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

Average Error: 20.3 → 6.4

Time: 40.8s

Precision: binary64

Cost: 6352

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+303}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \left(9 \cdot y\right) \cdot \frac{x}{z}}{c}\\ \end{array} \]

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 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_1 (- INFINITY))
     (* -4.0 (/ t (/ c a)))
     (if (<= t_1 -5e+68)
       t_1
       (if (<= t_1 0.0)
         (* (/ (+ b (+ (* x (* 9.0 y)) (* (* t a) (* z -4.0)))) z) (/ 1.0 c))
         (if (<= t_1 4e+303)
           t_1
           (/ (+ (* a (* t -4.0)) (* (* 9.0 y) (/ x 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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = -4.0 * (t / (c / a));
	} else if (t_1 <= -5e+68) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((b + ((x * (9.0 * y)) + ((t * a) * (z * -4.0)))) / z) * (1.0 / c);
	} else if (t_1 <= 4e+303) {
		tmp = t_1;
	} else {
		tmp = ((a * (t * -4.0)) + ((9.0 * y) * (x / z))) / c;
	}
	return tmp;
}

Java

public static 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);
}

↓

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = -4.0 * (t / (c / a));
	} else if (t_1 <= -5e+68) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((b + ((x * (9.0 * y)) + ((t * a) * (z * -4.0)))) / z) * (1.0 / c);
	} else if (t_1 <= 4e+303) {
		tmp = t_1;
	} else {
		tmp = ((a * (t * -4.0)) + ((9.0 * y) * (x / z))) / c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

↓

def code(x, y, z, t, a, b, c):
	t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = -4.0 * (t / (c / a))
	elif t_1 <= -5e+68:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = ((b + ((x * (9.0 * y)) + ((t * a) * (z * -4.0)))) / z) * (1.0 / c)
	elif t_1 <= 4e+303:
		tmp = t_1
	else:
		tmp = ((a * (t * -4.0)) + ((9.0 * y) * (x / 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 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	elseif (t_1 <= -5e+68)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) + Float64(Float64(t * a) * Float64(z * -4.0)))) / z) * Float64(1.0 / c));
	elseif (t_1 <= 4e+303)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(a * Float64(t * -4.0)) + Float64(Float64(9.0 * y) * Float64(x / z))) / c);
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

↓

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = -4.0 * (t / (c / a));
	elseif (t_1 <= -5e+68)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = ((b + ((x * (9.0 * y)) + ((t * a) * (z * -4.0)))) / z) * (1.0 / c);
	elseif (t_1 <= 4e+303)
		tmp = t_1;
	else
		tmp = ((a * (t * -4.0)) + ((9.0 * y) * (x / z))) / c;
	end
	tmp_2 = 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[(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]}, If[LessEqual[t$95$1, (-Infinity)], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e+68], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] + N[(N[(t * a), $MachinePrecision] * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+303], t$95$1, N[(N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(9.0 * y), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]]]]

Target

Original	20.3
Target	14.8
Herbie	6.4

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

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -inf.0

   1. Initial program 64.0

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

   2. Simplified 49.2

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

      [Start] 64.0	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-*l* [=>] 63.8	\[ \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-*l* [=>] 49.2	\[ \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Taylor expanded in x around 0 63.5

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

   4. Simplified 50.3

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

      [Start] 63.5	\[ \frac{-4 \cdot \left(a \cdot \left(t \cdot z\right)\right) + b}{z \cdot c} \]
      *-commutative [=>] 63.5	\[ \frac{\color{blue}{\left(a \cdot \left(t \cdot z\right)\right) \cdot -4} + b}{z \cdot c} \]
      associate-*r* [=>] 50.3	\[ \frac{\color{blue}{\left(\left(a \cdot t\right) \cdot z\right)} \cdot -4 + b}{z \cdot c} \]

   5. Taylor expanded in a around inf 32.9

      \[\leadsto \color{blue}{-4 \cdot \frac{a \cdot t}{c}} \]

   6. Simplified 28.2

      \[\leadsto \color{blue}{-4 \cdot \frac{t}{\frac{c}{a}}} \]
      Proof

      [Start] 32.9	\[ -4 \cdot \frac{a \cdot t}{c} \]
      *-commutative [=>] 32.9	\[ -4 \cdot \frac{\color{blue}{t \cdot a}}{c} \]
      associate-/l* [=>] 28.2	\[ -4 \cdot \color{blue}{\frac{t}{\frac{c}{a}}} \]

   if -inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -5.0000000000000004e68 or 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 4e303

   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 -5.0000000000000004e68 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 16.7

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

   2. Applied egg-rr 1.5

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

   if 4e303 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 62.7

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

   2. Simplified 26.8

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

      [Start] 62.7	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 60.9	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Taylor expanded in x around inf 30.1

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

   4. Simplified 20.3

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

      [Start] 30.1	\[ \frac{a \cdot \left(t \cdot -4\right) + 9 \cdot \frac{y \cdot x}{z}}{c} \]
      associate-*r/ [=>] 30.2	\[ \frac{a \cdot \left(t \cdot -4\right) + \color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z}}}{c} \]
      associate-*r* [=>] 30.2	\[ \frac{a \cdot \left(t \cdot -4\right) + \frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z}}{c} \]
      *-commutative [<=] 30.2	\[ \frac{a \cdot \left(t \cdot -4\right) + \frac{\color{blue}{x \cdot \left(9 \cdot y\right)}}{z}}{c} \]
      associate-/l* [=>] 20.3	\[ \frac{a \cdot \left(t \cdot -4\right) + \color{blue}{\frac{x}{\frac{z}{9 \cdot y}}}}{c} \]
      associate-/r/ [=>] 20.3	\[ \frac{a \cdot \left(t \cdot -4\right) + \color{blue}{\frac{x}{z} \cdot \left(9 \cdot y\right)}}{c} \]

3. Recombined 4 regimes into one program.

4. Final simplification 6.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -\infty:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -5 \cdot 10^{+68}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 4 \cdot 10^{+303}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \left(9 \cdot y\right) \cdot \frac{x}{z}}{c}\\ \end{array} \]

Alternatives

Alternative 1
Error	6.9
Cost	17484

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{+68}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} + \left(\frac{x}{\frac{z \cdot c}{9 \cdot y}} + -4 \cdot \frac{a}{\frac{c}{t}}\right)\\ \end{array} \]

Alternative 2
Error	6.9
Cost	11212

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{+68}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} + \left(\frac{x}{\frac{z \cdot c}{9 \cdot y}} + -4 \cdot \frac{a}{\frac{c}{t}}\right)\\ \end{array} \]

Alternative 3
Error	8.3
Cost	6352

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+303}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \left(9 \cdot y\right) \cdot \frac{x}{z}}{c}\\ \end{array} \]

Alternative 4
Error	6.4
Cost	6352

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \left(x \cdot \left(9 \cdot y\right) + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)\right)}{c}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+303}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \left(9 \cdot y\right) \cdot \frac{x}{z}}{c}\\ \end{array} \]

Alternative 5
Error	6.7
Cost	5324

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5000:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} + \left(\frac{x}{\frac{z \cdot c}{9 \cdot y}} + -4 \cdot \frac{a}{\frac{c}{t}}\right)\\ \end{array} \]

Alternative 6
Error	24.8
Cost	2024

\[\begin{array}{l} t_1 := b + 9 \cdot \left(x \cdot y\right)\\ t_2 := \frac{\frac{t_1}{z}}{c}\\ t_3 := \frac{t_1}{z \cdot c}\\ t_4 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;a \leq -4.8 \cdot 10^{-180}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-248}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{-114}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-44}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.12 \cdot 10^{+64}:\\ \;\;\;\;\frac{b + -4 \cdot \left(z \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.85 \cdot 10^{+93}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+153}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 7
Error	35.7
Cost	1504

\[\begin{array}{l} t_1 := \frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ t_2 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;a \leq -3.1 \cdot 10^{-177}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-291}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{-187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-103}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;a \leq 2.85 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-41}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;a \leq 1450000000:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 8
Error	35.8
Cost	1504

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{-177}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-281}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-100}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{y}{c} \cdot \frac{x \cdot 9}{z}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-43}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;a \leq 370000:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 9
Error	35.8
Cost	1504

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{-177}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-291}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-102}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{y}{c} \cdot \frac{x \cdot 9}{z}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-42}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;a \leq 680000000:\\ \;\;\;\;\frac{x}{\frac{z}{y} \cdot \frac{c}{9}}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 10
Error	35.7
Cost	1504

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{-177}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;a \leq -1.16 \cdot 10^{-281}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-103}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{c} \cdot \frac{x \cdot 9}{z}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-42}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;a \leq 66000:\\ \;\;\;\;\frac{x}{\frac{z \cdot c}{9 \cdot y}}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 11
Error	35.8
Cost	1504

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{-177}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-292}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-103}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;a \leq 1.28 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{c} \cdot \frac{x \cdot 9}{z}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;a \leq 235000:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot \frac{y}{z}\right)}{c}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 12
Error	35.8
Cost	1504

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{-178}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-295}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{elif}\;a \leq 4.25 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-103}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-71}:\\ \;\;\;\;\frac{y}{c} \cdot \frac{x \cdot 9}{z}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-41}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;a \leq 690000:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 13
Error	36.2
Cost	1500

\[\begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-177}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-279}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9}{\frac{c}{y}}\\ \mathbf{elif}\;a \leq 4.55 \cdot 10^{-187}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-104}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-71}:\\ \;\;\;\;\frac{y}{c} \cdot \frac{x \cdot 9}{z}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-42}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+35}:\\ \;\;\;\;\frac{x \cdot y}{\frac{z \cdot c}{9}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 14
Error	19.1
Cost	1484

\[\begin{array}{l} t_1 := 9 \cdot \left(x \cdot y\right)\\ t_2 := -4 \cdot \left(a \cdot \left(z \cdot t\right)\right)\\ t_3 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+175}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \left(9 \cdot y\right) \cdot \frac{x}{z}}{c}\\ \mathbf{elif}\;z \leq -63000000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-50}:\\ \;\;\;\;\frac{t_1 + t_2}{z \cdot c}\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-134}:\\ \;\;\;\;\frac{b + t_2}{z \cdot c}\\ \mathbf{elif}\;z \leq 31000:\\ \;\;\;\;\frac{b + t_1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 15
Error	13.9
Cost	1480

\[\begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+174}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \left(9 \cdot y\right) \cdot \frac{x}{z}}{c}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \end{array} \]

Alternative 16
Error	26.8
Cost	1364

\[\begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+185}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{+127}:\\ \;\;\;\;\frac{-4}{\frac{\frac{-c}{a}}{-t}}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+95}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 1900000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 17
Error	19.1
Cost	1364

\[\begin{array}{l} t_1 := \frac{a \cdot \left(t \cdot -4\right) + \left(9 \cdot y\right) \cdot \frac{x}{z}}{c}\\ t_2 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -67000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.1 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-134}:\\ \;\;\;\;\frac{b + -4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 470000:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Error	35.0
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := -4 \cdot \frac{t}{\frac{c}{a}}\\ t_3 := a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{-198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-171}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 19
Error	19.5
Cost	1233

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;z \leq -3.05 \cdot 10^{+211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+175}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;z \leq -0.00225 \lor \neg \left(z \leq 23000\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 20
Error	35.1
Cost	1108

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;a \leq -1.65 \cdot 10^{-178}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;a \leq -1.4 \cdot 10^{-291}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 21
Error	35.7
Cost	976

\[\begin{array}{l} t_1 := -4 \cdot \frac{t}{\frac{c}{a}}\\ t_2 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;b \leq -2.85 \cdot 10^{+137}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 10^{+79}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 22
Error	35.0
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;a \leq -9 \cdot 10^{-198}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.32 \cdot 10^{-114}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 23
Error	34.9
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{-198}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-115}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 24
Error	34.9
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{-198}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-114}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 25
Error	34.9
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;a \leq -1.6 \cdot 10^{-198}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-114}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 26
Error	43.1
Cost	320

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

Alternative 27
Error	43.3
Cost	320

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

Reproduce

herbie shell --seed 2023023 
(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)))