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

Percentage Accurate: 78.3% → 91.4%

Time: 18.1s

Precision: binary64

Cost: 20360

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

• 36.3% of points produce a very large (infinite) output. You may want to add a precondition.

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]

Math

\[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

↓

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{t_1}{c}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+27}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, t \cdot \left(z \cdot -4\right), b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{c}{t_1}\right)}^{-1}\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

↓

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (fma t (* a -4.0) (/ (fma x (* 9.0 y) b) z))))
   (if (<= z -9.5e-62)
     (/ t_1 c)
     (if (<= z 3e+27)
       (/ (fma x (* 9.0 y) (fma a (* t (* z -4.0)) b)) (* z c))
       (pow (/ c t_1) -1.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

↓

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = fma(t, (a * -4.0), (fma(x, (9.0 * y), b) / z));
	double tmp;
	if (z <= -9.5e-62) {
		tmp = t_1 / c;
	} else if (z <= 3e+27) {
		tmp = fma(x, (9.0 * y), fma(a, (t * (z * -4.0)), b)) / (z * c);
	} else {
		tmp = pow((c / t_1), -1.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

↓

function code(x, y, z, t, a, b, c)
	t_1 = fma(t, Float64(a * -4.0), Float64(fma(x, Float64(9.0 * y), b) / z))
	tmp = 0.0
	if (z <= -9.5e-62)
		tmp = Float64(t_1 / c);
	elseif (z <= 3e+27)
		tmp = Float64(fma(x, Float64(9.0 * y), fma(a, Float64(t * Float64(z * -4.0)), b)) / Float64(z * c));
	else
		tmp = Float64(c / t_1) ^ -1.0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(t * N[(a * -4.0), $MachinePrecision] + N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e-62], N[(t$95$1 / c), $MachinePrecision], If[LessEqual[z, 3e+27], N[(N[(x * N[(9.0 * y), $MachinePrecision] + N[(a * N[(t * N[(z * -4.0), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[Power[N[(c / t$95$1), $MachinePrecision], -1.0], $MachinePrecision]]]]

Target

Original	78.3%
Target	80.2%
Herbie	91.4%

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < 0:\\ \;\;\;\;\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} < 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if z < -9.49999999999999951e-62

   1. Initial program 71.3%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Simplified 88.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]
      Step-by-step derivation

      [Start] 71.3%	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 75.9%	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   if -9.49999999999999951e-62 < z < 2.99999999999999976e27

   1. Initial program 96.8%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Simplified 96.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, t \cdot \left(z \cdot -4\right), b\right)\right)}{z \cdot c}} \]
      Step-by-step derivation

      [Start] 96.8%	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-+l- [=>] 96.8%	\[ \frac{\color{blue}{\left(x \cdot 9\right) \cdot y - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}}{z \cdot c} \]
      associate-*l* [=>] 96.8%	\[ \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)}{z \cdot c} \]
      fma-neg [=>] 96.8%	\[ \frac{\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, -\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a - b\right)\right)}}{z \cdot c} \]
      sub-neg [=>] 96.8%	\[ \frac{\mathsf{fma}\left(x, 9 \cdot y, -\color{blue}{\left(\left(\left(z \cdot 4\right) \cdot t\right) \cdot a + \left(-b\right)\right)}\right)}{z \cdot c} \]
      distribute-neg-in [=>] 96.8%	\[ \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\left(-\left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + \left(-\left(-b\right)\right)}\right)}{z \cdot c} \]
      *-commutative [=>] 96.8%	\[ \frac{\mathsf{fma}\left(x, 9 \cdot y, \left(-\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}\right) + \left(-\left(-b\right)\right)\right)}{z \cdot c} \]
      distribute-rgt-neg-in [=>] 96.8%	\[ \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{a \cdot \left(-\left(z \cdot 4\right) \cdot t\right)} + \left(-\left(-b\right)\right)\right)}{z \cdot c} \]
      fma-def [=>] 96.8%	\[ \frac{\mathsf{fma}\left(x, 9 \cdot y, \color{blue}{\mathsf{fma}\left(a, -\left(z \cdot 4\right) \cdot t, -\left(-b\right)\right)}\right)}{z \cdot c} \]
      *-commutative [=>] 96.8%	\[ \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, -\color{blue}{t \cdot \left(z \cdot 4\right)}, -\left(-b\right)\right)\right)}{z \cdot c} \]
      distribute-rgt-neg-in [=>] 96.8%	\[ \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, \color{blue}{t \cdot \left(-z \cdot 4\right)}, -\left(-b\right)\right)\right)}{z \cdot c} \]
      distribute-rgt-neg-in [=>] 96.8%	\[ \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, t \cdot \color{blue}{\left(z \cdot \left(-4\right)\right)}, -\left(-b\right)\right)\right)}{z \cdot c} \]
      metadata-eval [=>] 96.8%	\[ \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, t \cdot \left(z \cdot \color{blue}{-4}\right), -\left(-b\right)\right)\right)}{z \cdot c} \]
      remove-double-neg [=>] 96.8%	\[ \frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, t \cdot \left(z \cdot -4\right), \color{blue}{b}\right)\right)}{z \cdot c} \]

   if 2.99999999999999976e27 < z

   1. Initial program 61.7%

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]

   2. Simplified 83.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]
      Step-by-step derivation

      [Start] 61.7%	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 66.6%	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Applied egg-rr 83.9%

      \[\leadsto \color{blue}{{\left(\frac{c}{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}\right)}^{-1}} \]
      Step-by-step derivation

      [Start] 83.8%	\[ \frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c} \]
      clear-num [=>] 83.9%	\[ \color{blue}{\frac{1}{\frac{c}{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}}} \]
      fma-udef [=>] 83.9%	\[ \frac{1}{\frac{c}{\color{blue}{t \cdot \left(a \cdot -4\right) + \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}}}} \]
      +-commutative [<=] 83.9%	\[ \frac{1}{\frac{c}{\color{blue}{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}}} \]
      inv-pow [=>] 83.9%	\[ \color{blue}{{\left(\frac{c}{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}\right)}^{-1}} \]
      +-commutative [=>] 83.9%	\[ {\left(\frac{c}{\color{blue}{t \cdot \left(a \cdot -4\right) + \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}}}\right)}^{-1} \]
      fma-udef [<=] 83.9%	\[ {\left(\frac{c}{\color{blue}{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}}\right)}^{-1} \]

3. Recombined 3 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+27}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, t \cdot \left(z \cdot -4\right), b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{c}{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}\right)}^{-1}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	91.4%
Cost	20360

\[\begin{array}{l} t_1 := \mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{t_1}{c}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+27}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, t \cdot \left(z \cdot -4\right), b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;{\left(\frac{c}{t_1}\right)}^{-1}\\ \end{array} \]

Alternative 2
Accuracy	91.5%
Cost	14088

\[\begin{array}{l} t_1 := \mathsf{fma}\left(x, 9 \cdot y, b\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{-61}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{t_1}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 25000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, t \cdot \left(z \cdot -4\right), b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(\frac{z}{t_1}\right)}^{-1} + t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]

Alternative 3
Accuracy	91.5%
Cost	14024

\[\begin{array}{l} t_1 := \mathsf{fma}\left(x, 9 \cdot y, b\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{-62}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{t_1}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 22500000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, 9 \cdot y, \mathsf{fma}\left(a, t \cdot \left(z \cdot -4\right), b\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + t_1 \cdot \frac{1}{z}}{c}\\ \end{array} \]

Alternative 4
Accuracy	90.7%
Cost	13764

\[\begin{array}{l} t_1 := \mathsf{fma}\left(x, 9 \cdot y, b\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{-54}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{t_1}{z}\right)}{c}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+93}:\\ \;\;\;\;{\left(\frac{z \cdot c}{b + \left(x \cdot \left(9 \cdot y\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + t_1 \cdot \frac{1}{z}}{c}\\ \end{array} \]

Alternative 5
Accuracy	90.7%
Cost	7944

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \mathsf{fma}\left(x, 9 \cdot y, b\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{-52}:\\ \;\;\;\;\frac{\frac{t_2}{z} + t_1}{c}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+93}:\\ \;\;\;\;{\left(\frac{z \cdot c}{b + \left(x \cdot \left(9 \cdot y\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + t_2 \cdot \frac{1}{z}}{c}\\ \end{array} \]

Alternative 6
Accuracy	91.1%
Cost	7752

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \mathsf{fma}\left(x, 9 \cdot y, b\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{-60}:\\ \;\;\;\;\frac{\frac{t_2}{z} + t_1}{c}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-96}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + t_2 \cdot \frac{1}{z}}{c}\\ \end{array} \]

Alternative 7
Accuracy	91.2%
Cost	7625

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{-60} \lor \neg \left(z \leq 1.25 \cdot 10^{-98}\right):\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 8
Accuracy	68.8%
Cost	1744

\[\begin{array}{l} t_1 := 9 \cdot \frac{\frac{y}{\frac{c}{x}}}{z}\\ \mathbf{if}\;x \cdot 9 \leq -1 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot 9 \leq -5 \cdot 10^{+38}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{z \cdot c}\\ \mathbf{elif}\;x \cdot 9 \leq -2 \cdot 10^{-21}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;x \cdot 9 \leq 10^{-61}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	73.2%
Cost	1620

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{t_1 + 9 \cdot \frac{x \cdot y}{z}}{c}\\ t_3 := -4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{z \cdot c}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+37}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-19}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-74}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+99}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Accuracy	83.1%
Cost	1481

\[\begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{+122} \lor \neg \left(z \leq 1.62 \cdot 10^{+124}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 11
Accuracy	84.3%
Cost	1481

\[\begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+124} \lor \neg \left(z \leq 2.9 \cdot 10^{+122}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}} + \frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(y \cdot \left(x \cdot 9\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 12
Accuracy	49.6%
Cost	1108

\[\begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+76}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-132}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-208}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-225}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;t \leq 10^{-98}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a}{\frac{c}{-4}}\\ \end{array} \]

Alternative 13
Accuracy	49.7%
Cost	1108

\[\begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+76}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-169}:\\ \;\;\;\;9 \cdot \frac{\frac{y}{\frac{c}{x}}}{z}\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-209}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-223}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-99}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a}{\frac{c}{-4}}\\ \end{array} \]

Alternative 14
Accuracy	64.1%
Cost	968

\[\begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+120}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{-69}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a}{\frac{c}{-4}}\\ \end{array} \]

Alternative 15
Accuracy	71.6%
Cost	968

\[\begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-67}:\\ \;\;\;\;9 \cdot \frac{\frac{y}{\frac{c}{x}}}{z}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+75}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 16
Accuracy	49.4%
Cost	844

\[\begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{+76}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-129}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-103}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a}{\frac{c}{-4}}\\ \end{array} \]

Alternative 17
Accuracy	50.5%
Cost	713

\[\begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-71} \lor \neg \left(t \leq 2.4 \cdot 10^{-31}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 18
Accuracy	50.0%
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-71}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-98}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a}{\frac{c}{-4}}\\ \end{array} \]

Alternative 19
Accuracy	34.7%
Cost	320

\[\frac{b}{z \cdot c} \]

Reproduce

herbie shell --seed 2023165 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))