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

Average Error: 20.9 → 4.3

Time: 34.2s

Precision: binary64

Cost: 12880

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{y}{\frac{z \cdot c}{x}}, -4 \cdot \frac{t}{\frac{c}{a}}\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{-120}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}}{c}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

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)))
        (t_2
         (+
          (/ b (* z c))
          (fma 9.0 (/ y (/ (* z c) x)) (* -4.0 (/ t (/ c a)))))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -5e-99)
       t_1
       (if (<= t_1 1e-120)
         (/ (+ (* a (* t -4.0)) (/ (fma x (* 9.0 y) b) z)) c)
         (if (<= t_1 5e+306) t_1 t_2))))))

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 t_2 = (b / (z * c)) + fma(9.0, (y / ((z * c) / x)), (-4.0 * (t / (c / a))));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -5e-99) {
		tmp = t_1;
	} else if (t_1 <= 1e-120) {
		tmp = ((a * (t * -4.0)) + (fma(x, (9.0 * y), b) / z)) / c;
	} else if (t_1 <= 5e+306) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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))
	t_2 = Float64(Float64(b / Float64(z * c)) + fma(9.0, Float64(y / Float64(Float64(z * c) / x)), Float64(-4.0 * Float64(t / Float64(c / a)))))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -5e-99)
		tmp = t_1;
	elseif (t_1 <= 1e-120)
		tmp = Float64(Float64(Float64(a * Float64(t * -4.0)) + Float64(fma(x, Float64(9.0 * y), b) / z)) / c);
	elseif (t_1 <= 5e+306)
		tmp = t_1;
	else
		tmp = t_2;
	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[(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$2 = N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(y / N[(N[(z * c), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -5e-99], t$95$1, If[LessEqual[t$95$1, 1e-120], N[(N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 5e+306], t$95$1, t$95$2]]]]]]

Target

Original	20.9
Target	14.8
Herbie	4.3

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -inf.0 or 4.99999999999999993e306 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 63.7

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

   2. Simplified 26.1

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

      [Start] 63.7	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 59.6	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]
      +-commutative [=>] 59.6	\[ \frac{\frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z}}{c} \]
      associate-+r- [=>] 59.6	\[ \frac{\frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z}}{c} \]
      div-sub [=>] 59.6	\[ \frac{\color{blue}{\frac{b + \left(x \cdot 9\right) \cdot y}{z} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}{z}}}{c} \]
      sub-neg [=>] 59.6	\[ \frac{\color{blue}{\frac{b + \left(x \cdot 9\right) \cdot y}{z} + \left(-\frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}{z}\right)}}{c} \]
      +-commutative [=>] 59.6	\[ \frac{\color{blue}{\left(-\frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}{z}\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}}{c} \]
      *-commutative [=>] 59.6	\[ \frac{\left(-\frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z}\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      associate-*l* [=>] 59.5	\[ \frac{\left(-\frac{a \cdot \color{blue}{\left(z \cdot \left(4 \cdot t\right)\right)}}{z}\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      associate-*r* [=>] 46.3	\[ \frac{\left(-\frac{\color{blue}{\left(a \cdot z\right) \cdot \left(4 \cdot t\right)}}{z}\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      associate-*l/ [<=] 36.7	\[ \frac{\left(-\color{blue}{\frac{a \cdot z}{z} \cdot \left(4 \cdot t\right)}\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      distribute-rgt-neg-in [=>] 36.7	\[ \frac{\color{blue}{\frac{a \cdot z}{z} \cdot \left(-4 \cdot t\right)} + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      associate-/l* [=>] 26.2	\[ \frac{\color{blue}{\frac{a}{\frac{z}{z}}} \cdot \left(-4 \cdot t\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      *-inverses [=>] 26.2	\[ \frac{\frac{a}{\color{blue}{1}} \cdot \left(-4 \cdot t\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      /-rgt-identity [=>] 26.2	\[ \frac{\color{blue}{a} \cdot \left(-4 \cdot t\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      *-commutative [=>] 26.2	\[ \frac{a \cdot \left(-\color{blue}{t \cdot 4}\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      distribute-rgt-neg-in [=>] 26.2	\[ \frac{a \cdot \color{blue}{\left(t \cdot \left(-4\right)\right)} + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      metadata-eval [=>] 26.2	\[ \frac{a \cdot \left(t \cdot \color{blue}{-4}\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      +-commutative [=>] 26.2	\[ \frac{a \cdot \left(t \cdot -4\right) + \frac{\color{blue}{\left(x \cdot 9\right) \cdot y + b}}{z}}{c} \]
      associate-*l* [=>] 26.1	\[ \frac{a \cdot \left(t \cdot -4\right) + \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z}}{c} \]
      fma-def [=>] 26.1	\[ \frac{a \cdot \left(t \cdot -4\right) + \frac{\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, b\right)}}{z}}{c} \]

   3. Taylor expanded in a around 0 31.4

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

   4. Simplified 14.1

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

      [Start] 31.4	\[ \frac{b}{c \cdot z} + \left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) \]
      *-commutative [=>] 31.4	\[ \frac{b}{\color{blue}{z \cdot c}} + \left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) \]
      +-commutative [=>] 31.4	\[ \frac{b}{z \cdot c} + \color{blue}{\left(9 \cdot \frac{y \cdot x}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]
      fma-def [=>] 31.4	\[ \frac{b}{z \cdot c} + \color{blue}{\mathsf{fma}\left(9, \frac{y \cdot x}{c \cdot z}, -4 \cdot \frac{a \cdot t}{c}\right)} \]
      associate-/l* [=>] 21.2	\[ \frac{b}{z \cdot c} + \mathsf{fma}\left(9, \color{blue}{\frac{y}{\frac{c \cdot z}{x}}}, -4 \cdot \frac{a \cdot t}{c}\right) \]
      *-commutative [=>] 21.2	\[ \frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{y}{\frac{\color{blue}{z \cdot c}}{x}}, -4 \cdot \frac{a \cdot t}{c}\right) \]
      *-commutative [=>] 21.2	\[ \frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{y}{\frac{z \cdot c}{x}}, -4 \cdot \frac{\color{blue}{t \cdot a}}{c}\right) \]
      associate-/l* [=>] 14.1	\[ \frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{y}{\frac{z \cdot c}{x}}, -4 \cdot \color{blue}{\frac{t}{\frac{c}{a}}}\right) \]

   if -inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -4.99999999999999969e-99 or 9.99999999999999979e-121 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 4.99999999999999993e306

   1. Initial program 0.8

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

   if -4.99999999999999969e-99 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 9.99999999999999979e-121

   1. Initial program 20.8

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

   2. Simplified 0.9

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

      [Start] 20.8	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 0.9	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]
      +-commutative [=>] 0.9	\[ \frac{\frac{\color{blue}{b + \left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right)}}{z}}{c} \]
      associate-+r- [=>] 0.9	\[ \frac{\frac{\color{blue}{\left(b + \left(x \cdot 9\right) \cdot y\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a}}{z}}{c} \]
      div-sub [=>] 0.9	\[ \frac{\color{blue}{\frac{b + \left(x \cdot 9\right) \cdot y}{z} - \frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}{z}}}{c} \]
      sub-neg [=>] 0.9	\[ \frac{\color{blue}{\frac{b + \left(x \cdot 9\right) \cdot y}{z} + \left(-\frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}{z}\right)}}{c} \]
      +-commutative [=>] 0.9	\[ \frac{\color{blue}{\left(-\frac{\left(\left(z \cdot 4\right) \cdot t\right) \cdot a}{z}\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}}{c} \]
      *-commutative [=>] 0.9	\[ \frac{\left(-\frac{\color{blue}{a \cdot \left(\left(z \cdot 4\right) \cdot t\right)}}{z}\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      associate-*l* [=>] 0.9	\[ \frac{\left(-\frac{a \cdot \color{blue}{\left(z \cdot \left(4 \cdot t\right)\right)}}{z}\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      associate-*r* [=>] 7.8	\[ \frac{\left(-\frac{\color{blue}{\left(a \cdot z\right) \cdot \left(4 \cdot t\right)}}{z}\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      associate-*l/ [<=] 7.8	\[ \frac{\left(-\color{blue}{\frac{a \cdot z}{z} \cdot \left(4 \cdot t\right)}\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      distribute-rgt-neg-in [=>] 7.8	\[ \frac{\color{blue}{\frac{a \cdot z}{z} \cdot \left(-4 \cdot t\right)} + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      associate-/l* [=>] 0.8	\[ \frac{\color{blue}{\frac{a}{\frac{z}{z}}} \cdot \left(-4 \cdot t\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      *-inverses [=>] 0.8	\[ \frac{\frac{a}{\color{blue}{1}} \cdot \left(-4 \cdot t\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      /-rgt-identity [=>] 0.8	\[ \frac{\color{blue}{a} \cdot \left(-4 \cdot t\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      *-commutative [=>] 0.8	\[ \frac{a \cdot \left(-\color{blue}{t \cdot 4}\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      distribute-rgt-neg-in [=>] 0.8	\[ \frac{a \cdot \color{blue}{\left(t \cdot \left(-4\right)\right)} + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      metadata-eval [=>] 0.8	\[ \frac{a \cdot \left(t \cdot \color{blue}{-4}\right) + \frac{b + \left(x \cdot 9\right) \cdot y}{z}}{c} \]
      +-commutative [=>] 0.8	\[ \frac{a \cdot \left(t \cdot -4\right) + \frac{\color{blue}{\left(x \cdot 9\right) \cdot y + b}}{z}}{c} \]
      associate-*l* [=>] 0.9	\[ \frac{a \cdot \left(t \cdot -4\right) + \frac{\color{blue}{x \cdot \left(9 \cdot y\right)} + b}{z}}{c} \]
      fma-def [=>] 0.9	\[ \frac{a \cdot \left(t \cdot -4\right) + \frac{\color{blue}{\mathsf{fma}\left(x, 9 \cdot y, b\right)}}{z}}{c} \]

3. Recombined 3 regimes into one program.

4. Final simplification 4.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -\infty:\\ \;\;\;\;\frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{y}{\frac{z \cdot c}{x}}, -4 \cdot \frac{t}{\frac{c}{a}}\right)\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -5 \cdot 10^{-99}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 10^{-120}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 5 \cdot 10^{+306}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{y}{\frac{z \cdot c}{x}}, -4 \cdot \frac{t}{\frac{c}{a}}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	7.2
Cost	11212

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{a \cdot \left(t \cdot -4\right) + \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}}{c}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+286}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]

Alternative 2
Error	8.3
Cost	6352

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-319}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]

Alternative 3
Error	7.1
Cost	6352

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-274}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \left(x \cdot \left(9 \cdot y\right) + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)\right)}{c}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]

Alternative 4
Error	7.1
Cost	6352

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;t_1 \leq -4 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-307}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \end{array} \]

Alternative 5
Error	25.1
Cost	2416

\[\begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ t_2 := b + 9 \cdot \left(x \cdot y\right)\\ t_3 := \frac{b}{z \cdot c} + -4 \cdot \frac{t \cdot a}{c}\\ t_4 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ t_5 := \frac{1}{c} \cdot \frac{t_2}{z}\\ t_6 := \frac{t_2}{z \cdot c}\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{+221}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.65:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-35}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-76}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{-111}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-160}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-180}:\\ \;\;\;\;y \cdot \frac{9}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-278}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-220}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-164}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{z}{\frac{y}{c}}}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+56}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	23.9
Cost	2020

\[\begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ t_3 := \frac{b}{z \cdot c} + -4 \cdot \frac{t \cdot a}{c}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+219}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{+139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-160}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -4.7 \cdot 10^{-180}:\\ \;\;\;\;y \cdot \frac{9}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;t \leq -1.04 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-161}:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+56}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	20.5
Cost	1876

\[\begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ t_2 := \frac{b + \left(x \cdot \left(9 \cdot y\right) + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)\right)}{z \cdot c}\\ \mathbf{if}\;t \leq -6 \cdot 10^{+224}:\\ \;\;\;\;\frac{b}{z \cdot c} + -4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-300}:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	36.0
Cost	1772

\[\begin{array}{l} t_1 := 9 \cdot \frac{x}{\frac{z}{\frac{y}{c}}}\\ t_2 := b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{if}\;b \leq -5.9 \cdot 10^{+152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-80}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-218}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-237}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-204}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 0.00086:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+173}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 9
Error	35.9
Cost	1772

\[\begin{array}{l} t_1 := 9 \cdot \frac{x}{\frac{z}{\frac{y}{c}}}\\ \mathbf{if}\;b \leq -1.5 \cdot 10^{+153}:\\ \;\;\;\;b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{-80}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq -2.4 \cdot 10^{-214}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right)\\ \mathbf{elif}\;b \leq 9.6 \cdot 10^{-237}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-204}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{-115}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 0.0075:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;b \leq 5.4 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.5 \cdot 10^{+154}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+173}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 10
Error	37.2
Cost	1764

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ t_2 := 9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ t_3 := -4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{+54}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{-147}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-240}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-73}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	37.4
Cost	1764

\[\begin{array}{l} t_1 := -4 \cdot \frac{t}{\frac{c}{a}}\\ t_2 := \frac{b}{z \cdot c}\\ t_3 := 9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{if}\;x \leq -1.65 \cdot 10^{+180}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{+170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+102}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.9 \cdot 10^{-147}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-73}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Error	37.2
Cost	1764

\[\begin{array}{l} t_1 := -4 \cdot \frac{t}{\frac{c}{a}}\\ t_2 := \frac{b}{z \cdot c}\\ \mathbf{if}\;x \leq -1.6 \cdot 10^{+180}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{+169}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+97}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.9 \cdot 10^{-147}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq -2.85 \cdot 10^{-164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-77}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 13
Error	32.0
Cost	1496

\[\begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+243}:\\ \;\;\;\;\frac{\frac{9 \cdot y}{z}}{\frac{c}{x}}\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.62 \cdot 10^{-146}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-165}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-250}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right)\\ \end{array} \]

Alternative 14
Error	19.4
Cost	969

\[\begin{array}{l} \mathbf{if}\;z \leq -6.6 \cdot 10^{-34} \lor \neg \left(z \leq 6 \cdot 10^{+33}\right):\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 15
Error	34.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;b \leq -6.6 \cdot 10^{+152}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq 0.0098:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 16
Error	34.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;b \leq -1.22 \cdot 10^{+154}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;b \leq 0.03:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 17
Error	34.7
Cost	712

\[\begin{array}{l} \mathbf{if}\;b \leq -5.9 \cdot 10^{+152}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;b \leq 0.023:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 18
Error	34.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+152}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;b \leq 4.9:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 19
Error	34.5
Cost	712

\[\begin{array}{l} \mathbf{if}\;b \leq -3.7 \cdot 10^{+153}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;b \leq 0.014:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 20
Error	43.9
Cost	452

\[\begin{array}{l} \mathbf{if}\;z \leq 4 \cdot 10^{+36}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 21
Error	43.2
Cost	452

\[\begin{array}{l} \mathbf{if}\;z \leq 10^{+64}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 22
Error	44.1
Cost	320

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

Reproduce

herbie shell --seed 2022356 
(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)))