x))) - Float64(t * Float64(z * Float64(4.5 / a))));
	else
		tmp = Float64(t_1 / Float64(a * 2.0));
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - ((z * 9.0) * t)) / (a * 2.0);
end

↓

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if ((t_1 <= -1e+221) || ~((t_1 <= 2e+202)))
		tmp = (0.5 * (y / (a / x))) - (t * (z * (4.5 / a)));
	else
		tmp = t_1 / (a * 2.0);
	end
	tmp_2 = 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[(x * y), $MachinePrecision] - N[(N[(z * 9.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+221], N[Not[LessEqual[t$95$1, 2e+202]], $MachinePrecision]], N[(N[(0.5 * N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z * N[(4.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]

Target

Original	88.3%
Target	91.1%
Herbie	98.4%

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

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -1e221 or 1.9999999999999998e202 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 53.9%

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

   2. Applied egg-rr 74.6%

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

      [Start] 53.9	\[ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
      div-sub [=>] 53.9	\[ \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]
      sub-neg [=>] 53.9	\[ \color{blue}{\frac{x \cdot y}{a \cdot 2} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right)} \]
      div-inv [=>] 53.9	\[ \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{a \cdot 2}} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right) \]
      *-commutative [=>] 53.9	\[ \left(x \cdot y\right) \cdot \frac{1}{\color{blue}{2 \cdot a}} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right) \]
      associate-/r* [=>] 53.9	\[ \left(x \cdot y\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right) \]
      metadata-eval [=>] 53.9	\[ \left(x \cdot y\right) \cdot \frac{\color{blue}{0.5}}{a} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right) \]
      times-frac [=>] 74.6	\[ \left(x \cdot y\right) \cdot \frac{0.5}{a} + \left(-\color{blue}{\frac{z \cdot 9}{a} \cdot \frac{t}{2}}\right) \]

   3. Simplified 75.4%

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

      [Start] 74.6	\[ \left(x \cdot y\right) \cdot \frac{0.5}{a} + \left(-\frac{z \cdot 9}{a} \cdot \frac{t}{2}\right) \]
      sub-neg [<=] 74.6	\[ \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a} - \frac{z \cdot 9}{a} \cdot \frac{t}{2}} \]
      associate-*r/ [=>] 74.6	\[ \color{blue}{\frac{\left(x \cdot y\right) \cdot 0.5}{a}} - \frac{z \cdot 9}{a} \cdot \frac{t}{2} \]
      *-commutative [=>] 74.6	\[ \frac{\color{blue}{0.5 \cdot \left(x \cdot y\right)}}{a} - \frac{z \cdot 9}{a} \cdot \frac{t}{2} \]
      *-commutative [=>] 74.6	\[ \frac{0.5 \cdot \color{blue}{\left(y \cdot x\right)}}{a} - \frac{z \cdot 9}{a} \cdot \frac{t}{2} \]
      associate-*r/ [<=] 74.6	\[ \color{blue}{0.5 \cdot \frac{y \cdot x}{a}} - \frac{z \cdot 9}{a} \cdot \frac{t}{2} \]
      associate-/l* [=>] 97.5	\[ 0.5 \cdot \color{blue}{\frac{y}{\frac{a}{x}}} - \frac{z \cdot 9}{a} \cdot \frac{t}{2} \]
      associate-/l* [=>] 97.8	\[ 0.5 \cdot \frac{y}{\frac{a}{x}} - \color{blue}{\frac{z}{\frac{a}{9}}} \cdot \frac{t}{2} \]
      associate-*l/ [=>] 75.4	\[ 0.5 \cdot \frac{y}{\frac{a}{x}} - \color{blue}{\frac{z \cdot \frac{t}{2}}{\frac{a}{9}}} \]

   4. Taylor expanded in z around 0 75.2%

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

   5. Simplified 97.8%

      \[\leadsto 0.5 \cdot \frac{y}{\frac{a}{x}} - \color{blue}{t \cdot \left(z \cdot \frac{4.5}{a}\right)} \]
      Proof

      [Start] 75.2	\[ 0.5 \cdot \frac{y}{\frac{a}{x}} - 4.5 \cdot \frac{t \cdot z}{a} \]
      associate-*r/ [=>] 75.2	\[ 0.5 \cdot \frac{y}{\frac{a}{x}} - \color{blue}{\frac{4.5 \cdot \left(t \cdot z\right)}{a}} \]
      metadata-eval [<=] 75.2	\[ 0.5 \cdot \frac{y}{\frac{a}{x}} - \frac{\color{blue}{\left(9 \cdot 0.5\right)} \cdot \left(t \cdot z\right)}{a} \]
      *-commutative [<=] 75.2	\[ 0.5 \cdot \frac{y}{\frac{a}{x}} - \frac{\left(9 \cdot 0.5\right) \cdot \color{blue}{\left(z \cdot t\right)}}{a} \]
      associate-*r* [<=] 75.2	\[ 0.5 \cdot \frac{y}{\frac{a}{x}} - \frac{\color{blue}{9 \cdot \left(0.5 \cdot \left(z \cdot t\right)\right)}}{a} \]
      *-commutative [<=] 75.2	\[ 0.5 \cdot \frac{y}{\frac{a}{x}} - \frac{9 \cdot \color{blue}{\left(\left(z \cdot t\right) \cdot 0.5\right)}}{a} \]
      associate-*l/ [<=] 75.2	\[ 0.5 \cdot \frac{y}{\frac{a}{x}} - \color{blue}{\frac{9}{a} \cdot \left(\left(z \cdot t\right) \cdot 0.5\right)} \]
      *-commutative [<=] 75.2	\[ 0.5 \cdot \frac{y}{\frac{a}{x}} - \color{blue}{\left(\left(z \cdot t\right) \cdot 0.5\right) \cdot \frac{9}{a}} \]
      associate-*l* [=>] 75.2	\[ 0.5 \cdot \frac{y}{\frac{a}{x}} - \color{blue}{\left(z \cdot t\right) \cdot \left(0.5 \cdot \frac{9}{a}\right)} \]
      *-commutative [=>] 75.2	\[ 0.5 \cdot \frac{y}{\frac{a}{x}} - \color{blue}{\left(t \cdot z\right)} \cdot \left(0.5 \cdot \frac{9}{a}\right) \]
      associate-*l* [=>] 97.8	\[ 0.5 \cdot \frac{y}{\frac{a}{x}} - \color{blue}{t \cdot \left(z \cdot \left(0.5 \cdot \frac{9}{a}\right)\right)} \]
      associate-*r/ [=>] 97.8	\[ 0.5 \cdot \frac{y}{\frac{a}{x}} - t \cdot \left(z \cdot \color{blue}{\frac{0.5 \cdot 9}{a}}\right) \]
      metadata-eval [=>] 97.8	\[ 0.5 \cdot \frac{y}{\frac{a}{x}} - t \cdot \left(z \cdot \frac{\color{blue}{4.5}}{a}\right) \]

   if -1e221 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 1.9999999999999998e202

   1. Initial program 98.5%

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -1 \cdot 10^{+221} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 2 \cdot 10^{+202}\right):\\ \;\;\;\;0.5 \cdot \frac{y}{\frac{a}{x}} - t \cdot \left(z \cdot \frac{4.5}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	93.5%
Cost	2248

\[\begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{t}{\frac{\frac{a}{-4.5}}{z}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a} + 0.5 \cdot \frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]

Alternative 2
Accuracy	93.5%
Cost	2120

\[\begin{array}{l} t_1 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{t}{\frac{\frac{a}{-4.5}}{z}}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+302}:\\ \;\;\;\;\frac{t_1}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \end{array} \]

Alternative 3
Accuracy	61.1%
Cost	1372

\[\begin{array}{l} t_1 := 0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{-30}:\\ \;\;\;\;0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{-150}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-170}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-40}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+65}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+264}:\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	93.4%
Cost	1352

\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+255}:\\ \;\;\;\;\frac{x \cdot y - 9 \cdot \left(z \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{\frac{a}{x}}\\ \end{array} \]

Alternative 5
Accuracy	60.5%
Cost	1241

\[\begin{array}{l} t_1 := 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{-150}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-39}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+40} \lor \neg \left(y \leq 1.8 \cdot 10^{+65}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 6
Accuracy	61.1%
Cost	1240

\[\begin{array}{l} t_1 := 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ t_2 := 0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{-150}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-39}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+64}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	61.0%
Cost	1240

\[\begin{array}{l} t_1 := 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{-42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{-150}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-170}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-40}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+40}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+65}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	61.0%
Cost	1240

\[\begin{array}{l} t_1 := 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{-150}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-170}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{y}{a}\right)\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-40}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+39}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	61.1%
Cost	1240

\[\begin{array}{l} t_1 := 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{if}\;y \leq -5 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-150}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-170}:\\ \;\;\;\;\frac{0.5}{\frac{a}{x \cdot y}}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-40}:\\ \;\;\;\;-4.5 \cdot \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+40}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+64}:\\ \;\;\;\;z \cdot \left(-4.5 \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Accuracy	49.7%
Cost	580

\[\begin{array}{l} \mathbf{if}\;t \leq 10^{+219}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 11
Accuracy	49.2%
Cost	448

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

Alternative 12
Accuracy	5.8%
Cost	192

\[x \cdot y \]

Reproduce

herbie shell --seed 2023147 
(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)))