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

Average Error: 20.5 → 6.7

Time: 49.9s

Precision: binary64

Cost: 11340

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

Math

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

↓

\[\begin{array}{l} t_1 := \mathsf{fma}\left(x, 9 \cdot y, b\right)\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_3 := a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+279}:\\ \;\;\;\;\frac{t_3 + \frac{t_1}{z}}{c}\\ \mathbf{elif}\;t_2 \leq -0.002:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{t_3 + t_1 \cdot \frac{1}{z}}{c}\\ \mathbf{elif}\;t_2 \leq 10^{+307}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t_3 + y \cdot \frac{x \cdot 9}{z}}{c}\\ \end{array} \]

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 x (* 9.0 y) b))
        (t_2 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))
        (t_3 (* a (* t -4.0))))
   (if (<= t_2 -5e+279)
     (/ (+ t_3 (/ t_1 z)) c)
     (if (<= t_2 -0.002)
       t_2
       (if (<= t_2 0.0)
         (/ (+ t_3 (* t_1 (/ 1.0 z))) c)
         (if (<= t_2 1e+307) t_2 (/ (+ t_3 (* y (/ (* x 9.0) z))) c)))))))

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(x, (9.0 * y), b);
	double t_2 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double t_3 = a * (t * -4.0);
	double tmp;
	if (t_2 <= -5e+279) {
		tmp = (t_3 + (t_1 / z)) / c;
	} else if (t_2 <= -0.002) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = (t_3 + (t_1 * (1.0 / z))) / c;
	} else if (t_2 <= 1e+307) {
		tmp = t_2;
	} else {
		tmp = (t_3 + (y * ((x * 9.0) / z))) / c;
	}
	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(x, Float64(9.0 * y), b)
	t_2 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	t_3 = Float64(a * Float64(t * -4.0))
	tmp = 0.0
	if (t_2 <= -5e+279)
		tmp = Float64(Float64(t_3 + Float64(t_1 / z)) / c);
	elseif (t_2 <= -0.002)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = Float64(Float64(t_3 + Float64(t_1 * Float64(1.0 / z))) / c);
	elseif (t_2 <= 1e+307)
		tmp = t_2;
	else
		tmp = Float64(Float64(t_3 + Float64(y * Float64(Float64(x * 9.0) / z))) / c);
	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[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision]}, Block[{t$95$2 = 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]}, Block[{t$95$3 = N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+279], N[(N[(t$95$3 + N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, -0.002], t$95$2, If[LessEqual[t$95$2, 0.0], N[(N[(t$95$3 + N[(t$95$1 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, 1e+307], t$95$2, N[(N[(t$95$3 + N[(y * N[(N[(x * 9.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]]]

Target

Original	20.5
Target	14.8
Herbie	6.7

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

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -5.0000000000000002e279

   1. Initial program 50.6

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

   2. Simplified 25.8

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

      [Start] 50.6	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 51.9	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   if -5.0000000000000002e279 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -2e-3 or 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 9.99999999999999986e306

   1. Initial program 0.6

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

   if -2e-3 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 19.5

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

   2. Simplified 0.8

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

      [Start] 19.5	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 1.1	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Applied egg-rr 0.9

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

   if 9.99999999999999986e306 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 63.9

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

   2. Simplified 28.0

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

      [Start] 63.9	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 61.9	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Taylor expanded in x around inf 30.6

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

   4. Simplified 31.1

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

      [Start] 30.6	\[ \frac{a \cdot \left(t \cdot -4\right) + 9 \cdot \frac{y \cdot x}{z}}{c} \]
      associate-*r/ [=>] 30.8	\[ \frac{a \cdot \left(t \cdot -4\right) + \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z}}}{c} \]
      associate-*r* [=>] 30.8	\[ \frac{a \cdot \left(t \cdot -4\right) + \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z}}{c} \]
      *-commutative [<=] 30.8	\[ \frac{a \cdot \left(t \cdot -4\right) + \frac{\color{blue}{x \cdot \left(9 \cdot y\right)}}{z}}{c} \]
      associate-*r* [=>] 31.1	\[ \frac{a \cdot \left(t \cdot -4\right) + \frac{\color{blue}{\left(x \cdot 9\right) \cdot y}}{z}}{c} \]

   5. Applied egg-rr 20.7

      \[\leadsto \frac{a \cdot \left(t \cdot -4\right) + \color{blue}{\frac{x \cdot 9}{z} \cdot y}}{c} \]
3. Recombined 4 regimes into one program.

4. Final simplification 6.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -5 \cdot 10^{+279}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -0.002:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \mathsf{fma}\left(x, 9 \cdot y, b\right) \cdot \frac{1}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 10^{+307}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + y \cdot \frac{x \cdot 9}{z}}{c}\\ \end{array} \]

Alternatives

Alternative 1
Error	6.9
Cost	11212

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := a \cdot \left(t \cdot -4\right)\\ t_3 := \frac{t_2 + \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}}{c}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+279}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-137}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq 10^{+307}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2 + y \cdot \frac{x \cdot 9}{z}}{c}\\ \end{array} \]

Alternative 2
Error	7.4
Cost	6352

\[\begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{\left(t_1 - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_3 := a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{t_3 + \frac{9 \cdot y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-243}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{t_3 + \frac{t_1}{z}}{c}\\ \mathbf{elif}\;t_2 \leq 10^{+307}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t_3 + y \cdot \frac{x \cdot 9}{z}}{c}\\ \end{array} \]

Alternative 3
Error	6.1
Cost	6352

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{t_2 + \frac{9 \cdot y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-185}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \left(x \cdot \left(9 \cdot y\right) + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)\right)}{c}\\ \mathbf{elif}\;t_1 \leq 10^{+307}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2 + y \cdot \frac{x \cdot 9}{z}}{c}\\ \end{array} \]

Alternative 4
Error	17.2
Cost	2512

\[\begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \frac{a \cdot \left(t \cdot -4\right) + \frac{t_1}{z}}{c}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+177}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-45}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+228}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 5
Error	37.8
Cost	2424

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := -4 \cdot \frac{t}{\frac{c}{a}}\\ t_3 := 9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+200}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+182}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{+101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+55}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+17}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-16}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-119}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-119}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-288}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-203}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-50}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	36.1
Cost	2424

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ t_3 := \frac{x}{\frac{c}{9}}\\ t_4 := \frac{b}{z \cdot c}\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{+125}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-48}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-192}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-215}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-302}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-174}:\\ \;\;\;\;\frac{y}{\frac{z}{t_3}}\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-116}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;b \leq 1.2 \cdot 10^{-54}:\\ \;\;\;\;\frac{y \cdot t_3}{z}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+40}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{+80}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+83}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 7
Error	24.2
Cost	2149

\[\begin{array}{l} t_1 := \frac{a \cdot \left(t \cdot -4\right) + y \cdot \frac{x \cdot 9}{z}}{c}\\ t_2 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 230000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+213} \lor \neg \left(y \leq 3.2 \cdot 10^{+272}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{\frac{x}{\frac{c}{9}}}}\\ \end{array} \]

Alternative 8
Error	24.2
Cost	2148

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ t_2 := a \cdot \left(t \cdot -4\right)\\ t_3 := \frac{t_2 + \frac{9 \cdot y}{\frac{z}{x}}}{c}\\ t_4 := \frac{t_2 + y \cdot \frac{x \cdot 9}{z}}{c}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{-185}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-171}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-33}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 490000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+54}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+84}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+213}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+270}:\\ \;\;\;\;\frac{y}{\frac{z}{\frac{x}{\frac{c}{9}}}}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Error	36.2
Cost	2028

\[\begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ t_2 := \frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+187}:\\ \;\;\;\;\frac{\frac{a}{\frac{-0.25}{t}}}{c}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+161}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-10}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-306}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-80}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+163}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+189}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]

Alternative 10
Error	36.6
Cost	2028

\[\begin{array}{l} t_1 := 9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ t_2 := \frac{\frac{b}{c}}{z}\\ t_3 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+125}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-25}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-51}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq -2.65 \cdot 10^{-192}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-301}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-174}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-115}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 11
Error	36.5
Cost	2028

\[\begin{array}{l} t_1 := 9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ t_2 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -7.6 \cdot 10^{+125}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-22}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-51}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq -3.15 \cdot 10^{-192}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-303}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;b \leq 5.6 \cdot 10^{-174}:\\ \;\;\;\;9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;b \leq 1.92 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 12
Error	36.6
Cost	2028

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+125}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq -1.2 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.22 \cdot 10^{-23}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;b \leq -7.8 \cdot 10^{-51}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq -3.15 \cdot 10^{-189}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -5 \cdot 10^{-217}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-302}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-174}:\\ \;\;\;\;9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;b \leq 1.46 \cdot 10^{+85}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 13
Error	35.9
Cost	2028

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{+125}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-23}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-49}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-189}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{-215}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-302}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;b \leq 10^{-173}:\\ \;\;\;\;9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{-115}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-54}:\\ \;\;\;\;\frac{x \cdot y}{c} \cdot \frac{9}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 14
Error	35.8
Cost	2028

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{+125}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{+33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-20}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-49}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-189}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-216}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-301}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-174}:\\ \;\;\;\;\frac{y}{\frac{z}{\frac{x}{\frac{c}{9}}}}\\ \mathbf{elif}\;b \leq 2.9 \cdot 10^{-118}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;b \leq 1.24 \cdot 10^{-54}:\\ \;\;\;\;\frac{x \cdot y}{c} \cdot \frac{9}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 15
Error	29.1
Cost	2025

\[\begin{array}{l} t_1 := \frac{x}{\frac{c}{9}}\\ t_2 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;b \leq -6.5 \cdot 10^{-78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-127}:\\ \;\;\;\;9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ \mathbf{elif}\;b \leq -7.4 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-215}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-302}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{-174}:\\ \;\;\;\;\frac{y}{\frac{z}{t_1}}\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-115}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-58}:\\ \;\;\;\;\frac{y \cdot t_1}{z}\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+86} \lor \neg \left(b \leq 2.9 \cdot 10^{+254}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 16
Error	29.1
Cost	2024

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ t_2 := \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{if}\;b \leq -2.3 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-128}:\\ \;\;\;\;9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.45 \cdot 10^{-216}:\\ \;\;\;\;\left(x \cdot 9\right) \cdot \frac{y}{z \cdot c}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{-302}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.85 \cdot 10^{-158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-112}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 1.18 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 17
Error	19.5
Cost	1996

\[\begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+108}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-30}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+220}:\\ \;\;\;\;\frac{\frac{t_1}{z} + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 18
Error	23.3
Cost	1624

\[\begin{array}{l} t_1 := \frac{b + -4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ t_2 := \frac{\frac{\left(x \cdot 9\right) \cdot y}{z} + \frac{b}{z}}{c}\\ t_3 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;z \leq -2.65 \cdot 10^{+79}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-210}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 19
Error	14.4
Cost	1480

\[\begin{array}{l} t_1 := a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+161}:\\ \;\;\;\;\frac{t_1 + y \cdot \frac{x \cdot 9}{z}}{c}\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+25}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{9 \cdot y}{\frac{z}{x}}}{c}\\ \end{array} \]

Alternative 20
Error	34.4
Cost	976

\[\begin{array}{l} t_1 := -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ t_2 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -8.2 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.9 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 21
Error	34.4
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;b \leq -4.8 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-53}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 22
Error	34.4
Cost	976

\[\begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ t_2 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -6.4 \cdot 10^{+153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.3 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 23
Error	34.2
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{+123}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.24 \cdot 10^{-54}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 24
Error	42.0
Cost	585

\[\begin{array}{l} \mathbf{if}\;c \leq -1.35 \cdot 10^{-113} \lor \neg \left(c \leq 1.65 \cdot 10^{-75}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 25
Error	43.1
Cost	452

\[\begin{array}{l} \mathbf{if}\;y \leq 1.75 \cdot 10^{-147}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 26
Error	43.0
Cost	320

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

Reproduce

herbie shell --seed 2023073 
(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)))