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

Average Error: 20.9 → 8.6

Time: 39.6s

Precision: binary64

Cost: 6352

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{b + \left(\left(x \cdot 9\right) \cdot y + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-34}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{z} + -4 \cdot \left(a \cdot t\right)\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

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 (/ (+ b (+ (* (* x 9.0) y) (* a (* t (* z -4.0))))) (* z c))))
   (if (<= t_1 (- INFINITY))
     (* a (* t (/ -4.0 c)))
     (if (<= t_1 -2e+132)
       t_1
       (if (<= t_1 5e-34)
         (/ (+ (+ (* 9.0 (/ (* x y) z)) (* -4.0 (* a t))) (/ b z)) c)
         (if (<= t_1 2e+287) t_1 (* -4.0 (/ t (/ c a)))))))))

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 = (b + (((x * 9.0) * y) + (a * (t * (z * -4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = a * (t * (-4.0 / c));
	} else if (t_1 <= -2e+132) {
		tmp = t_1;
	} else if (t_1 <= 5e-34) {
		tmp = (((9.0 * ((x * y) / z)) + (-4.0 * (a * t))) + (b / z)) / c;
	} else if (t_1 <= 2e+287) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
}

↓

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (b + (((x * 9.0) * y) + (a * (t * (z * -4.0))))) / (z * c);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = a * (t * (-4.0 / c));
	} else if (t_1 <= -2e+132) {
		tmp = t_1;
	} else if (t_1 <= 5e-34) {
		tmp = (((9.0 * ((x * y) / z)) + (-4.0 * (a * t))) + (b / z)) / c;
	} else if (t_1 <= 2e+287) {
		tmp = t_1;
	} else {
		tmp = -4.0 * (t / (c / a));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a, b, c):
	t_1 = (b + (((x * 9.0) * y) + (a * (t * (z * -4.0))))) / (z * c)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = a * (t * (-4.0 / c))
	elif t_1 <= -2e+132:
		tmp = t_1
	elif t_1 <= 5e-34:
		tmp = (((9.0 * ((x * y) / z)) + (-4.0 * (a * t))) + (b / z)) / c
	elif t_1 <= 2e+287:
		tmp = t_1
	else:
		tmp = -4.0 * (t / (c / a))
	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(b + Float64(Float64(Float64(x * 9.0) * y) + Float64(a * Float64(t * Float64(z * -4.0))))) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(a * Float64(t * Float64(-4.0 / c)));
	elseif (t_1 <= -2e+132)
		tmp = t_1;
	elseif (t_1 <= 5e-34)
		tmp = Float64(Float64(Float64(Float64(9.0 * Float64(Float64(x * y) / z)) + Float64(-4.0 * Float64(a * t))) + Float64(b / z)) / c);
	elseif (t_1 <= 2e+287)
		tmp = t_1;
	else
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (b + (((x * 9.0) * y) + (a * (t * (z * -4.0))))) / (z * c);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = a * (t * (-4.0 / c));
	elseif (t_1 <= -2e+132)
		tmp = t_1;
	elseif (t_1 <= 5e-34)
		tmp = (((9.0 * ((x * y) / z)) + (-4.0 * (a * t))) + (b / z)) / c;
	elseif (t_1 <= 2e+287)
		tmp = t_1;
	else
		tmp = -4.0 * (t / (c / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_] := N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(b + N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] + N[(a * N[(t * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(a * N[(t * N[(-4.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+132], t$95$1, If[LessEqual[t$95$1, 5e-34], N[(N[(N[(N[(9.0 * N[(N[(x * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 2e+287], t$95$1, N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	20.9
Target	14.5
Herbie	8.6

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

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. Applied egg-rr 48.9

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

   3. Taylor expanded in z around inf 33.0

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

   4. Simplified 31.6

      \[\leadsto \color{blue}{a \cdot \frac{-4}{\frac{c}{t}}} \]
      Proof
      (*.f64 a (/.f64 -4 (/.f64 c t))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> *-commutative_binary64 (*.f64 (/.f64 -4 (/.f64 c t)) a)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 -4 (/.f64 (/.f64 c t) a))): 36 points increase in error, 32 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 -4 a) (/.f64 c t))): 26 points increase in error, 29 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 -4 (/.f64 a (/.f64 c t)))): 1 points increase in error, 1 points decrease in error
      (*.f64 -4 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 a t) c))): 56 points increase in error, 54 points decrease in error

   5. Applied egg-rr 31.6

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

   if -inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -1.99999999999999998e132 or 5.0000000000000003e-34 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 2.0000000000000002e287

   1. Initial program 0.7

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

   if -1.99999999999999998e132 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 5.0000000000000003e-34

   1. Initial program 11.5

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

   2. Simplified 2.4

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]
      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): 4 points increase in error, 4 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): 23 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 (*.f64 (*.f64 z 4) (*.f64 t a)) z))) c): 26 points increase in error, 23 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): 18 points increase in error, 2 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): 1 points increase in error, 2 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))): 44 points increase in error, 52 points decrease in error

   3. Taylor expanded in c around 0 2.4

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

   if 2.0000000000000002e287 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 59.2

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

   2. Simplified 25.8

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]
      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): 4 points increase in error, 4 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): 23 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 (*.f64 (*.f64 z 4) (*.f64 t a)) z))) c): 26 points increase in error, 23 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): 18 points increase in error, 2 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): 1 points increase in error, 2 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))): 44 points increase in error, 52 points decrease in error

   3. Taylor expanded in t around inf 30.9

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

   4. Simplified 26.0

      \[\leadsto \color{blue}{-4 \cdot \frac{t}{\frac{c}{a}}} \]
      Proof
      (*.f64 -4 (/.f64 t (/.f64 c a))): 0 points increase in error, 0 points decrease in error
      (*.f64 -4 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 t a) c))): 59 points increase in error, 48 points decrease in error
      (*.f64 -4 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 a t)) c)): 0 points increase in error, 0 points decrease in error
3. Recombined 4 regimes into one program.

4. Final simplification 8.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{b + \left(\left(x \cdot 9\right) \cdot y + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c} \leq -\infty:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;\frac{b + \left(\left(x \cdot 9\right) \cdot y + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c} \leq -2 \cdot 10^{+132}:\\ \;\;\;\;\frac{b + \left(\left(x \cdot 9\right) \cdot y + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \mathbf{elif}\;\frac{b + \left(\left(x \cdot 9\right) \cdot y + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c} \leq 5 \cdot 10^{-34}:\\ \;\;\;\;\frac{\left(9 \cdot \frac{x \cdot y}{z} + -4 \cdot \left(a \cdot t\right)\right) + \frac{b}{z}}{c}\\ \mathbf{elif}\;\frac{b + \left(\left(x \cdot 9\right) \cdot y + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c} \leq 2 \cdot 10^{+287}:\\ \;\;\;\;\frac{b + \left(\left(x \cdot 9\right) \cdot y + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternatives

Alternative 1
Error	9.7
Cost	14796

\[\begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) + -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+283}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, \frac{y}{\frac{z}{x}}, a \cdot \left(t \cdot -4\right)\right)}{c}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-111}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{elif}\;t_1 \leq 10^{+242}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+271}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z} + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \end{array} \]

Alternative 2
Error	9.6
Cost	7620

\[\begin{array}{l} t_1 := \left(x \cdot 9\right) \cdot y\\ t_2 := \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) + -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_3 := 9 \cdot \frac{x \cdot y}{z} + -4 \cdot \left(a \cdot t\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+283}:\\ \;\;\;\;\frac{\mathsf{fma}\left(9, \frac{y}{\frac{z}{x}}, a \cdot \left(t \cdot -4\right)\right)}{c}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-111}:\\ \;\;\;\;\frac{t_3 + \frac{b}{z}}{c}\\ \mathbf{elif}\;t_1 \leq 10^{+242}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+271}:\\ \;\;\;\;\frac{t_3}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \end{array} \]

Alternative 3
Error	11.2
Cost	5068

\[\begin{array}{l} t_1 := \frac{b + \left(\left(x \cdot 9\right) \cdot y + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)\right)}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \left(x \cdot \left(9 \cdot y\right) + z \cdot \left(a \cdot \left(t \cdot -4\right)\right)\right)}{c}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+287}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 4
Error	9.2
Cost	3024

\[\begin{array}{l} t_1 := 9 \cdot \frac{x \cdot y}{z} + -4 \cdot \left(a \cdot t\right)\\ t_2 := \left(x \cdot 9\right) \cdot y\\ t_3 := \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) + -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{9 \cdot y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{+110}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-111}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{elif}\;t_2 \leq 10^{+242}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+271}:\\ \;\;\;\;\frac{t_1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \end{array} \]

Alternative 5
Error	36.7
Cost	2296

\[\begin{array}{l} t_1 := -4 \cdot \frac{t}{\frac{c}{a}}\\ t_2 := 9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ t_3 := \frac{b}{z \cdot c}\\ \mathbf{if}\;b \leq -3 \cdot 10^{+123}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.599125800224817 \cdot 10^{+53}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.7571553797366962 \cdot 10^{-12}:\\ \;\;\;\;\frac{a \cdot -4}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq -3.3615329640243758 \cdot 10^{-15}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -3.5398485314701586 \cdot 10^{-161}:\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right)}{c}}{z}\\ \mathbf{elif}\;b \leq -2.0670304787456182 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.2581483386722188 \cdot 10^{-278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.479972488261769 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9.378034005526313 \cdot 10^{-55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 8.548911308376416 \cdot 10^{-48}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;b \leq 6.854075994228213 \cdot 10^{-7}:\\ \;\;\;\;\frac{y}{\frac{z}{x}} \cdot \frac{9}{c}\\ \mathbf{elif}\;b \leq 8440915703.619878:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 6.11215283005894 \cdot 10^{+28}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 6
Error	27.3
Cost	2152

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c} - \frac{t \cdot 4}{\frac{c}{a}}\\ t_2 := \frac{\frac{b}{z} + a \cdot \left(t \cdot -4\right)}{c}\\ t_3 := 9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ t_4 := 9 \cdot \frac{x \cdot y}{z}\\ \mathbf{if}\;y \leq -2.2733365473917347 \cdot 10^{-101}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.638464069061409 \cdot 10^{-210}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.60212077070575 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.44991756102685 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.99531322706214 \cdot 10^{+53}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 10^{+118}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;y \leq 10^{+170}:\\ \;\;\;\;\frac{t_4 + -4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+183}:\\ \;\;\;\;\frac{t_4 + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+215}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \end{array} \]

Alternative 7
Error	38.2
Cost	1896

\[\begin{array}{l} t_1 := a \cdot \left(t \cdot \frac{-4}{c}\right)\\ t_2 := 9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{if}\;y \leq -1.2829497415736341 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.60212077070575 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2653283508414437 \cdot 10^{-96}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;y \leq 7.44991756102685 \cdot 10^{+34}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;y \leq 9.99531322706214 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+88}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+118}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+159}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+180}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \end{array} \]

Alternative 8
Error	27.5
Cost	1888

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c} - \frac{t \cdot 4}{\frac{c}{a}}\\ t_2 := \frac{\frac{b}{z} + a \cdot \left(t \cdot -4\right)}{c}\\ t_3 := 9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{if}\;y \leq -2.2733365473917347 \cdot 10^{-101}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.638464069061409 \cdot 10^{-210}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.60212077070575 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.44991756102685 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.99531322706214 \cdot 10^{+53}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{+183}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+215}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \end{array} \]

Alternative 9
Error	19.3
Cost	1876

\[\begin{array}{l} t_1 := \frac{\left(9 \cdot \frac{x \cdot y}{z} + -4 \cdot \left(a \cdot t\right)\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;x \leq -5 \cdot 10^{+282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+240}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z}{\frac{x}{c}}}\\ \mathbf{elif}\;x \leq -3.933223562283489 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.5414415178849865 \cdot 10^{-260}:\\ \;\;\;\;\frac{b}{z \cdot c} - \frac{t \cdot 4}{\frac{c}{a}}\\ \mathbf{elif}\;x \leq 2.8150731626054623 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \end{array} \]

Alternative 10
Error	38.6
Cost	1632

\[\begin{array}{l} t_1 := a \cdot \left(t \cdot \frac{-4}{c}\right)\\ t_2 := \frac{y}{\frac{z}{x}} \cdot \frac{9}{c}\\ \mathbf{if}\;y \leq -1.2829497415736341 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.60212077070575 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.582061201570782 \cdot 10^{-96}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+88}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+118}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.05 \cdot 10^{+204}:\\ \;\;\;\;\frac{a \cdot -4}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x \cdot \left(9 \cdot y\right)}{c}}{z}\\ \end{array} \]

Alternative 11
Error	28.0
Cost	1496

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} + a \cdot \left(t \cdot -4\right)}{c}\\ t_2 := 9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ t_3 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;y \leq -2.2733365473917347 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.44991756102685 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.99531322706214 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+84}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+159}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+203}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Error	38.2
Cost	1368

\[\begin{array}{l} t_1 := a \cdot \left(t \cdot \frac{-4}{c}\right)\\ t_2 := \frac{y}{\frac{z}{x}} \cdot \frac{9}{c}\\ \mathbf{if}\;y \leq -1.2829497415736341 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.60212077070575 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.582061201570782 \cdot 10^{-96}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+88}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+118}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	35.4
Cost	1240

\[\begin{array}{l} t_1 := -4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{if}\;b \leq -3 \cdot 10^{+123}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;b \leq -7.2 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.599125800224817 \cdot 10^{+53}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;b \leq -1.7571553797366962 \cdot 10^{-12}:\\ \;\;\;\;\frac{a \cdot -4}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq -4.465205074757549 \cdot 10^{-129}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;b \leq 6.11215283005894 \cdot 10^{+28}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 14
Error	27.7
Cost	1232

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} + a \cdot \left(t \cdot -4\right)}{c}\\ t_2 := 9 \cdot \left(x \cdot \frac{y}{z \cdot c}\right)\\ \mathbf{if}\;y \leq -2.2733365473917347 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.44991756102685 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.99531322706214 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+203}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{\frac{c}{x}}}{z}\\ \end{array} \]

Alternative 15
Error	35.5
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := \frac{a \cdot -4}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.059444394935725 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.378175401097156 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.8987642656286172 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	35.5
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.059444394935725 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.378175401097156 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.8987642656286172 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Error	35.5
Cost	976

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.059444394935725 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.378175401097156 \cdot 10^{-71}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq 1.8987642656286172 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Error	35.5
Cost	976

\[\begin{array}{l} t_1 := a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.059444394935725 \cdot 10^{-22}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -9.378175401097156 \cdot 10^{-71}:\\ \;\;\;\;\frac{-4 \cdot \left(a \cdot t\right)}{c}\\ \mathbf{elif}\;t \leq 6.869645161090821 \cdot 10^{-108}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	44.8
Cost	320

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

Alternative 20
Error	43.9
Cost	320

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

Reproduce

herbie shell --seed 2022295 
(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)))