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

Average Error: 20.4 → 4.2

Time: 35.9s

Precision: binary64

Cost: 12880

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{\frac{b}{c}}{z} + \left(\frac{x}{\frac{z \cdot c}{9 \cdot y}} + \frac{a}{\frac{c}{t}} \cdot -4\right)\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+53}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+282}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{y}{\frac{z}{\frac{x}{c}}}, -4 \cdot \left(t \cdot \frac{a}{c}\right)\right)\\ \end{array} \]

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))
     (+ (/ (/ b c) z) (+ (/ x (/ (* z c) (* 9.0 y))) (* (/ a (/ c t)) -4.0)))
     (if (<= t_1 -1e-92)
       t_1
       (if (<= t_1 2e+53)
         (/ (+ (* a (* t -4.0)) (/ (+ b (* x (* 9.0 y))) z)) c)
         (if (<= t_1 5e+282)
           t_1
           (+
            (/ b (* z c))
            (fma 9.0 (/ y (/ z (/ x c))) (* -4.0 (* t (/ a 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 = ((b / c) / z) + ((x / ((z * c) / (9.0 * y))) + ((a / (c / t)) * -4.0));
	} else if (t_1 <= -1e-92) {
		tmp = t_1;
	} else if (t_1 <= 2e+53) {
		tmp = ((a * (t * -4.0)) + ((b + (x * (9.0 * y))) / z)) / c;
	} else if (t_1 <= 5e+282) {
		tmp = t_1;
	} else {
		tmp = (b / (z * c)) + fma(9.0, (y / (z / (x / c))), (-4.0 * (t * (a / 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(Float64(Float64(b / c) / z) + Float64(Float64(x / Float64(Float64(z * c) / Float64(9.0 * y))) + Float64(Float64(a / Float64(c / t)) * -4.0)));
	elseif (t_1 <= -1e-92)
		tmp = t_1;
	elseif (t_1 <= 2e+53)
		tmp = Float64(Float64(Float64(a * Float64(t * -4.0)) + Float64(Float64(b + Float64(x * Float64(9.0 * y))) / z)) / c);
	elseif (t_1 <= 5e+282)
		tmp = t_1;
	else
		tmp = Float64(Float64(b / Float64(z * c)) + fma(9.0, Float64(y / Float64(z / Float64(x / c))), Float64(-4.0 * Float64(t * Float64(a / 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[(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[(N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision] + N[(N[(x / N[(N[(z * c), $MachinePrecision] / N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-92], t$95$1, If[LessEqual[t$95$1, 2e+53], N[(N[(N[(a * N[(t * -4.0), $MachinePrecision]), $MachinePrecision] + N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 5e+282], t$95$1, N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(y / N[(z / N[(x / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	20.4
Target	14.4
Herbie	4.2

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

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 49.7

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
      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* [=>] 63.7	\[ \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-*l* [=>] 49.7	\[ \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Taylor expanded in x around 0 30.1

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

   4. Simplified 14.6

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

      [Start] 30.1	\[ \left(\frac{b}{c \cdot z} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c} \]
      associate--l+ [=>] 30.1	\[ \color{blue}{\frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]
      associate-/r* [=>] 33.7	\[ \color{blue}{\frac{\frac{b}{c}}{z}} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]
      *-commutative [<=] 33.7	\[ \frac{\frac{b}{c}}{z} + \left(9 \cdot \frac{y \cdot x}{\color{blue}{z \cdot c}} - 4 \cdot \frac{a \cdot t}{c}\right) \]
      associate-*r/ [=>] 34.0	\[ \frac{\frac{b}{c}}{z} + \left(\color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c}} - 4 \cdot \frac{a \cdot t}{c}\right) \]
      associate-*r* [=>] 34.0	\[ \frac{\frac{b}{c}}{z} + \left(\frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - 4 \cdot \frac{a \cdot t}{c}\right) \]
      *-commutative [<=] 34.0	\[ \frac{\frac{b}{c}}{z} + \left(\frac{\color{blue}{x \cdot \left(9 \cdot y\right)}}{z \cdot c} - 4 \cdot \frac{a \cdot t}{c}\right) \]
      associate-/l* [=>] 18.9	\[ \frac{\frac{b}{c}}{z} + \left(\color{blue}{\frac{x}{\frac{z \cdot c}{9 \cdot y}}} - 4 \cdot \frac{a \cdot t}{c}\right) \]
      associate-/l* [=>] 14.6	\[ \frac{\frac{b}{c}}{z} + \left(\frac{x}{\frac{z \cdot c}{9 \cdot y}} - 4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}}\right) \]

   if -inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -9.99999999999999988e-93 or 2e53 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 4.99999999999999978e282

   1. Initial program 0.5

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

   if -9.99999999999999988e-93 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 2e53

   1. Initial program 13.8

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

   2. Simplified 1.5

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

      [Start] 13.8	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 1.8	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Applied egg-rr 1.5

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

   if 4.99999999999999978e282 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 58.7

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

   2. Simplified 27.3

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

      [Start] 58.7	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 57.7	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Taylor expanded in a around 0 29.9

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

   4. Simplified 12.6

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

      [Start] 29.9	\[ \frac{b}{c \cdot z} + \left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) \]
      *-commutative [=>] 29.9	\[ \frac{b}{\color{blue}{z \cdot c}} + \left(-4 \cdot \frac{a \cdot t}{c} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) \]
      +-commutative [=>] 29.9	\[ \frac{b}{z \cdot c} + \color{blue}{\left(9 \cdot \frac{y \cdot x}{c \cdot z} + -4 \cdot \frac{a \cdot t}{c}\right)} \]
      fma-def [=>] 29.9	\[ \frac{b}{z \cdot c} + \color{blue}{\mathsf{fma}\left(9, \frac{y \cdot x}{c \cdot z}, -4 \cdot \frac{a \cdot t}{c}\right)} \]
      associate-/l* [=>] 22.2	\[ \frac{b}{z \cdot c} + \mathsf{fma}\left(9, \color{blue}{\frac{y}{\frac{c \cdot z}{x}}}, -4 \cdot \frac{a \cdot t}{c}\right) \]
      *-commutative [=>] 22.2	\[ \frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{y}{\frac{\color{blue}{z \cdot c}}{x}}, -4 \cdot \frac{a \cdot t}{c}\right) \]
      associate-/l* [=>] 18.6	\[ \frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{y}{\color{blue}{\frac{z}{\frac{x}{c}}}}, -4 \cdot \frac{a \cdot t}{c}\right) \]
      associate-/l* [=>] 11.2	\[ \frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{y}{\frac{z}{\frac{x}{c}}}, -4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}}\right) \]
      associate-/r/ [=>] 12.6	\[ \frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{y}{\frac{z}{\frac{x}{c}}}, -4 \cdot \color{blue}{\left(\frac{a}{c} \cdot t\right)}\right) \]

3. Recombined 4 regimes into one program.

4. Final simplification 4.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -\infty:\\ \;\;\;\;\frac{\frac{b}{c}}{z} + \left(\frac{x}{\frac{z \cdot c}{9 \cdot y}} + \frac{a}{\frac{c}{t}} \cdot -4\right)\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -1 \cdot 10^{-92}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 2 \cdot 10^{+53}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 5 \cdot 10^{+282}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{y}{\frac{z}{\frac{x}{c}}}, -4 \cdot \left(t \cdot \frac{a}{c}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	3.8
Cost	6608

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{\frac{b}{c}}{z} + \left(\frac{x}{z} \cdot \frac{y}{\frac{c}{9}} + \frac{a}{\frac{c}{t}} \cdot -4\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+286}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+53}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+294}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	3.4
Cost	6608

\[\begin{array}{l} t_1 := \frac{a}{\frac{c}{t}} \cdot -4\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_3 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3 + \left(\frac{x}{\frac{z \cdot c}{9 \cdot y}} + t_1\right)\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+53}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+294}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3 + \left(\frac{x}{z} \cdot \frac{y}{\frac{c}{9}} + t_1\right)\\ \end{array} \]

Alternative 3
Error	6.8
Cost	6352

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+53}:\\ \;\;\;\;\frac{t_2 + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+294}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2 + 9 \cdot \left(y \cdot \frac{x}{z}\right)}{c}\\ \end{array} \]

Alternative 4
Error	37.9
Cost	2820

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ t_2 := \frac{a}{\frac{c}{t}} \cdot -4\\ t_3 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+124}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{+101}:\\ \;\;\;\;\frac{\frac{1}{c}}{\frac{z}{b}}\\ \mathbf{elif}\;z \leq -7.1 \cdot 10^{+59}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-79}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-149}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-234}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-297}:\\ \;\;\;\;\frac{y}{z \cdot c} \cdot \frac{x}{0.1111111111111111}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-199}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-156}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-128}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+62}:\\ \;\;\;\;\frac{-b}{\frac{c}{\frac{-1}{z}}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+153}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+199}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	37.9
Cost	2820

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ t_2 := \frac{a}{\frac{c}{t}} \cdot -4\\ t_3 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{+125}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+101}:\\ \;\;\;\;\frac{\frac{1}{c}}{\frac{z}{b}}\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{+60}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{-82}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-147}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-236}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-297}:\\ \;\;\;\;\frac{y}{z \cdot c} \cdot \frac{x}{0.1111111111111111}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-203}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 10^{-154}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-128}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.85 \cdot 10^{+63}:\\ \;\;\;\;\frac{-b}{\frac{c}{\frac{-1}{z}}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+153}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8.1 \cdot 10^{+198}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot \frac{x}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	38.5
Cost	2556

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ t_2 := \frac{a}{\frac{c}{t}} \cdot -4\\ t_3 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_4 := 9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -4 \cdot 10^{+127}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+101}:\\ \;\;\;\;\frac{\frac{1}{c}}{\frac{z}{b}}\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{+58}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-81}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{elif}\;z \leq -1.12 \cdot 10^{-147}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-239}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-300}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-128}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{-b}{\frac{c}{\frac{-1}{z}}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+153}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8.1 \cdot 10^{+198}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	38.3
Cost	2556

\[\begin{array}{l} t_1 := \frac{a}{\frac{c}{t}} \cdot -4\\ t_2 := \frac{b}{z \cdot c}\\ t_3 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{+102}:\\ \;\;\;\;\frac{\frac{1}{c}}{\frac{z}{b}}\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{+60}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-81}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-148}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-227}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-203}:\\ \;\;\;\;\frac{y}{z \cdot c} \cdot \frac{x}{0.1111111111111111}\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-154}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-128}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+62}:\\ \;\;\;\;\frac{-b}{\frac{c}{\frac{-1}{z}}}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+153}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+199}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	37.9
Cost	2292

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := \frac{b}{z \cdot c}\\ t_3 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_4 := \frac{\left(9 \cdot y\right) \cdot \frac{x}{c}}{z}\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+101}:\\ \;\;\;\;\frac{\frac{1}{c}}{\frac{z}{b}}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+59}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-82}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-236}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-297}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-277}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-128}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+153}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8.1 \cdot 10^{+198}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot \frac{x}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \end{array} \]

Alternative 9
Error	37.9
Cost	2229

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_3 := 9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -5.5 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{+102}:\\ \;\;\;\;\frac{\frac{1}{c}}{\frac{z}{b}}\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{+58}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-82}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-149}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq -1.22 \cdot 10^{-228}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-300}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-205}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-84}:\\ \;\;\;\;\frac{\frac{1}{z}}{\frac{c}{b}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-56} \lor \neg \left(z \leq 1.02 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{\frac{c}{\frac{-1}{z}}}\\ \end{array} \]

Alternative 10
Error	37.9
Cost	2229

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_3 := 9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -9.2 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{+101}:\\ \;\;\;\;\frac{\frac{1}{c}}{\frac{z}{b}}\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{+58}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-78}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-149}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-228}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-300}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-128}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-54} \lor \neg \left(z \leq 2.5 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{\frac{c}{\frac{-1}{z}}}\\ \end{array} \]

Alternative 11
Error	37.9
Cost	2229

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_3 := 9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+101}:\\ \;\;\;\;\frac{\frac{1}{c}}{\frac{z}{b}}\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+59}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-78}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-148}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-235}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.75 \cdot 10^{-300}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-128}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-54} \lor \neg \left(z \leq 1.22 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{\frac{c}{\frac{-1}{z}}}\\ \end{array} \]

Alternative 12
Error	25.8
Cost	1752

\[\begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x \cdot \frac{9}{c}\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-241}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-220}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-7}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+112}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+269}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + 9 \cdot \left(y \cdot \frac{x}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(y \cdot \frac{x}{z \cdot c}\right)\\ \end{array} \]

Alternative 13
Error	28.2
Cost	1496

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{+41}:\\ \;\;\;\;\frac{y}{z} \cdot \left(x \cdot \frac{9}{c}\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-240}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-220}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{+128}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{+226}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z}{\frac{x}{c}}}\\ \end{array} \]

Alternative 14
Error	12.7
Cost	1484

\[\begin{array}{l} t_1 := b + x \cdot \left(9 \cdot y\right)\\ t_2 := a \cdot \left(t \cdot -4\right)\\ t_3 := \frac{t_2 + \frac{t_1}{z}}{c}\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{-64}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{t_1}{z \cdot c}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+154}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2 + 9 \cdot \left(y \cdot \frac{x}{z}\right)}{c}\\ \end{array} \]

Alternative 15
Error	10.5
Cost	1484

\[\begin{array}{l} t_1 := x \cdot \left(9 \cdot y\right)\\ t_2 := a \cdot \left(t \cdot -4\right)\\ t_3 := \frac{t_2 + \frac{b + t_1}{z}}{c}\\ \mathbf{if}\;z \leq -4.9 \cdot 10^{-29}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\frac{b + \left(t_1 + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+154}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2 + 9 \cdot \left(y \cdot \frac{x}{z}\right)}{c}\\ \end{array} \]

Alternative 16
Error	26.9
Cost	1368

\[\begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+151}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8.1 \cdot 10^{+198}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot \frac{x}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \end{array} \]

Alternative 17
Error	35.9
Cost	1305

\[\begin{array}{l} t_1 := \frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{+127}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+23}:\\ \;\;\;\;\frac{\frac{1}{c}}{\frac{z}{b}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-85}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-55} \lor \neg \left(z \leq 4.6 \cdot 10^{+62}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-b}{\frac{c}{\frac{-1}{z}}}\\ \end{array} \]

Alternative 18
Error	36.1
Cost	1241

\[\begin{array}{l} t_1 := \frac{\frac{b}{z}}{c}\\ t_2 := \frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-85}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-56} \lor \neg \left(z \leq 6.5 \cdot 10^{+81}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	36.1
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{z}}{c}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_3 := \frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-70}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-83}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 20
Error	36.1
Cost	1240

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_2 := \frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{if}\;z \leq -8.2 \cdot 10^{+123}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+23}:\\ \;\;\;\;\frac{\frac{1}{c}}{\frac{z}{b}}\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-86}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+78}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 21
Error	42.8
Cost	585

\[\begin{array}{l} \mathbf{if}\;c \leq -2.6 \cdot 10^{-36} \lor \neg \left(c \leq 1.35 \cdot 10^{+200}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 22
Error	43.7
Cost	320

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

Reproduce

herbie shell --seed 2023018 
(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)))