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

Percentage Accurate: 91.1% → 97.4%

Time: 15.0s

Precision: binary64

Cost: 3665

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

• 28.6% 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

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

↓

\[\begin{array}{l} t_1 := x \cdot \left(y \cdot \frac{0.5}{a}\right) - \frac{z}{\frac{a}{9}} \cdot \frac{t}{2}\\ t_2 := x \cdot y - \left(z \cdot 9\right) \cdot t\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-175}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-177} \lor \neg \left(t_2 \leq 5 \cdot 10^{+297}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{a \cdot 2}\\ \end{array} \]

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 (/ 0.5 a))) (* (/ z (/ a 9.0)) (/ t 2.0))))
        (t_2 (- (* x y) (* (* z 9.0) t))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e-175)
       (* (/ 0.5 a) (+ (* x y) (* z (* t -9.0))))
       (if (or (<= t_2 5e-177) (not (<= t_2 5e+297)))
         t_1
         (/ t_2 (* 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 * (0.5 / a))) - ((z / (a / 9.0)) * (t / 2.0));
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e-175) {
		tmp = (0.5 / a) * ((x * y) + (z * (t * -9.0)));
	} else if ((t_2 <= 5e-177) || !(t_2 <= 5e+297)) {
		tmp = t_1;
	} else {
		tmp = t_2 / (a * 2.0);
	}
	return tmp;
}

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 * (0.5 / a))) - ((z / (a / 9.0)) * (t / 2.0));
	double t_2 = (x * y) - ((z * 9.0) * t);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e-175) {
		tmp = (0.5 / a) * ((x * y) + (z * (t * -9.0)));
	} else if ((t_2 <= 5e-177) || !(t_2 <= 5e+297)) {
		tmp = t_1;
	} else {
		tmp = t_2 / (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 * (0.5 / a))) - ((z / (a / 9.0)) * (t / 2.0))
	t_2 = (x * y) - ((z * 9.0) * t)
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e-175:
		tmp = (0.5 / a) * ((x * y) + (z * (t * -9.0)))
	elif (t_2 <= 5e-177) or not (t_2 <= 5e+297):
		tmp = t_1
	else:
		tmp = t_2 / (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 * Float64(y * Float64(0.5 / a))) - Float64(Float64(z / Float64(a / 9.0)) * Float64(t / 2.0)))
	t_2 = Float64(Float64(x * y) - Float64(Float64(z * 9.0) * t))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e-175)
		tmp = Float64(Float64(0.5 / a) * Float64(Float64(x * y) + Float64(z * Float64(t * -9.0))));
	elseif ((t_2 <= 5e-177) || !(t_2 <= 5e+297))
		tmp = t_1;
	else
		tmp = Float64(t_2 / 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 * (0.5 / a))) - ((z / (a / 9.0)) * (t / 2.0));
	t_2 = (x * y) - ((z * 9.0) * t);
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e-175)
		tmp = (0.5 / a) * ((x * y) + (z * (t * -9.0)));
	elseif ((t_2 <= 5e-177) || ~((t_2 <= 5e+297)))
		tmp = t_1;
	else
		tmp = t_2 / (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 * N[(y * N[(0.5 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(z / N[(a / 9.0), $MachinePrecision]), $MachinePrecision] * N[(t / 2.0), $MachinePrecision]), $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)], t$95$1, If[LessEqual[t$95$2, -2e-175], N[(N[(0.5 / a), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] + N[(z * N[(t * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$2, 5e-177], N[Not[LessEqual[t$95$2, 5e+297]], $MachinePrecision]], t$95$1, N[(t$95$2 / N[(a * 2.0), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	91.1%
Target	93.2%
Herbie	97.4%

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

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -inf.0 or -2e-175 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 5e-177 or 4.9999999999999998e297 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t))

   1. Initial program 72.1%

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

   2. Applied egg-rr 80.6%

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

      [Start] 72.1	\[ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
      div-sub [=>] 67.9	\[ \color{blue}{\frac{x \cdot y}{a \cdot 2} - \frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}} \]
      sub-neg [=>] 67.9	\[ \color{blue}{\frac{x \cdot y}{a \cdot 2} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right)} \]
      div-inv [=>] 67.9	\[ \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{a \cdot 2}} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right) \]
      *-commutative [=>] 67.9	\[ \left(x \cdot y\right) \cdot \frac{1}{\color{blue}{2 \cdot a}} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right) \]
      associate-/r* [=>] 67.9	\[ \left(x \cdot y\right) \cdot \color{blue}{\frac{\frac{1}{2}}{a}} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right) \]
      metadata-eval [=>] 67.9	\[ \left(x \cdot y\right) \cdot \frac{\color{blue}{0.5}}{a} + \left(-\frac{\left(z \cdot 9\right) \cdot t}{a \cdot 2}\right) \]
      times-frac [=>] 80.6	\[ \left(x \cdot y\right) \cdot \frac{0.5}{a} + \left(-\color{blue}{\frac{z \cdot 9}{a} \cdot \frac{t}{2}}\right) \]

   3. Simplified 93.4%

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

      [Start] 80.6	\[ \left(x \cdot y\right) \cdot \frac{0.5}{a} + \left(-\frac{z \cdot 9}{a} \cdot \frac{t}{2}\right) \]
      sub-neg [<=] 80.6	\[ \color{blue}{\left(x \cdot y\right) \cdot \frac{0.5}{a} - \frac{z \cdot 9}{a} \cdot \frac{t}{2}} \]
      associate-*l* [=>] 93.4	\[ \color{blue}{x \cdot \left(y \cdot \frac{0.5}{a}\right)} - \frac{z \cdot 9}{a} \cdot \frac{t}{2} \]
      associate-/l* [=>] 93.4	\[ x \cdot \left(y \cdot \frac{0.5}{a}\right) - \color{blue}{\frac{z}{\frac{a}{9}}} \cdot \frac{t}{2} \]

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < -2e-175

   1. Initial program 99.5%

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

   2. Simplified 99.7%

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

      [Start] 99.5	\[ \frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2} \]
      sub-neg [=>] 99.5	\[ \frac{\color{blue}{x \cdot y + \left(-\left(z \cdot 9\right) \cdot t\right)}}{a \cdot 2} \]
      +-commutative [=>] 99.5	\[ \frac{\color{blue}{\left(-\left(z \cdot 9\right) \cdot t\right) + x \cdot y}}{a \cdot 2} \]
      neg-sub0 [=>] 99.5	\[ \frac{\color{blue}{\left(0 - \left(z \cdot 9\right) \cdot t\right)} + x \cdot y}{a \cdot 2} \]
      associate-+l- [=>] 99.5	\[ \frac{\color{blue}{0 - \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]
      sub0-neg [=>] 99.5	\[ \frac{\color{blue}{-\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]
      neg-mul-1 [=>] 99.5	\[ \frac{\color{blue}{-1 \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)}}{a \cdot 2} \]
      associate-/l* [=>] 99.2	\[ \color{blue}{\frac{-1}{\frac{a \cdot 2}{\left(z \cdot 9\right) \cdot t - x \cdot y}}} \]
      associate-/r/ [=>] 99.7	\[ \color{blue}{\frac{-1}{a \cdot 2} \cdot \left(\left(z \cdot 9\right) \cdot t - x \cdot y\right)} \]
      *-commutative [=>] 99.7	\[ \color{blue}{\left(\left(z \cdot 9\right) \cdot t - x \cdot y\right) \cdot \frac{-1}{a \cdot 2}} \]
      sub-neg [=>] 99.7	\[ \color{blue}{\left(\left(z \cdot 9\right) \cdot t + \left(-x \cdot y\right)\right)} \cdot \frac{-1}{a \cdot 2} \]
      +-commutative [=>] 99.7	\[ \color{blue}{\left(\left(-x \cdot y\right) + \left(z \cdot 9\right) \cdot t\right)} \cdot \frac{-1}{a \cdot 2} \]
      neg-sub0 [=>] 99.7	\[ \left(\color{blue}{\left(0 - x \cdot y\right)} + \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2} \]
      associate-+l- [=>] 99.7	\[ \color{blue}{\left(0 - \left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]
      sub0-neg [=>] 99.7	\[ \color{blue}{\left(-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right)\right)} \cdot \frac{-1}{a \cdot 2} \]
      distribute-lft-neg-out [=>] 99.7	\[ \color{blue}{-\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \frac{-1}{a \cdot 2}} \]
      distribute-rgt-neg-in [=>] 99.7	\[ \color{blue}{\left(x \cdot y - \left(z \cdot 9\right) \cdot t\right) \cdot \left(-\frac{-1}{a \cdot 2}\right)} \]

   3. Applied egg-rr 99.7%

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

      [Start] 99.7	\[ \mathsf{fma}\left(x, y, z \cdot \left(t \cdot -9\right)\right) \cdot \frac{0.5}{a} \]
      fma-udef [=>] 99.7	\[ \color{blue}{\left(x \cdot y + z \cdot \left(t \cdot -9\right)\right)} \cdot \frac{0.5}{a} \]
      +-commutative [=>] 99.7	\[ \color{blue}{\left(z \cdot \left(t \cdot -9\right) + x \cdot y\right)} \cdot \frac{0.5}{a} \]

   if 5e-177 < (-.f64 (*.f64 x y) (*.f64 (*.f64 z 9) t)) < 4.9999999999999998e297

   1. Initial program 99.6%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -\infty:\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right) - \frac{z}{\frac{a}{9}} \cdot \frac{t}{2}\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq -2 \cdot 10^{-175}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{-177} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \leq 5 \cdot 10^{+297}\right):\\ \;\;\;\;x \cdot \left(y \cdot \frac{0.5}{a}\right) - \frac{z}{\frac{a}{9}} \cdot \frac{t}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	92.6%
Cost	1613

\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+287}:\\ \;\;\;\;x \cdot \frac{y}{a + a}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-321} \lor \neg \left(x \cdot y \leq 10^{-322}\right):\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \end{array} \]

Alternative 2
Accuracy	92.7%
Cost	1612

\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+287}:\\ \;\;\;\;x \cdot \frac{y}{a + a}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-321}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-322}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \end{array} \]

Alternative 3
Accuracy	92.7%
Cost	1612

\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+287}:\\ \;\;\;\;x \cdot \frac{y}{a + a}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-321}:\\ \;\;\;\;\frac{0.5}{a} \cdot \left(x \cdot y + z \cdot \left(t \cdot -9\right)\right)\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-310}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\\ \end{array} \]

Alternative 4
Accuracy	65.5%
Cost	977

\[\begin{array}{l} t_1 := 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{if}\;x \leq -5.6 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-18}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \leq -6.9 \cdot 10^{-65} \lor \neg \left(x \leq 460\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \end{array} \]

Alternative 5
Accuracy	65.4%
Cost	977

\[\begin{array}{l} t_1 := 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-18}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-64} \lor \neg \left(x \leq 450\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-4.5}{\frac{a}{z}}\\ \end{array} \]

Alternative 6
Accuracy	64.8%
Cost	976

\[\begin{array}{l} t_1 := 0.5 \cdot \left(y \cdot \frac{x}{a}\right)\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-18}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 210:\\ \;\;\;\;t \cdot \frac{-4.5}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 7
Accuracy	52.0%
Cost	844

\[\begin{array}{l} \mathbf{if}\;y \leq 4.4 \cdot 10^{-205}:\\ \;\;\;\;-4.5 \cdot \left(z \cdot \frac{t}{a}\right)\\ \mathbf{elif}\;y \leq 10^{+81}:\\ \;\;\;\;-4.5 \cdot \frac{z \cdot t}{a}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+267}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{0}\\ \end{array} \]

Alternative 8
Accuracy	17.8%
Cost	588

\[\begin{array}{l} \mathbf{if}\;a \leq -1.85 \cdot 10^{+41}:\\ \;\;\;\;0\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{0}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+25}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{0}\\ \end{array} \]

Alternative 9
Accuracy	51.2%
Cost	580

\[\begin{array}{l} \mathbf{if}\;y \leq 3.9 \cdot 10^{+267}:\\ \;\;\;\;-4.5 \cdot \left(t \cdot \frac{z}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{0}\\ \end{array} \]

Alternative 10
Accuracy	51.1%
Cost	580

\[\begin{array}{l} \mathbf{if}\;y \leq 4.1 \cdot 10^{+267}:\\ \;\;\;\;-4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{0}\\ \end{array} \]

Alternative 11
Accuracy	10.8%
Cost	456

\[\begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-103}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+70}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 12
Accuracy	7.3%
Cost	64

\[0 \]

Reproduce

herbie shell --seed 2023160 
(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)))