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

Average Error: 19.6 → 6.7

Time: 55.0s

Precision: binary64

Cost: 17484

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+298}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+305}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

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)))
        (t_2 (/ (fma t (* a -4.0) (/ (fma x (* 9.0 y) b) z)) c)))
   (if (<= t_1 -5e+298)
     t_2
     (if (<= t_1 -1e+70)
       t_1
       (if (<= t_1 5e-122)
         t_2
         (if (<= t_1 4e+305) t_1 (* a (* t (/ -4.0 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 t_2 = fma(t, (a * -4.0), (fma(x, (9.0 * y), b) / z)) / c;
	double tmp;
	if (t_1 <= -5e+298) {
		tmp = t_2;
	} else if (t_1 <= -1e+70) {
		tmp = t_1;
	} else if (t_1 <= 5e-122) {
		tmp = t_2;
	} else if (t_1 <= 4e+305) {
		tmp = t_1;
	} else {
		tmp = a * (t * (-4.0 / 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))
	t_2 = Float64(fma(t, Float64(a * -4.0), Float64(fma(x, Float64(9.0 * y), b) / z)) / c)
	tmp = 0.0
	if (t_1 <= -5e+298)
		tmp = t_2;
	elseif (t_1 <= -1e+70)
		tmp = t_1;
	elseif (t_1 <= 5e-122)
		tmp = t_2;
	elseif (t_1 <= 4e+305)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(t * Float64(-4.0 / 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]}, Block[{t$95$2 = N[(N[(t * N[(a * -4.0), $MachinePrecision] + N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+298], t$95$2, If[LessEqual[t$95$1, -1e+70], t$95$1, If[LessEqual[t$95$1, 5e-122], t$95$2, If[LessEqual[t$95$1, 4e+305], t$95$1, N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	19.6
Target	14.3
Herbie	6.7

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -5.0000000000000003e298 or -1.00000000000000007e70 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 4.9999999999999999e-122

   1. Initial program 23.1

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

   2. Simplified 6.7

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]
      Proof
      (/.f64 (fma.f64 t (*.f64 a -4) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (*.f64 a (Rewrite<= metadata-eval (neg.f64 4))) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a 4))) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 a) 4)) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (Rewrite=> *-commutative_binary64 (*.f64 4 (neg.f64 a))) (/.f64 (fma.f64 x (*.f64 9 y) b) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (*.f64 4 (neg.f64 a)) (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (*.f64 9 y)) b)) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 t (*.f64 4 (neg.f64 a)) (/.f64 (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x 9) y)) b) z)) c): 2 points increase in error, 12 points decrease in error
      (/.f64 (fma.f64 t (*.f64 4 (neg.f64 a)) (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 b (*.f64 (*.f64 x 9) y))) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 t (*.f64 4 (neg.f64 a))) (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 t 4) (neg.f64 a))) (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 4 t)) (neg.f64 a)) (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (Rewrite=> distribute-rgt-neg-out_binary64 (neg.f64 (*.f64 (*.f64 4 t) a))) (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (neg.f64 (*.f64 (*.f64 4 t) a)))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite=> unsub-neg_binary64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (*.f64 4 t) a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite=> associate-*l*_binary64 (*.f64 4 (*.f64 t a)))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (Rewrite<= metadata-eval (/.f64 4 1)) (*.f64 t a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (/.f64 4 (Rewrite<= *-inverses_binary64 (/.f64 z z))) (*.f64 t a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 4 z) z)) (*.f64 t a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 z 4)) z) (*.f64 t a))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= associate-/r/_binary64 (/.f64 (*.f64 z 4) (/.f64 z (*.f64 t a))))) c): 20 points increase in error, 1 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (*.f64 z 4) (*.f64 t a)) z))) c): 24 points increase in error, 20 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (/.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 z 4) t) a)) z)) c): 19 points increase in error, 3 points decrease in error
      (/.f64 (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) (*.f64 (*.f64 (*.f64 z 4) t) a)) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (/.f64 (Rewrite<= associate-+r-_binary64 (+.f64 b (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)))) z) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b)) z) c): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r*_binary64 (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))): 51 points increase in error, 51 points decrease in error

   if -5.0000000000000003e298 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -1.00000000000000007e70 or 4.9999999999999999e-122 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 3.9999999999999998e305

   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 3.9999999999999998e305 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 63.5

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

   2. Taylor expanded in z around inf 30.8

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

   3. Simplified 23.4

      \[\leadsto \color{blue}{a \cdot \left(t \cdot \frac{-4}{c}\right)} \]
      Proof
      (*.f64 a (*.f64 t (/.f64 -4 c))): 0 points increase in error, 0 points decrease in error
      (*.f64 a (*.f64 t (/.f64 (Rewrite<= metadata-eval (neg.f64 4)) c))): 0 points increase in error, 0 points decrease in error
      (*.f64 a (*.f64 t (Rewrite<= distribute-neg-frac_binary64 (neg.f64 (/.f64 4 c))))): 0 points increase in error, 0 points decrease in error
      (*.f64 a (Rewrite<= *-commutative_binary64 (*.f64 (neg.f64 (/.f64 4 c)) t))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (neg.f64 (/.f64 4 c)) t) a)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*r*_binary64 (*.f64 (neg.f64 (/.f64 4 c)) (*.f64 t a))): 63 points increase in error, 49 points decrease in error
      (*.f64 (Rewrite=> distribute-neg-frac_binary64 (/.f64 (neg.f64 4) c)) (*.f64 t a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (Rewrite=> metadata-eval -4) c) (*.f64 t a)): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 -4 c) (Rewrite<= *-commutative_binary64 (*.f64 a t))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 -4 (*.f64 a t)) c)): 21 points increase in error, 30 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 -4 (/.f64 (*.f64 a t) c))): 0 points increase in error, 1 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 6.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -5 \cdot 10^{+298}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -1 \cdot 10^{+70}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 5 \cdot 10^{-122}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 4 \cdot 10^{+305}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	7.7
Cost	6352

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+298}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+305}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 2
Error	6.7
Cost	6352

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+298}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2.2 \cdot 10^{-262}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \left(x \cdot \left(9 \cdot y\right) + z \cdot \left(a \cdot \left(t \cdot -4\right)\right)\right)}{c}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+305}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 3
Error	6.7
Cost	6352

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+298}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;t_1 \leq -300000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-122}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) + z \cdot \left(a \cdot \left(t \cdot -4\right)\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+305}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 4
Error	38.9
Cost	2688

\[\begin{array}{l} t_1 := \frac{-4 \cdot \left(t \cdot a\right)}{c}\\ t_2 := a \cdot \frac{t \cdot -4}{c}\\ t_3 := 9 \cdot \frac{\frac{y}{z}}{\frac{c}{x}}\\ t_4 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;y \leq -1.3315517894667007 \cdot 10^{+20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.440238329187886 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.370560022145559 \cdot 10^{-158}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.9262798250003566 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.8547129842921665 \cdot 10^{-210}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;y \leq 1.3302055092561217 \cdot 10^{-241}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 1.955434981335379 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.625028808941394 \cdot 10^{-95}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 6.776862349400102 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 608091790620.2697:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 2.330049791276335 \cdot 10^{+25}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+76}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+185}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+219}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Error	37.2
Cost	2292

\[\begin{array}{l} t_1 := a \cdot \frac{t \cdot -4}{c}\\ t_2 := \frac{9 \cdot y}{c \cdot \frac{z}{x}}\\ t_3 := 9 \cdot \frac{\frac{y}{z}}{\frac{c}{x}}\\ t_4 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;y \leq -1.3315517894667007 \cdot 10^{+20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.440238329187886 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.370560022145559 \cdot 10^{-158}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.9262798250003566 \cdot 10^{-188}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;y \leq -2.8547129842921665 \cdot 10^{-210}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;y \leq 1.3302055092561217 \cdot 10^{-241}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 1.955434981335379 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.625028808941394 \cdot 10^{-95}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 6.776862349400102 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 608091790620.2697:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 2.330049791276335 \cdot 10^{+25}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+76}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	37.2
Cost	2292

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := a \cdot \frac{t \cdot -4}{c}\\ t_3 := \frac{9 \cdot y}{c \cdot \frac{z}{x}}\\ \mathbf{if}\;y \leq -1.3315517894667007 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{9}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;y \leq -7.440238329187886 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.370560022145559 \cdot 10^{-158}:\\ \;\;\;\;9 \cdot \frac{\frac{y}{z}}{\frac{c}{x}}\\ \mathbf{elif}\;y \leq -1.8523637837355967 \cdot 10^{-164}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;y \leq -2.8547129842921665 \cdot 10^{-210}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;y \leq 1.3302055092561217 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.955434981335379 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.625028808941394 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.776862349400102 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 608091790620.2697:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 2.330049791276335 \cdot 10^{+25}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+52}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+76}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	37.2
Cost	2292

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := a \cdot \frac{t \cdot -4}{c}\\ \mathbf{if}\;y \leq -1.3315517894667007 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \frac{9}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;y \leq -7.440238329187886 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.370560022145559 \cdot 10^{-158}:\\ \;\;\;\;9 \cdot \frac{\frac{y}{z}}{\frac{c}{x}}\\ \mathbf{elif}\;y \leq -1.8523637837355967 \cdot 10^{-164}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;y \leq -2.8547129842921665 \cdot 10^{-210}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;y \leq 1.3302055092561217 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.955434981335379 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.625028808941394 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.776862349400102 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 608091790620.2697:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 2.330049791276335 \cdot 10^{+25}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+52}:\\ \;\;\;\;\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+76}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot y}{c \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 8
Error	37.2
Cost	2292

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := a \cdot \frac{t \cdot -4}{c}\\ \mathbf{if}\;y \leq -1.3315517894667007 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;y \leq -7.440238329187886 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.370560022145559 \cdot 10^{-158}:\\ \;\;\;\;9 \cdot \frac{\frac{y}{z}}{\frac{c}{x}}\\ \mathbf{elif}\;y \leq -1.8523637837355967 \cdot 10^{-164}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;y \leq -2.8547129842921665 \cdot 10^{-210}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;y \leq 1.3302055092561217 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.955434981335379 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.625028808941394 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.776862349400102 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 608091790620.2697:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 2.330049791276335 \cdot 10^{+25}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+52}:\\ \;\;\;\;\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+76}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot y}{c \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 9
Error	36.2
Cost	2160

\[\begin{array}{l} t_1 := \frac{9 \cdot y}{c \cdot \frac{z}{x}}\\ t_2 := \frac{\frac{b}{c}}{z}\\ t_3 := t \cdot \frac{a \cdot -4}{c}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+133}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+109}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \mathbf{elif}\;t \leq -1.4687265609429895 \cdot 10^{+47}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t \leq -1.4736604674778383 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.468082714007008 \cdot 10^{+36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -21000000000000:\\ \;\;\;\;9 \cdot \frac{\frac{y}{z}}{\frac{c}{x}}\\ \mathbf{elif}\;t \leq -8.808899104754383 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.79344921420195 \cdot 10^{-144}:\\ \;\;\;\;x \cdot \frac{9}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;t \leq -2.5621270493195514 \cdot 10^{-211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9.39754759821627 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.642202461665761 \cdot 10^{-226}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;t \leq 1.4089714241817235 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	36.2
Cost	2160

\[\begin{array}{l} t_1 := \frac{9 \cdot y}{c \cdot \frac{z}{x}}\\ t_2 := \frac{\frac{b}{c}}{z}\\ t_3 := t \cdot \frac{a \cdot -4}{c}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+133}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+109}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \mathbf{elif}\;t \leq -1.4687265609429895 \cdot 10^{+47}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t \leq -1.4736604674778383 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.468082714007008 \cdot 10^{+36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -21000000000000:\\ \;\;\;\;9 \cdot \frac{\frac{y}{z}}{\frac{c}{x}}\\ \mathbf{elif}\;t \leq -8.808899104754383 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.79344921420195 \cdot 10^{-144}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;t \leq -2.5621270493195514 \cdot 10^{-211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9.39754759821627 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.642202461665761 \cdot 10^{-226}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;t \leq 1.4089714241817235 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 11
Error	36.2
Cost	2160

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := t \cdot \frac{a \cdot -4}{c}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+133}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+109}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \mathbf{elif}\;t \leq -1.4687265609429895 \cdot 10^{+47}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t \leq -1.4736604674778383 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.468082714007008 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -21000000000000:\\ \;\;\;\;9 \cdot \frac{\frac{y}{z}}{\frac{c}{x}}\\ \mathbf{elif}\;t \leq -8.808899104754383 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.79344921420195 \cdot 10^{-144}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;t \leq -2.5621270493195514 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.39754759821627 \cdot 10^{-278}:\\ \;\;\;\;\frac{9 \cdot y}{c \cdot \frac{z}{x}}\\ \mathbf{elif}\;t \leq 3.642202461665761 \cdot 10^{-226}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;t \leq 1.4089714241817235 \cdot 10^{-102}:\\ \;\;\;\;\frac{9 \cdot y}{\frac{z \cdot c}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	36.2
Cost	2160

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := t \cdot \frac{a \cdot -4}{c}\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+133}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{+109}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \mathbf{elif}\;t \leq -1.4687265609429895 \cdot 10^{+47}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t \leq -1.4736604674778383 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.468082714007008 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -21000000000000:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{elif}\;t \leq -8.808899104754383 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.79344921420195 \cdot 10^{-144}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{elif}\;t \leq -2.5621270493195514 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.39754759821627 \cdot 10^{-278}:\\ \;\;\;\;\frac{9 \cdot y}{c \cdot \frac{z}{x}}\\ \mathbf{elif}\;t \leq 3.642202461665761 \cdot 10^{-226}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;t \leq 1.4089714241817235 \cdot 10^{-102}:\\ \;\;\;\;\frac{9 \cdot y}{\frac{z \cdot c}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	23.5
Cost	1892

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ t_2 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;y \leq -1.3315517894667007 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;y \leq -3.0369498496774584 \cdot 10^{-34}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;y \leq -6.370560022145559 \cdot 10^{-158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.955434981335379 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8915240062351865 \cdot 10^{-124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 11687931.980519522:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{+185}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot y}{c \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 14
Error	23.3
Cost	1756

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ t_2 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;y \leq -1.3315517894667007 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;y \leq -3.0369498496774584 \cdot 10^{-34}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;y \leq -6.370560022145559 \cdot 10^{-158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.955434981335379 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8915240062351865 \cdot 10^{-124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.559048931494642 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{+188}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{\left(x \cdot 9\right) \cdot y + b}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot y}{c \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 15
Error	25.0
Cost	1496

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;y \leq -1.3315517894667007 \cdot 10^{+20}:\\ \;\;\;\;x \cdot \left(9 \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;y \leq -7.440238329187886 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;y \leq -6.370560022145559 \cdot 10^{-158}:\\ \;\;\;\;9 \cdot \frac{\frac{y}{z}}{\frac{c}{x}}\\ \mathbf{elif}\;y \leq 2.559048931494642 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+52}:\\ \;\;\;\;\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+219}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot y}{c \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 16
Error	35.4
Cost	976

\[\begin{array}{l} t_1 := t \cdot \frac{a \cdot -4}{c}\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+97}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.5541461410299066 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 0.0003973968352686732:\\ \;\;\;\;\frac{\frac{1}{c}}{\frac{z}{b}}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{\frac{c}{\frac{1}{z}}}\\ \end{array} \]

Alternative 17
Error	35.4
Cost	976

\[\begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+97}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.5541461410299066 \cdot 10^{-110}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;b \leq 0.0003973968352686732:\\ \;\;\;\;\frac{\frac{1}{c}}{\frac{z}{b}}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+90}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{\frac{c}{\frac{1}{z}}}\\ \end{array} \]

Alternative 18
Error	35.4
Cost	976

\[\begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+97}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.5541461410299066 \cdot 10^{-110}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;b \leq 0.0003973968352686732:\\ \;\;\;\;\frac{\frac{1}{c}}{\frac{z}{b}}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+90}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \end{array} \]

Alternative 19
Error	35.6
Cost	976

\[\begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+97}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.5541461410299066 \cdot 10^{-110}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;b \leq 1.1569722708082551 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{1}{c}}{\frac{z}{b}}\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+90}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \end{array} \]

Alternative 20
Error	44.4
Cost	320

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

Alternative 21
Error	43.3
Cost	320

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

Reproduce

herbie shell --seed 2022294 
(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)))