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

Average Error: 5.8 → 2.5

Time: 47.9s

Precision: binary64

Cost: 21956

\[ \begin{array}{c}[y, z] = \mathsf{sort}([y, z])\\ [j, k] = \mathsf{sort}([j, k])\\ \end{array} \]

Math

\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

↓

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+281}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(x, \mathsf{fma}\left(y, z \cdot \left(18 \cdot t\right), i \cdot -4\right), k \cdot \left(-27 \cdot j\right)\right)\right)\\ \mathbf{elif}\;t_1 \leq 10^{+300}:\\ \;\;\;\;t_1 + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(y \cdot \left(t \cdot \left(x \cdot \left(18 \cdot z\right)\right)\right) + \left(-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(k \cdot j\right)\right)\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a b c i j k)
 :precision binary64
 (-
  (-
   (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c))
   (* (* x 4.0) i))
  (* (* j 27.0) k)))

↓

(FPCore (x y z t a b c i j k)
 :precision binary64
 (let* ((t_1
         (+
          (+ (+ (* (* (* (* x 18.0) y) z) t) (* t (* a -4.0))) (* b c))
          (* i (* x -4.0)))))
   (if (<= t_1 -5e+281)
     (fma c b (fma x (fma y (* z (* 18.0 t)) (* i -4.0)) (* k (* -27.0 j))))
     (if (<= t_1 1e+300)
       (+ t_1 (* j (* k -27.0)))
       (+
        (* b c)
        (+
         (* y (* t (* x (* 18.0 z))))
         (+ (* -4.0 (* x i)) (* -27.0 (* k j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	return (((((((x * 18.0) * y) * z) * t) - ((a * 4.0) * t)) + (b * c)) - ((x * 4.0) * i)) - ((j * 27.0) * k);
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
	double t_1 = ((((((x * 18.0) * y) * z) * t) + (t * (a * -4.0))) + (b * c)) + (i * (x * -4.0));
	double tmp;
	if (t_1 <= -5e+281) {
		tmp = fma(c, b, fma(x, fma(y, (z * (18.0 * t)), (i * -4.0)), (k * (-27.0 * j))));
	} else if (t_1 <= 1e+300) {
		tmp = t_1 + (j * (k * -27.0));
	} else {
		tmp = (b * c) + ((y * (t * (x * (18.0 * z)))) + ((-4.0 * (x * i)) + (-27.0 * (k * j))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j, k)
	return Float64(Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) - Float64(Float64(a * 4.0) * t)) + Float64(b * c)) - Float64(Float64(x * 4.0) * i)) - Float64(Float64(j * 27.0) * k))
end

↓

function code(x, y, z, t, a, b, c, i, j, k)
	t_1 = Float64(Float64(Float64(Float64(Float64(Float64(Float64(x * 18.0) * y) * z) * t) + Float64(t * Float64(a * -4.0))) + Float64(b * c)) + Float64(i * Float64(x * -4.0)))
	tmp = 0.0
	if (t_1 <= -5e+281)
		tmp = fma(c, b, fma(x, fma(y, Float64(z * Float64(18.0 * t)), Float64(i * -4.0)), Float64(k * Float64(-27.0 * j))));
	elseif (t_1 <= 1e+300)
		tmp = Float64(t_1 + Float64(j * Float64(k * -27.0)));
	else
		tmp = Float64(Float64(b * c) + Float64(Float64(y * Float64(t * Float64(x * Float64(18.0 * z)))) + Float64(Float64(-4.0 * Float64(x * i)) + Float64(-27.0 * Float64(k * j)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := N[(N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] - N[(N[(a * 4.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] - N[(N[(x * 4.0), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] - N[(N[(j * 27.0), $MachinePrecision] * k), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_, c_, i_, j_, k_] := Block[{t$95$1 = N[(N[(N[(N[(N[(N[(N[(x * 18.0), $MachinePrecision] * y), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * c), $MachinePrecision]), $MachinePrecision] + N[(i * N[(x * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+281], N[(c * b + N[(x * N[(y * N[(z * N[(18.0 * t), $MachinePrecision]), $MachinePrecision] + N[(i * -4.0), $MachinePrecision]), $MachinePrecision] + N[(k * N[(-27.0 * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+300], N[(t$95$1 + N[(j * N[(k * -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * c), $MachinePrecision] + N[(N[(y * N[(t * N[(x * N[(18.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(-4.0 * N[(x * i), $MachinePrecision]), $MachinePrecision] + N[(-27.0 * N[(k * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Target

Original	5.8
Target	1.6
Herbie	2.5

\[\begin{array}{l} \mathbf{if}\;t < -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{elif}\;t < 165.68027943805222:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) < -5.00000000000000016e281

   1. Initial program 35.0

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Simplified 25.3

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(t, \mathsf{fma}\left(x, y \cdot \left(18 \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right)\right)} \]
      Proof
      (fma.f64 j (*.f64 k -27) (fma.f64 t (fma.f64 x (*.f64 y (*.f64 18 z)) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (*.f64 k (Rewrite<= metadata-eval (neg.f64 27))) (fma.f64 t (fma.f64 x (*.f64 y (*.f64 18 z)) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 k 27))) (fma.f64 t (fma.f64 x (*.f64 y (*.f64 18 z)) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 27 k))) (fma.f64 t (fma.f64 x (*.f64 y (*.f64 18 z)) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (fma.f64 x (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 y 18) z)) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 1 points increase in error, 2 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (fma.f64 x (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 18 y)) z) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (fma.f64 x (*.f64 (*.f64 18 y) z) (*.f64 a (Rewrite<= metadata-eval (neg.f64 4)))) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (fma.f64 x (*.f64 (*.f64 18 y) z) (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a 4)))) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 x (*.f64 (*.f64 18 y) z)) (*.f64 a 4))) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x (*.f64 18 y)) z)) (*.f64 a 4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 7 points increase in error, 9 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x 18) y)) z) (*.f64 a 4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 1 points increase in error, 2 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4)) (fma.f64 b c (*.f64 i (*.f64 x (Rewrite<= metadata-eval (neg.f64 4))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4)) (fma.f64 b c (*.f64 i (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 x 4))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4)) (fma.f64 b c (Rewrite<= *-commutative_binary64 (*.f64 (neg.f64 (*.f64 x 4)) i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4)) (fma.f64 b c (Rewrite=> distribute-lft-neg-out_binary64 (neg.f64 (*.f64 (*.f64 x 4) i)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4)) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 b c) (*.f64 (*.f64 x 4) i))))): 0 points increase in error, 1 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4))) (-.f64 (*.f64 b c) (*.f64 (*.f64 x 4) i))))): 1 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (+.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t))) (-.f64 (*.f64 b c) (*.f64 (*.f64 x 4) i)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 j (neg.f64 (*.f64 27 k))) (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 j (*.f64 27 k)))) (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i))): 0 points increase in error, 0 points decrease in error
      (+.f64 (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 j 27) k))) (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i))): 12 points increase in error, 10 points decrease in error
      (+.f64 (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 (*.f64 j 27)) k)) (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (neg.f64 (*.f64 j 27)) k))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in a around 0 19.8

      \[\leadsto \color{blue}{c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + \left(-4 \cdot \left(i \cdot x\right) + -27 \cdot \left(k \cdot j\right)\right)\right)} \]

   4. Simplified 16.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(c, b, \mathsf{fma}\left(x, \mathsf{fma}\left(y, z \cdot \left(18 \cdot t\right), -4 \cdot i\right), k \cdot \left(-27 \cdot j\right)\right)\right)} \]
      Proof
      (fma.f64 c b (fma.f64 x (fma.f64 y (*.f64 z (*.f64 18 t)) (*.f64 -4 i)) (*.f64 k (*.f64 -27 j)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c b (fma.f64 x (fma.f64 y (*.f64 z (Rewrite<= *-commutative_binary64 (*.f64 t 18))) (*.f64 -4 i)) (*.f64 k (*.f64 -27 j)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c b (fma.f64 x (fma.f64 y (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 z t) 18)) (*.f64 -4 i)) (*.f64 k (*.f64 -27 j)))): 3 points increase in error, 4 points decrease in error
      (fma.f64 c b (fma.f64 x (fma.f64 y (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 t z)) 18) (*.f64 -4 i)) (*.f64 k (*.f64 -27 j)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c b (fma.f64 x (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y (*.f64 (*.f64 t z) 18)) (*.f64 -4 i))) (*.f64 k (*.f64 -27 j)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c b (fma.f64 x (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 y (*.f64 t z)) 18)) (*.f64 -4 i)) (*.f64 k (*.f64 -27 j)))): 3 points increase in error, 4 points decrease in error
      (fma.f64 c b (fma.f64 x (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 18 (*.f64 y (*.f64 t z)))) (*.f64 -4 i)) (*.f64 k (*.f64 -27 j)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c b (fma.f64 x (+.f64 (*.f64 18 (*.f64 y (*.f64 t z))) (*.f64 -4 i)) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 k -27) j)))): 14 points increase in error, 13 points decrease in error
      (fma.f64 c b (fma.f64 x (+.f64 (*.f64 18 (*.f64 y (*.f64 t z))) (*.f64 -4 i)) (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 -27 k)) j))): 0 points increase in error, 0 points decrease in error
      (fma.f64 c b (fma.f64 x (+.f64 (*.f64 18 (*.f64 y (*.f64 t z))) (*.f64 -4 i)) (Rewrite<= associate-*r*_binary64 (*.f64 -27 (*.f64 k j))))): 18 points increase in error, 9 points decrease in error
      (fma.f64 c b (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x (+.f64 (*.f64 18 (*.f64 y (*.f64 t z))) (*.f64 -4 i))) (*.f64 -27 (*.f64 k j))))): 1 points increase in error, 1 points decrease in error
      (fma.f64 c b (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (*.f64 18 (*.f64 y (*.f64 t z))) (*.f64 -4 i)) x)) (*.f64 -27 (*.f64 k j)))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> fma-udef_binary64 (+.f64 (*.f64 c b) (+.f64 (*.f64 (+.f64 (*.f64 18 (*.f64 y (*.f64 t z))) (*.f64 -4 i)) x) (*.f64 -27 (*.f64 k j))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 c b) (+.f64 (Rewrite=> *-commutative_binary64 (*.f64 x (+.f64 (*.f64 18 (*.f64 y (*.f64 t z))) (*.f64 -4 i)))) (*.f64 -27 (*.f64 k j)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 c b) (+.f64 (Rewrite=> distribute-rgt-in_binary64 (+.f64 (*.f64 (*.f64 18 (*.f64 y (*.f64 t z))) x) (*.f64 (*.f64 -4 i) x))) (*.f64 -27 (*.f64 k j)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 c b) (+.f64 (+.f64 (Rewrite=> associate-*l*_binary64 (*.f64 18 (*.f64 (*.f64 y (*.f64 t z)) x))) (*.f64 (*.f64 -4 i) x)) (*.f64 -27 (*.f64 k j)))): 6 points increase in error, 5 points decrease in error
      (+.f64 (*.f64 c b) (+.f64 (+.f64 (*.f64 18 (Rewrite<= associate-*r*_binary64 (*.f64 y (*.f64 (*.f64 t z) x)))) (*.f64 (*.f64 -4 i) x)) (*.f64 -27 (*.f64 k j)))): 9 points increase in error, 11 points decrease in error
      (+.f64 (*.f64 c b) (+.f64 (+.f64 (*.f64 18 (*.f64 y (Rewrite<= associate-*r*_binary64 (*.f64 t (*.f64 z x))))) (*.f64 (*.f64 -4 i) x)) (*.f64 -27 (*.f64 k j)))): 18 points increase in error, 12 points decrease in error
      (+.f64 (*.f64 c b) (+.f64 (+.f64 (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x)))) (Rewrite<= associate-*r*_binary64 (*.f64 -4 (*.f64 i x)))) (*.f64 -27 (*.f64 k j)))): 0 points increase in error, 1 points decrease in error
      (+.f64 (*.f64 c b) (Rewrite<= associate-+r+_binary64 (+.f64 (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x)))) (+.f64 (*.f64 -4 (*.f64 i x)) (*.f64 -27 (*.f64 k j)))))): 0 points increase in error, 0 points decrease in error

   if -5.00000000000000016e281 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) < 1.0000000000000001e300

   1. Initial program 0.4

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Applied egg-rr 0.4

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \color{blue}{\left(0 + j \cdot \left(27 \cdot k\right)\right)} \]

   if 1.0000000000000001e300 < (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i))

   1. Initial program 51.2

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k \]

   2. Simplified 33.0

      \[\leadsto \color{blue}{\mathsf{fma}\left(j, k \cdot -27, \mathsf{fma}\left(t, \mathsf{fma}\left(x, y \cdot \left(18 \cdot z\right), a \cdot -4\right), \mathsf{fma}\left(b, c, i \cdot \left(x \cdot -4\right)\right)\right)\right)} \]
      Proof
      (fma.f64 j (*.f64 k -27) (fma.f64 t (fma.f64 x (*.f64 y (*.f64 18 z)) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (*.f64 k (Rewrite<= metadata-eval (neg.f64 27))) (fma.f64 t (fma.f64 x (*.f64 y (*.f64 18 z)) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 k 27))) (fma.f64 t (fma.f64 x (*.f64 y (*.f64 18 z)) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (Rewrite<= *-commutative_binary64 (*.f64 27 k))) (fma.f64 t (fma.f64 x (*.f64 y (*.f64 18 z)) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (fma.f64 x (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 y 18) z)) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 1 points increase in error, 2 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (fma.f64 x (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 18 y)) z) (*.f64 a -4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (fma.f64 x (*.f64 (*.f64 18 y) z) (*.f64 a (Rewrite<= metadata-eval (neg.f64 4)))) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (fma.f64 x (*.f64 (*.f64 18 y) z) (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a 4)))) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 x (*.f64 (*.f64 18 y) z)) (*.f64 a 4))) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x (*.f64 18 y)) z)) (*.f64 a 4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 7 points increase in error, 9 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x 18) y)) z) (*.f64 a 4)) (fma.f64 b c (*.f64 i (*.f64 x -4))))): 1 points increase in error, 2 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4)) (fma.f64 b c (*.f64 i (*.f64 x (Rewrite<= metadata-eval (neg.f64 4))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4)) (fma.f64 b c (*.f64 i (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 x 4))))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4)) (fma.f64 b c (Rewrite<= *-commutative_binary64 (*.f64 (neg.f64 (*.f64 x 4)) i))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4)) (fma.f64 b c (Rewrite=> distribute-lft-neg-out_binary64 (neg.f64 (*.f64 (*.f64 x 4) i)))))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (fma.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4)) (Rewrite<= fma-neg_binary64 (-.f64 (*.f64 b c) (*.f64 (*.f64 x 4) i))))): 0 points increase in error, 1 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 t (-.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) (*.f64 a 4))) (-.f64 (*.f64 b c) (*.f64 (*.f64 x 4) i))))): 1 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (+.f64 (Rewrite<= distribute-rgt-out--_binary64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t))) (-.f64 (*.f64 b c) (*.f64 (*.f64 x 4) i)))): 0 points increase in error, 0 points decrease in error
      (fma.f64 j (neg.f64 (*.f64 27 k)) (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fma-def_binary64 (+.f64 (*.f64 j (neg.f64 (*.f64 27 k))) (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 j (*.f64 27 k)))) (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i))): 0 points increase in error, 0 points decrease in error
      (+.f64 (neg.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 j 27) k))) (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i))): 12 points increase in error, 10 points decrease in error
      (+.f64 (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 (*.f64 j 27)) k)) (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (neg.f64 (*.f64 j 27)) k))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (-.f64 (+.f64 (-.f64 (*.f64 (*.f64 (*.f64 (*.f64 x 18) y) z) t) (*.f64 (*.f64 a 4) t)) (*.f64 b c)) (*.f64 (*.f64 x 4) i)) (*.f64 (*.f64 j 27) k))): 0 points increase in error, 0 points decrease in error

   3. Taylor expanded in a around 0 16.5

      \[\leadsto \color{blue}{c \cdot b + \left(18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right) + \left(-4 \cdot \left(i \cdot x\right) + -27 \cdot \left(k \cdot j\right)\right)\right)} \]

   4. Applied egg-rr 39.2

      \[\leadsto c \cdot b + \left(\color{blue}{\left(0 + \left(t \cdot \left(\left(z \cdot x\right) \cdot y\right)\right) \cdot 18\right)} + \left(-4 \cdot \left(i \cdot x\right) + -27 \cdot \left(k \cdot j\right)\right)\right) \]

   5. Taylor expanded in t around 0 16.5

      \[\leadsto c \cdot b + \left(\left(0 + \color{blue}{18 \cdot \left(y \cdot \left(t \cdot \left(z \cdot x\right)\right)\right)}\right) + \left(-4 \cdot \left(i \cdot x\right) + -27 \cdot \left(k \cdot j\right)\right)\right) \]

   6. Simplified 16.7

      \[\leadsto c \cdot b + \left(\left(0 + \color{blue}{y \cdot \left(t \cdot \left(x \cdot \left(z \cdot 18\right)\right)\right)}\right) + \left(-4 \cdot \left(i \cdot x\right) + -27 \cdot \left(k \cdot j\right)\right)\right) \]
      Proof
      (*.f64 y (*.f64 t (*.f64 x (*.f64 z 18)))): 0 points increase in error, 0 points decrease in error
      (*.f64 y (*.f64 t (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x z) 18)))): 16 points increase in error, 13 points decrease in error
      (*.f64 y (*.f64 t (*.f64 (Rewrite<= *-commutative_binary64 (*.f64 z x)) 18))): 0 points increase in error, 0 points decrease in error
      (*.f64 y (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 t (*.f64 z x)) 18))): 13 points increase in error, 20 points decrease in error
      (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 y (*.f64 t (*.f64 z x))) 18)): 23 points increase in error, 25 points decrease in error
      (Rewrite<= *-commutative_binary64 (*.f64 18 (*.f64 y (*.f64 t (*.f64 z x))))): 0 points increase in error, 0 points decrease in error
3. Recombined 3 regimes into one program.

4. Final simplification 2.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq -5 \cdot 10^{+281}:\\ \;\;\;\;\mathsf{fma}\left(c, b, \mathsf{fma}\left(x, \mathsf{fma}\left(y, z \cdot \left(18 \cdot t\right), i \cdot -4\right), k \cdot \left(-27 \cdot j\right)\right)\right)\\ \mathbf{elif}\;\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right) \leq 10^{+300}:\\ \;\;\;\;\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\right) + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(y \cdot \left(t \cdot \left(x \cdot \left(18 \cdot z\right)\right)\right) + \left(-4 \cdot \left(x \cdot i\right) + -27 \cdot \left(k \cdot j\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	1.9
Cost	5320

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\\ t_2 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+281}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + \left(t_2 + -4 \cdot \left(t \cdot a\right)\right)\right)\\ \mathbf{elif}\;t_1 \leq 10^{+300}:\\ \;\;\;\;t_1 + k \cdot \left(-27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(y \cdot \left(t \cdot \left(x \cdot \left(18 \cdot z\right)\right)\right) + \left(-4 \cdot \left(x \cdot i\right) + t_2\right)\right)\\ \end{array} \]

Alternative 2
Error	1.9
Cost	5320

\[\begin{array}{l} t_1 := \left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t + t \cdot \left(a \cdot -4\right)\right) + b \cdot c\right) + i \cdot \left(x \cdot -4\right)\\ t_2 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+281}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + \left(t_2 + -4 \cdot \left(t \cdot a\right)\right)\right)\\ \mathbf{elif}\;t_1 \leq 10^{+300}:\\ \;\;\;\;t_1 + j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(y \cdot \left(t \cdot \left(x \cdot \left(18 \cdot z\right)\right)\right) + \left(-4 \cdot \left(x \cdot i\right) + t_2\right)\right)\\ \end{array} \]

Alternative 3
Error	1.9
Cost	2248

\[\begin{array}{l} t_1 := b \cdot c + \left(x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + \left(-27 \cdot \left(k \cdot j\right) + -4 \cdot \left(t \cdot a\right)\right)\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 10^{+100}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(18 \cdot y\right) \cdot \left(t \cdot \left(x \cdot z\right)\right) + t \cdot \left(a \cdot -4\right)\right)\right) + i \cdot \left(x \cdot -4\right)\right) + k \cdot \left(-27 \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	25.3
Cost	2016

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := b \cdot c + \left(-4 \cdot \left(x \cdot i\right) + t_1\right)\\ t_3 := -4 \cdot \left(t \cdot a\right)\\ t_4 := t_1 + t_3\\ t_5 := b \cdot c + t_3\\ \mathbf{if}\;z \leq -9.438656480794805 \cdot 10^{-225}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.7274131825414014 \cdot 10^{-261}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.2991228754669708 \cdot 10^{-196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.3838686907233953 \cdot 10^{-164}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.0160481138281751 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 0.0003372036272539984:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+260}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	5.9
Cost	1988

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right) + -4 \cdot \left(t \cdot a\right)\\ \mathbf{if}\;y \leq -5.0225292254629244 \cdot 10^{-223}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(i \cdot -4 + 18 \cdot \left(y \cdot \left(z \cdot t\right)\right)\right) + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(-4 \cdot \left(x \cdot i\right) + t_1\right)\\ \end{array} \]

Alternative 6
Error	8.1
Cost	1864

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right) + -4 \cdot \left(t \cdot a\right)\\ t_2 := b \cdot c + \left(-4 \cdot \left(x \cdot i\right) + t_1\right)\\ \mathbf{if}\;i \leq -6.588222875541499 \cdot 10^{-202}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 8.489072804031185 \cdot 10^{-47}:\\ \;\;\;\;b \cdot c + \left(x \cdot \left(\left(y \cdot t\right) \cdot \left(18 \cdot z\right)\right) + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	9.2
Cost	1736

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + \left(t_1 + \left(-27 \cdot \left(k \cdot j\right) + -4 \cdot \left(t \cdot a\right)\right)\right)\\ \mathbf{if}\;j \leq -2.3952802714951335 \cdot 10^{-280}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.756742492348588 \cdot 10^{-131}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right) + \left(b \cdot c + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	8.8
Cost	1736

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := b \cdot c + \left(-4 \cdot \left(x \cdot i\right) + \left(t_1 + -4 \cdot \left(t \cdot a\right)\right)\right)\\ \mathbf{if}\;i \leq -5.805764201947989 \cdot 10^{-231}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 3.0731044033738332 \cdot 10^{-15}:\\ \;\;\;\;t \cdot \left(18 \cdot \left(y \cdot \left(x \cdot z\right)\right) + a \cdot -4\right) + \left(b \cdot c + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	8.1
Cost	1732

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := -27 \cdot \left(k \cdot j\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+120}:\\ \;\;\;\;b \cdot c + \left(\left(t_1 + t_2\right) + 18 \cdot \left(y \cdot \left(t \cdot \left(x \cdot z\right)\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(t_1 + \left(t_2 + -4 \cdot \left(t \cdot a\right)\right)\right)\\ \end{array} \]

Alternative 10
Error	8.1
Cost	1732

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+120}:\\ \;\;\;\;b \cdot c + \left(y \cdot \left(t \cdot \left(x \cdot \left(18 \cdot z\right)\right)\right) + \left(t_2 + t_1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c + \left(t_2 + \left(t_1 + -4 \cdot \left(t \cdot a\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	31.6
Cost	1632

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot a\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ t_3 := t_2 + t_1\\ t_4 := -27 \cdot \left(k \cdot j\right) + t_1\\ t_5 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;c \leq -1.1955799664779454 \cdot 10^{-119}:\\ \;\;\;\;b \cdot c + t_1\\ \mathbf{elif}\;c \leq -5.1393098076691304 \cdot 10^{-232}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 3.32480165109398 \cdot 10^{-159}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 7.616121024501434 \cdot 10^{-44}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq 5.0098822002777326 \cdot 10^{+45}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq 1.2777678059006857 \cdot 10^{+50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq 10^{+85}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+165}:\\ \;\;\;\;b \cdot c + t_2\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 12
Error	18.4
Cost	1620

\[\begin{array}{l} t_1 := -27 \cdot \left(k \cdot j\right)\\ t_2 := -4 \cdot \left(x \cdot i\right)\\ t_3 := -4 \cdot \left(t \cdot a\right)\\ t_4 := b \cdot c + \left(t_2 + t_1\right)\\ t_5 := b \cdot c + \left(t_2 + t_3\right)\\ t_6 := b \cdot c + \left(t_1 + t_3\right)\\ \mathbf{if}\;i \leq -2.2 \cdot 10^{+64}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;i \leq 5.675326802349735 \cdot 10^{-15}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+98}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;i \leq 4.2 \cdot 10^{+198}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;i \leq 10^{+237}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 13
Error	9.5
Cost	1344

\[b \cdot c + \left(-4 \cdot \left(x \cdot i\right) + \left(-27 \cdot \left(k \cdot j\right) + -4 \cdot \left(t \cdot a\right)\right)\right) \]

Alternative 14
Error	44.7
Cost	1244

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := i \cdot \left(x \cdot -4\right)\\ \mathbf{if}\;b \leq -1.2438677836112035 \cdot 10^{+36}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;b \leq -7.476805486783293 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.313134723982449 \cdot 10^{-199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.1721020868581426 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.997625096443074 \cdot 10^{-265}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 9.517862251778626 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.394023219195286 \cdot 10^{-85}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 15
Error	33.4
Cost	1236

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_3 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;j \leq -2.4 \cdot 10^{+98}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -2.0689022737959197 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.0460628095943213 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.018791062636505 \cdot 10^{-242}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 7.662462787507289 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 16
Error	30.2
Cost	1236

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_3 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;j \leq -2.4 \cdot 10^{+98}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -2.0689022737959197 \cdot 10^{-112}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.0460628095943213 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.018791062636505 \cdot 10^{-242}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 8.147934836601766 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 17
Error	30.6
Cost	1236

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + t_1\\ t_3 := -4 \cdot \left(t \cdot a\right)\\ t_4 := b \cdot c + j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;j \leq -2.4 \cdot 10^{+98}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq -2.0689022737959197 \cdot 10^{-112}:\\ \;\;\;\;b \cdot c + t_3\\ \mathbf{elif}\;j \leq -4.132512642072593 \cdot 10^{-152}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -8.72420200831487 \cdot 10^{-242}:\\ \;\;\;\;t_1 + t_3\\ \mathbf{elif}\;j \leq 8.147934836601766 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 18
Error	18.0
Cost	1224

\[\begin{array}{l} t_1 := -4 \cdot \left(x \cdot i\right)\\ t_2 := b \cdot c + \left(t_1 + -27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{if}\;j \leq -2.4 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 8.147934836601766 \cdot 10^{-63}:\\ \;\;\;\;b \cdot c + \left(t_1 + -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Error	33.4
Cost	1104

\[\begin{array}{l} t_1 := b \cdot c + -4 \cdot \left(t \cdot a\right)\\ t_2 := j \cdot \left(k \cdot -27\right)\\ \mathbf{if}\;j \leq -2.4 \cdot 10^{+98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -4.007662334523319 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.0460628095943213 \cdot 10^{-156}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;j \leq 7.662462787507289 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 20
Error	45.0
Cost	980

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;c \leq -8.722544248359933 \cdot 10^{-141}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq -9.871467593184014 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.503233530434003 \cdot 10^{-185}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{elif}\;c \leq 2.314837923050132 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.4 \cdot 10^{+63}:\\ \;\;\;\;j \cdot \left(k \cdot -27\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 21
Error	45.9
Cost	584

\[\begin{array}{l} \mathbf{if}\;c \leq -5.1393098076691304 \cdot 10^{-232}:\\ \;\;\;\;b \cdot c\\ \mathbf{elif}\;c \leq 6.165961589246704 \cdot 10^{-36}:\\ \;\;\;\;i \cdot \left(x \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot c\\ \end{array} \]

Alternative 22
Error	48.7
Cost	192

\[b \cdot c \]

Reproduce

herbie shell --seed 2022317 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))