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

Average Error: 19.8 → 4.5

Time: 42.8s

Precision: binary64

Cost: 19152

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}\\ t_2 := \mathsf{fma}\left(9, \frac{y}{c \cdot \frac{z}{x}}, \mathsf{fma}\left(-4, \frac{t}{\frac{c}{a}}, \frac{b}{z \cdot c}\right)\right)\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+292}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 500000000000:\\ \;\;\;\;\frac{\frac{b}{z} + \left(\frac{9}{\frac{z}{x \cdot y}} + -4 \cdot \left(t \cdot a\right)\right)}{c}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))

↓

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (+ (* (* x 9.0) y) (* a (* t (* z -4.0)))) b) (* z c)))
        (t_2
         (fma 9.0 (/ y (* c (/ z x))) (fma -4.0 (/ t (/ c a)) (/ b (* z c))))))
   (if (<= t_1 -2e+292)
     t_2
     (if (<= t_1 -5e-220)
       t_1
       (if (<= t_1 500000000000.0)
         (/ (+ (/ b z) (+ (/ 9.0 (/ z (* x y))) (* -4.0 (* t a)))) c)
         (if (<= t_1 5e+216) t_1 t_2))))))

C

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

↓

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) + (a * (t * (z * -4.0)))) + b) / (z * c);
	double t_2 = fma(9.0, (y / (c * (z / x))), fma(-4.0, (t / (c / a)), (b / (z * c))));
	double tmp;
	if (t_1 <= -2e+292) {
		tmp = t_2;
	} else if (t_1 <= -5e-220) {
		tmp = t_1;
	} else if (t_1 <= 500000000000.0) {
		tmp = ((b / z) + ((9.0 / (z / (x * y))) + (-4.0 * (t * a)))) / c;
	} else if (t_1 <= 5e+216) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c)
	return Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
end

↓

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) + Float64(a * Float64(t * Float64(z * -4.0)))) + b) / Float64(z * c))
	t_2 = fma(9.0, Float64(y / Float64(c * Float64(z / x))), fma(-4.0, Float64(t / Float64(c / a)), Float64(b / Float64(z * c))))
	tmp = 0.0
	if (t_1 <= -2e+292)
		tmp = t_2;
	elseif (t_1 <= -5e-220)
		tmp = t_1;
	elseif (t_1 <= 500000000000.0)
		tmp = Float64(Float64(Float64(b / z) + Float64(Float64(9.0 / Float64(z / Float64(x * y))) + Float64(-4.0 * Float64(t * a)))) / c);
	elseif (t_1 <= 5e+216)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] + N[(a * N[(t * N[(z * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(9.0 * N[(y / N[(c * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision] + N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+292], t$95$2, If[LessEqual[t$95$1, -5e-220], t$95$1, If[LessEqual[t$95$1, 500000000000.0], N[(N[(N[(b / z), $MachinePrecision] + N[(N[(9.0 / N[(z / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 5e+216], t$95$1, t$95$2]]]]]]

Target

Original	19.8
Target	14.1
Herbie	4.5

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

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)) < -2e292 or 4.9999999999999998e216 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 48.8

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

   2. Simplified 25.1

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]
      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): 2 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): 5 points increase in error, 8 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): 2 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): 24 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): 20 points increase in error, 25 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): 29 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): 0 points increase in error, 1 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))): 42 points increase in error, 41 points decrease in error

   3. Taylor expanded in t around 0 24.4

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

   4. Simplified 13.3

      \[\leadsto \color{blue}{\mathsf{fma}\left(9, \frac{y}{\frac{z}{\frac{x}{c}}}, \mathsf{fma}\left(-4, \frac{t}{\frac{c}{a}}, \frac{b}{z \cdot c}\right)\right)} \]
      Proof
      (fma.f64 9 (/.f64 y (/.f64 z (/.f64 x c))) (fma.f64 -4 (/.f64 t (/.f64 c a)) (/.f64 b (*.f64 z c)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 9 (/.f64 y (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 z c) x))) (fma.f64 -4 (/.f64 t (/.f64 c a)) (/.f64 b (*.f64 z c)))): 17 points increase in error, 18 points decrease in error
      (fma.f64 9 (/.f64 y (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 c z)) x)) (fma.f64 -4 (/.f64 t (/.f64 c a)) (/.f64 b (*.f64 z c)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 9 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y x) (*.f64 c z))) (fma.f64 -4 (/.f64 t (/.f64 c a)) (/.f64 b (*.f64 z c)))): 23 points increase in error, 14 points decrease in error
      (fma.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)) (fma.f64 -4 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 t a) c)) (/.f64 b (*.f64 z c)))): 24 points increase in error, 31 points decrease in error
      (fma.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)) (fma.f64 -4 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 a t)) c) (/.f64 b (*.f64 z c)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)) (fma.f64 -4 (/.f64 (*.f64 a t) c) (/.f64 b (Rewrite<= *-commutative_binary64 (*.f64 c z))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 -4 (/.f64 (*.f64 a t) c)) (/.f64 b (*.f64 c z))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)) (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 -4 (/.f64 (*.f64 a t) c))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z))) (+.f64 (/.f64 b (*.f64 c z)) (*.f64 -4 (/.f64 (*.f64 a t) c))))): 5 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 -4 (/.f64 (*.f64 a t) c))) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+r+_binary64 (+.f64 (/.f64 b (*.f64 c z)) (+.f64 (*.f64 -4 (/.f64 (*.f64 a t) c)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))))): 0 points increase in error, 0 points decrease in error

   5. Applied egg-rr 12.4

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

   if -2e292 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -5.0000000000000002e-220 or 5e11 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 4.9999999999999998e216

   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 -5.0000000000000002e-220 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 5e11

   1. Initial program 17.2

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

   2. Simplified 1.2

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]
      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): 2 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): 5 points increase in error, 8 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): 2 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): 24 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): 20 points increase in error, 25 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): 29 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): 0 points increase in error, 1 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))): 42 points increase in error, 41 points decrease in error

   3. Taylor expanded in c around 0 1.1

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

   4. Applied egg-rr 1.1

      \[\leadsto \frac{\frac{b}{z} + \left(\color{blue}{\frac{9}{\frac{z}{y \cdot x}}} + -4 \cdot \left(a \cdot t\right)\right)}{c} \]
3. Recombined 3 regimes into one program.

4. Final simplification 4.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c} \leq -2 \cdot 10^{+292}:\\ \;\;\;\;\mathsf{fma}\left(9, \frac{y}{c \cdot \frac{z}{x}}, \mathsf{fma}\left(-4, \frac{t}{\frac{c}{a}}, \frac{b}{z \cdot c}\right)\right)\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c} \leq -5 \cdot 10^{-220}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c} \leq 500000000000:\\ \;\;\;\;\frac{\frac{b}{z} + \left(\frac{9}{\frac{z}{x \cdot y}} + -4 \cdot \left(t \cdot a\right)\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c} \leq 5 \cdot 10^{+216}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(9, \frac{y}{c \cdot \frac{z}{x}}, \mathsf{fma}\left(-4, \frac{t}{\frac{c}{a}}, \frac{b}{z \cdot c}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	5.5
Cost	15236

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;{\left(\frac{c}{\frac{b}{z} + \mathsf{fma}\left(-4, t \cdot a, x \cdot \frac{y}{\frac{z}{9}}\right)}\right)}^{-1}\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-220}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 500000000000:\\ \;\;\;\;\frac{\frac{b}{z} + \left(\frac{9}{\frac{z}{x \cdot y}} + t_1\right)}{c}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+265}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + \left(t_1 + 9 \cdot \frac{y}{\frac{z}{x}}\right)}{c}\\ \end{array} \]

Alternative 2
Error	5.5
Cost	6352

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y + a \cdot \left(t \cdot \left(z \cdot -4\right)\right)\right) + b}{z \cdot c}\\ t_3 := \frac{\frac{b}{z} + \left(t_1 + 9 \cdot \frac{y}{\frac{z}{x}}\right)}{c}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{-220}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 500000000000:\\ \;\;\;\;\frac{\frac{b}{z} + \left(\frac{9}{\frac{z}{x \cdot y}} + t_1\right)}{c}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+265}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 3
Error	35.7
Cost	1900

\[\begin{array}{l} t_1 := \frac{x \cdot 9}{c \cdot \frac{z}{y}}\\ t_2 := \frac{b}{z \cdot c}\\ t_3 := \frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+82}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t \leq -7.895107994918041 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.145509000675511 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;t \leq -9.752073144121254 \cdot 10^{-89}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.331372654187209 \cdot 10^{-124}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -9.8596521043098 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.3423237103320284 \cdot 10^{-210}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.520060278082683 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.065200861475986 \cdot 10^{-238}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.137968078408609 \cdot 10^{-190}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 6.456848820236613 \cdot 10^{-150}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 4
Error	35.7
Cost	1900

\[\begin{array}{l} t_1 := \frac{x \cdot 9}{c \cdot \frac{z}{y}}\\ t_2 := \frac{t \cdot \left(a \cdot -4\right)}{c}\\ t_3 := \frac{b}{z \cdot c}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+82}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t \leq -7.895107994918041 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.145509000675511 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;t \leq -9.752073144121254 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.331372654187209 \cdot 10^{-124}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -9.8596521043098 \cdot 10^{-183}:\\ \;\;\;\;\frac{9 \cdot y}{z} \cdot \frac{x}{c}\\ \mathbf{elif}\;t \leq -2.3423237103320284 \cdot 10^{-210}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.520060278082683 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.065200861475986 \cdot 10^{-238}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 7.137968078408609 \cdot 10^{-190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.456848820236613 \cdot 10^{-150}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 5
Error	35.7
Cost	1900

\[\begin{array}{l} t_1 := \frac{x \cdot 9}{c \cdot \frac{z}{y}}\\ t_2 := \frac{t \cdot \left(a \cdot -4\right)}{c}\\ t_3 := \frac{b}{z \cdot c}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+82}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t \leq -7.895107994918041 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.145509000675511 \cdot 10^{-53}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;t \leq -9.752073144121254 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.331372654187209 \cdot 10^{-124}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -9.8596521043098 \cdot 10^{-183}:\\ \;\;\;\;9 \cdot \frac{\frac{y}{z}}{\frac{c}{x}}\\ \mathbf{elif}\;t \leq -2.3423237103320284 \cdot 10^{-210}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.520060278082683 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.065200861475986 \cdot 10^{-238}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 7.137968078408609 \cdot 10^{-190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.456848820236613 \cdot 10^{-150}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 6
Error	35.7
Cost	1900

\[\begin{array}{l} t_1 := \frac{x \cdot 9}{c \cdot \frac{z}{y}}\\ t_2 := \frac{t \cdot \left(a \cdot -4\right)}{c}\\ t_3 := b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+82}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t \leq -7.895107994918041 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.145509000675511 \cdot 10^{-53}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -9.752073144121254 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.331372654187209 \cdot 10^{-124}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -9.8596521043098 \cdot 10^{-183}:\\ \;\;\;\;9 \cdot \frac{\frac{y}{z}}{\frac{c}{x}}\\ \mathbf{elif}\;t \leq -2.3423237103320284 \cdot 10^{-210}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.520060278082683 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.065200861475986 \cdot 10^{-238}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 7.137968078408609 \cdot 10^{-190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.456848820236613 \cdot 10^{-150}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 7
Error	35.7
Cost	1900

\[\begin{array}{l} t_1 := \frac{x \cdot 9}{c \cdot \frac{z}{y}}\\ t_2 := \frac{t \cdot \left(a \cdot -4\right)}{c}\\ t_3 := b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+82}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t \leq -7.895107994918041 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.145509000675511 \cdot 10^{-53}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -9.752073144121254 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.331372654187209 \cdot 10^{-124}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -9.8596521043098 \cdot 10^{-183}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;t \leq -2.3423237103320284 \cdot 10^{-210}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.520060278082683 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.065200861475986 \cdot 10^{-238}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 7.137968078408609 \cdot 10^{-190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.456848820236613 \cdot 10^{-150}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 8
Error	35.7
Cost	1900

\[\begin{array}{l} t_1 := 9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right)\\ t_2 := \frac{t \cdot \left(a \cdot -4\right)}{c}\\ t_3 := b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+82}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t \leq -7.895107994918041 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.145509000675511 \cdot 10^{-53}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -9.752073144121254 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.331372654187209 \cdot 10^{-124}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -9.8596521043098 \cdot 10^{-183}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{elif}\;t \leq -2.3423237103320284 \cdot 10^{-210}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.520060278082683 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.065200861475986 \cdot 10^{-238}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 7.137968078408609 \cdot 10^{-190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.456848820236613 \cdot 10^{-150}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 9
Error	35.7
Cost	1900

\[\begin{array}{l} t_1 := 9 \cdot \left(x \cdot \frac{\frac{y}{z}}{c}\right)\\ t_2 := \frac{t \cdot \left(a \cdot -4\right)}{c}\\ t_3 := b \cdot \frac{\frac{1}{c}}{z}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+82}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t \leq -7.895107994918041 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.145509000675511 \cdot 10^{-53}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -9.752073144121254 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.331372654187209 \cdot 10^{-124}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -9.8596521043098 \cdot 10^{-183}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;t \leq -2.3423237103320284 \cdot 10^{-210}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.520060278082683 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.065200861475986 \cdot 10^{-238}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 7.137968078408609 \cdot 10^{-190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.456848820236613 \cdot 10^{-150}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 10
Error	24.0
Cost	1744

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;x \cdot 9 \leq -1 \cdot 10^{+194}:\\ \;\;\;\;9 \cdot \frac{\frac{y}{z}}{\frac{c}{x}}\\ \mathbf{elif}\;x \cdot 9 \leq -5 \cdot 10^{+163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot 9 \leq -5 \cdot 10^{+114}:\\ \;\;\;\;\frac{9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;x \cdot 9 \leq 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{\frac{x}{\frac{c}{9}}}}\\ \end{array} \]

Alternative 11
Error	9.6
Cost	1480

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} + \left(-4 \cdot \left(t \cdot a\right) + 9 \cdot \frac{y}{\frac{z}{x}}\right)}{c}\\ \mathbf{if}\;z \leq -1 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 10^{-64}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	9.6
Cost	1480

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{-155}:\\ \;\;\;\;\frac{\frac{b}{z} + \left(t_1 + 9 \cdot \frac{y}{\frac{z}{x}}\right)}{c}\\ \mathbf{elif}\;z \leq 10^{-64}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + \left(t_1 + \frac{9 \cdot y}{\frac{z}{x}}\right)}{c}\\ \end{array} \]

Alternative 13
Error	23.7
Cost	1368

\[\begin{array}{l} t_1 := \frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}\\ t_2 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.103581210448201 \cdot 10^{+58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.571675334089098 \cdot 10^{-70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.537097566453152 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.2966670352562915 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.522763019327632 \cdot 10^{-119}:\\ \;\;\;\;\frac{x \cdot 9}{c \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 14
Error	23.7
Cost	1368

\[\begin{array}{l} t_1 := b + 9 \cdot \left(x \cdot y\right)\\ t_2 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.103581210448201 \cdot 10^{+58}:\\ \;\;\;\;\frac{\frac{t_1}{z}}{c}\\ \mathbf{elif}\;t \leq -2.331372654187209 \cdot 10^{-124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.0077143760548363 \cdot 10^{-250}:\\ \;\;\;\;\frac{t_1}{z \cdot c}\\ \mathbf{elif}\;t \leq 3.2966670352562915 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.522763019327632 \cdot 10^{-119}:\\ \;\;\;\;\frac{x \cdot 9}{c \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 15
Error	20.4
Cost	1364

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := \frac{\frac{b}{z} + t_1}{c}\\ \mathbf{if}\;z \leq -4.171972737833388 \cdot 10^{+199}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-70}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-247}:\\ \;\;\;\;\frac{b + -4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-63}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	35.7
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{z}}{c}\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;z \leq -8.198803630252889 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-65}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.0585934212921955 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Error	35.8
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{z}}{c}\\ t_2 := \frac{t \cdot \left(a \cdot -4\right)}{c}\\ t_3 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;z \leq -8.198803630252889 \cdot 10^{+80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-154}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-65}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.0585934212921955 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Error	42.0
Cost	716

\[\begin{array}{l} t_1 := \frac{\frac{b}{z}}{c}\\ t_2 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;c \leq -5.2 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 2.208010249435899 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.5946614940802727 \cdot 10^{+266}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	43.3
Cost	320

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

Alternative 20
Error	43.0
Cost	320

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

Reproduce

herbie shell --seed 2022291 
(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)))