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

Average Error: 20.7 → 7.3

Time: 51.2s

Precision: binary64

Cost: 20180

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{a}{c} \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{b - x \cdot \left(y \cdot -9\right)}{z}\right)}{c}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(x, 9 \cdot y, b\right) \cdot \frac{1}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

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 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_1 (- INFINITY))
     (* (/ a c) (* t -4.0))
     (if (<= t_1 -2e+96)
       t_1
       (if (<= t_1 0.0)
         (/ (fma t (* a -4.0) (/ (- b (* x (* y -9.0))) z)) c)
         (if (<= t_1 2e+305)
           t_1
           (if (<= t_1 INFINITY)
             (/ (fma t (* a -4.0) (* (fma x (* 9.0 y) b) (/ 1.0 z))) c)
             (* -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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (a / c) * (t * -4.0);
	} else if (t_1 <= -2e+96) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = fma(t, (a * -4.0), ((b - (x * (y * -9.0))) / z)) / c;
	} else if (t_1 <= 2e+305) {
		tmp = t_1;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = fma(t, (a * -4.0), (fma(x, (9.0 * y), b) * (1.0 / z))) / c;
	} 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(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(a / c) * Float64(t * -4.0));
	elseif (t_1 <= -2e+96)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(fma(t, Float64(a * -4.0), Float64(Float64(b - Float64(x * Float64(y * -9.0))) / z)) / c);
	elseif (t_1 <= 2e+305)
		tmp = t_1;
	elseif (t_1 <= Inf)
		tmp = Float64(fma(t, Float64(a * -4.0), Float64(fma(x, Float64(9.0 * y), b) * Float64(1.0 / z))) / c);
	else
		tmp = Float64(-4.0 * Float64(t / Float64(c / a)));
	end
	return tmp
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(a / c), $MachinePrecision] * N[(t * -4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e+96], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(t * N[(a * -4.0), $MachinePrecision] + N[(N[(b - N[(x * N[(y * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 2e+305], t$95$1, If[LessEqual[t$95$1, Infinity], N[(N[(t * N[(a * -4.0), $MachinePrecision] + N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], N[(-4.0 * N[(t / N[(c / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	20.7
Target	14.6
Herbie	7.3

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

Derivation

1. Split input into 5 regimes

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

   1. Initial program 64.0

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

   2. Simplified 24.5

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]
      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): 7 points increase in error, 3 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): 1 points increase in error, 1 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): 15 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): 18 points increase in error, 13 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): 21 points increase in error, 1 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, 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))): 53 points increase in error, 55 points decrease in error

   3. Applied egg-rr 24.5

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

   4. Taylor expanded in t around inf 33.6

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

   5. Simplified 26.6

      \[\leadsto \color{blue}{-4 \cdot \frac{t}{\frac{c}{a}}} \]
      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))): 58 points increase in error, 41 points decrease in error
      (*.f64 -4 (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 a t)) c)): 0 points increase in error, 0 points decrease in error

   6. Taylor expanded in t around 0 33.6

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

   7. Simplified 26.7

      \[\leadsto \color{blue}{\frac{a}{c} \cdot \left(t \cdot -4\right)} \]
      Proof
      (*.f64 (/.f64 a c) (*.f64 t -4)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (/.f64 a c) t) -4)): 2 points increase in error, 1 points decrease in error
      (*.f64 (Rewrite=> associate-*l/_binary64 (/.f64 (*.f64 a t) c)) -4): 48 points increase in error, 50 points decrease in error
      (Rewrite<= *-commutative_binary64 (*.f64 -4 (/.f64 (*.f64 a t) c))): 0 points increase in error, 0 points decrease in error

   if -inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -2.0000000000000001e96 or -0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 1.9999999999999999e305

   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 -2.0000000000000001e96 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -0.0

   1. Initial program 14.9

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

   2. Simplified 2.1

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]
      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): 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): 7 points increase in error, 3 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): 1 points increase in error, 1 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): 15 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): 18 points increase in error, 13 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): 21 points increase in error, 1 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, 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))): 53 points increase in error, 55 points decrease in error

   3. Applied egg-rr 2.1

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

   if 1.9999999999999999e305 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 62.1

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

   2. Simplified 23.5

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]
      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): 7 points increase in error, 3 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): 1 points increase in error, 1 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): 15 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): 18 points increase in error, 13 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): 21 points increase in error, 1 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, 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))): 53 points increase in error, 55 points decrease in error

   3. Applied egg-rr 23.5

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

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

   1. Initial program 64.0

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

   2. Simplified 30.0

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}} \]
      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): 7 points increase in error, 3 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): 1 points increase in error, 1 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): 15 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): 18 points increase in error, 13 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): 21 points increase in error, 1 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, 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))): 53 points increase in error, 55 points decrease in error

   3. Applied egg-rr 30.0

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

   4. Taylor expanded in t around inf 29.9

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

   5. Simplified 24.4

      \[\leadsto \color{blue}{-4 \cdot \frac{t}{\frac{c}{a}}} \]
      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))): 58 points increase in error, 41 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 5 regimes into one program.

4. Final simplification 7.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -\infty:\\ \;\;\;\;\frac{a}{c} \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -2 \cdot 10^{+96}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{b - x \cdot \left(y \cdot -9\right)}{z}\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 2 \cdot 10^{+305}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \mathsf{fma}\left(x, 9 \cdot y, b\right) \cdot \frac{1}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternatives

Alternative 1
Error	7.3
Cost	13780

\[\begin{array}{l} t_1 := \frac{\mathsf{fma}\left(t, a \cdot -4, \frac{b - x \cdot \left(y \cdot -9\right)}{z}\right)}{c}\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{a}{c} \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 2
Error	7.3
Cost	13524

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{a}{c} \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t_1 \leq -4 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \left(x \cdot \left(9 \cdot y\right) + z \cdot \left(a \cdot \left(t \cdot -4\right)\right)\right)}{c}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, b \cdot \frac{1}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 3
Error	8.7
Cost	7124

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{a}{c} \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t_1 \leq -4 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 4
Error	7.3
Cost	7124

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{a}{c} \cdot \left(t \cdot -4\right)\\ \mathbf{elif}\;t_1 \leq -4 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \left(x \cdot \left(9 \cdot y\right) + z \cdot \left(a \cdot \left(t \cdot -4\right)\right)\right)}{c}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;\frac{\frac{b}{z} - 4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 5
Error	25.2
Cost	1760

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} - 4 \cdot \left(t \cdot a\right)}{c}\\ t_2 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;a \leq -5.312250734990058 \cdot 10^{-52}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;a \leq 1.642250581311466 \cdot 10^{-217}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7.54257787497075 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 57284383549330970:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.890309290654721 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.16 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-4}{\frac{c}{t}}\\ \end{array} \]

Alternative 6
Error	21.3
Cost	1488

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} - 4 \cdot \left(t \cdot a\right)}{c}\\ t_2 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;b \leq -4.9350541328636045 \cdot 10^{+101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.829015771350769 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.1304786032518291 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.0767716828963849 \cdot 10^{-100}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;b \leq 1.5257029343611677 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	21.4
Cost	1488

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} - 4 \cdot \left(t \cdot a\right)}{c}\\ t_2 := \frac{x \cdot \left(9 \cdot y\right)}{z \cdot c} + \frac{b}{z \cdot c}\\ \mathbf{if}\;b \leq -4.9350541328636045 \cdot 10^{+101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.829015771350769 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.170640008691446 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.0767716828963849 \cdot 10^{-100}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;b \leq 1.5257029343611677 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 8
Error	29.2
Cost	1368

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} - 4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;y \leq -2.618607136506946 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z}}{\frac{c}{9}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+123}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot \left(c \cdot 0.1111111111111111\right)}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+236}:\\ \;\;\;\;\frac{y}{\frac{z}{\frac{x}{\frac{c}{9}}}}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+280}:\\ \;\;\;\;a \cdot \frac{-4}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot \frac{c \cdot 0.1111111111111111}{x}}\\ \end{array} \]

Alternative 9
Error	35.0
Cost	1108

\[\begin{array}{l} t_1 := \frac{y}{\frac{c \cdot 0.1111111111111111}{\frac{x}{z}}}\\ \mathbf{if}\;b \leq -4.87522260859717 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;b \leq -5.075764247378945 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.805419458200613 \cdot 10^{-245}:\\ \;\;\;\;\frac{-4}{c \cdot \frac{\frac{1}{t}}{a}}\\ \mathbf{elif}\;b \leq 2.001053900145543 \cdot 10^{-208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.396431659284203 \cdot 10^{+77}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 10
Error	35.1
Cost	1108

\[\begin{array}{l} \mathbf{if}\;b \leq -4.87522260859717 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;b \leq -5.075764247378945 \cdot 10^{-143}:\\ \;\;\;\;\frac{y}{\frac{c \cdot 0.1111111111111111}{\frac{x}{z}}}\\ \mathbf{elif}\;b \leq 1.805419458200613 \cdot 10^{-245}:\\ \;\;\;\;\frac{-4}{c \cdot \frac{\frac{1}{t}}{a}}\\ \mathbf{elif}\;b \leq 2.001053900145543 \cdot 10^{-208}:\\ \;\;\;\;\frac{9}{\frac{\frac{c}{y}}{\frac{x}{z}}}\\ \mathbf{elif}\;b \leq 3.396431659284203 \cdot 10^{+77}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 11
Error	35.1
Cost	1108

\[\begin{array}{l} \mathbf{if}\;b \leq -4.87522260859717 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;b \leq -5.075764247378945 \cdot 10^{-143}:\\ \;\;\;\;\frac{y}{\frac{c \cdot 0.1111111111111111}{\frac{x}{z}}}\\ \mathbf{elif}\;b \leq 1.1741638755735829 \cdot 10^{-258}:\\ \;\;\;\;\frac{-4}{c \cdot \frac{\frac{1}{t}}{a}}\\ \mathbf{elif}\;b \leq 2.001053900145543 \cdot 10^{-208}:\\ \;\;\;\;\frac{\frac{x \cdot 9}{\frac{c}{y}}}{z}\\ \mathbf{elif}\;b \leq 3.396431659284203 \cdot 10^{+77}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 12
Error	35.1
Cost	1108

\[\begin{array}{l} \mathbf{if}\;b \leq -4.87522260859717 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;b \leq -5.075764247378945 \cdot 10^{-143}:\\ \;\;\;\;\frac{y}{\frac{c \cdot 0.1111111111111111}{\frac{x}{z}}}\\ \mathbf{elif}\;b \leq 1.4648334213736762 \cdot 10^{-251}:\\ \;\;\;\;\frac{-4}{c \cdot \frac{\frac{1}{t}}{a}}\\ \mathbf{elif}\;b \leq 2.001053900145543 \cdot 10^{-208}:\\ \;\;\;\;9 \cdot \frac{x}{\frac{z}{\frac{y}{c}}}\\ \mathbf{elif}\;b \leq 3.396431659284203 \cdot 10^{+77}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 13
Error	35.1
Cost	1108

\[\begin{array}{l} t_1 := y \cdot \frac{x}{z \cdot \left(c \cdot 0.1111111111111111\right)}\\ \mathbf{if}\;b \leq -4.87522260859717 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;b \leq -5.075764247378945 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.4648334213736762 \cdot 10^{-251}:\\ \;\;\;\;\frac{-4}{c \cdot \frac{\frac{1}{t}}{a}}\\ \mathbf{elif}\;b \leq 2.001053900145543 \cdot 10^{-208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.396431659284203 \cdot 10^{+77}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 14
Error	35.2
Cost	1108

\[\begin{array}{l} \mathbf{if}\;b \leq -4.87522260859717 \cdot 10^{-10}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;b \leq -5.075764247378945 \cdot 10^{-143}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot \left(c \cdot 0.1111111111111111\right)}\\ \mathbf{elif}\;b \leq 1.1741638755735829 \cdot 10^{-258}:\\ \;\;\;\;\frac{-4}{c \cdot \frac{\frac{1}{t}}{a}}\\ \mathbf{elif}\;b \leq 2.001053900145543 \cdot 10^{-208}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z}}{\frac{c}{9}}\\ \mathbf{elif}\;b \leq 3.396431659284203 \cdot 10^{+77}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 15
Error	34.4
Cost	844

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ \mathbf{if}\;b \leq -1.1304786032518291 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.840625904972336 \cdot 10^{-278}:\\ \;\;\;\;a \cdot \frac{-4}{\frac{c}{t}}\\ \mathbf{elif}\;b \leq 3.396431659284203 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	34.4
Cost	712

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ \mathbf{if}\;b \leq -1.1304786032518291 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.396431659284203 \cdot 10^{+77}:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	34.4
Cost	712

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ \mathbf{if}\;b \leq -1.1304786032518291 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.396431659284203 \cdot 10^{+77}:\\ \;\;\;\;\frac{-4}{\frac{\frac{c}{a}}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	34.4
Cost	712

\[\begin{array}{l} \mathbf{if}\;b \leq -1.1304786032518291 \cdot 10^{-57}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;b \leq 3.396431659284203 \cdot 10^{+77}:\\ \;\;\;\;\frac{-4}{\frac{\frac{c}{a}}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 19
Error	34.3
Cost	712

\[\begin{array}{l} \mathbf{if}\;b \leq -1.1304786032518291 \cdot 10^{-57}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;b \leq 3.396431659284203 \cdot 10^{+77}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 20
Error	43.9
Cost	320

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

Alternative 21
Error	43.6
Cost	320

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

Reproduce

herbie shell --seed 2022317 
(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)))