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

Average Error: 20.2 → 6.3

Time: 27.4s

Precision: binary64

Cost: 9928

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

Math

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

↓

\[\begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_3 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+191}:\\ \;\;\;\;t_3 + \left(t_1 + \frac{a}{\frac{c}{t}} \cdot -4\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;\left(b + \left(9 \cdot \left(x \cdot y\right) - a \cdot \left(z \cdot \left(4 \cdot t\right)\right)\right)\right) \cdot \frac{\frac{-1}{z}}{-c}\\ \mathbf{else}:\\ \;\;\;\;t_3 + \left(t_1 + -4 \cdot \left(a \cdot \frac{t}{c}\right)\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* 9.0 (* (/ y c) (/ x z))))
        (t_2 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))
        (t_3 (/ (/ b c) z)))
   (if (<= t_2 -1e+191)
     (+ t_3 (+ t_1 (* (/ a (/ c t)) -4.0)))
     (if (<= t_2 5e+14)
       (/ (+ (/ (fma (* x 9.0) y b) z) (* t (* a -4.0))) c)
       (if (<= t_2 2e+300)
         (*
          (+ b (- (* 9.0 (* x y)) (* a (* z (* 4.0 t)))))
          (/ (/ -1.0 z) (- c)))
         (+ t_3 (+ t_1 (* -4.0 (* a (/ t c))))))))))

C

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

↓

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = 9.0 * ((y / c) * (x / z));
	double t_2 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double t_3 = (b / c) / z;
	double tmp;
	if (t_2 <= -1e+191) {
		tmp = t_3 + (t_1 + ((a / (c / t)) * -4.0));
	} else if (t_2 <= 5e+14) {
		tmp = ((fma((x * 9.0), y, b) / z) + (t * (a * -4.0))) / c;
	} else if (t_2 <= 2e+300) {
		tmp = (b + ((9.0 * (x * y)) - (a * (z * (4.0 * t))))) * ((-1.0 / z) / -c);
	} else {
		tmp = t_3 + (t_1 + (-4.0 * (a * (t / c))));
	}
	return tmp;
}

Julia

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

↓

function code(x, y, z, t, a, b, c)
	t_1 = Float64(9.0 * Float64(Float64(y / c) * Float64(x / z)))
	t_2 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	t_3 = Float64(Float64(b / c) / z)
	tmp = 0.0
	if (t_2 <= -1e+191)
		tmp = Float64(t_3 + Float64(t_1 + Float64(Float64(a / Float64(c / t)) * -4.0)));
	elseif (t_2 <= 5e+14)
		tmp = Float64(Float64(Float64(fma(Float64(x * 9.0), y, b) / z) + Float64(t * Float64(a * -4.0))) / c);
	elseif (t_2 <= 2e+300)
		tmp = Float64(Float64(b + Float64(Float64(9.0 * Float64(x * y)) - Float64(a * Float64(z * Float64(4.0 * t))))) * Float64(Float64(-1.0 / z) / Float64(-c)));
	else
		tmp = Float64(t_3 + Float64(t_1 + Float64(-4.0 * Float64(a * Float64(t / c)))));
	end
	return tmp
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(9.0 * N[(N[(y / c), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(b / c), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+191], N[(t$95$3 + N[(t$95$1 + N[(N[(a / N[(c / t), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+14], N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y + b), $MachinePrecision] / z), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, 2e+300], N[(N[(b + N[(N[(9.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(z * N[(4.0 * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(-1.0 / z), $MachinePrecision] / (-c)), $MachinePrecision]), $MachinePrecision], N[(t$95$3 + N[(t$95$1 + N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	20.2
Target	14.1
Herbie	6.3

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

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -1.00000000000000007e191

   1. Initial program 30.0

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

   2. Simplified 24.6

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
      Proof
      (/.f64 (+.f64 (-.f64 (*.f64 x (*.f64 9 y)) (*.f64 (*.f64 z 4) (*.f64 t a))) b) (*.f64 z c)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (-.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x 9) y)) (*.f64 (*.f64 z 4) (*.f64 t a))) b) (*.f64 z c)): 6 points increase in error, 6 points decrease in error
      (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 z 4) t) a))) b) (*.f64 z c)): 24 points increase in error, 10 points decrease in error

   3. Taylor expanded in x around 0 16.1

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

   4. Simplified 19.9

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z} + \left(9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right) - 4 \cdot \frac{a}{\frac{c}{t}}\right)} \]
      Proof
      (+.f64 (/.f64 (/.f64 b c) z) (-.f64 (*.f64 9 (*.f64 (/.f64 y c) (/.f64 x z))) (*.f64 4 (/.f64 a (/.f64 c t))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-/r*_binary64 (/.f64 b (*.f64 c z))) (-.f64 (*.f64 9 (*.f64 (/.f64 y c) (/.f64 x z))) (*.f64 4 (/.f64 a (/.f64 c t))))): 29 points increase in error, 19 points decrease in error
      (+.f64 (/.f64 b (*.f64 c z)) (-.f64 (*.f64 9 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (/.f64 a (/.f64 c t))))): 38 points increase in error, 29 points decrease in error
      (+.f64 (/.f64 b (*.f64 c z)) (-.f64 (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z))) (*.f64 4 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 a t) c))))): 31 points increase in error, 24 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))): 0 points increase in error, 0 points decrease in error

   if -1.00000000000000007e191 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 5e14

   1. Initial program 9.3

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

   2. Simplified 3.7

      \[\leadsto \color{blue}{\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}} \]
      Proof
      (/.f64 (+.f64 (/.f64 (fma.f64 (*.f64 x 9) y b) z) (*.f64 t (*.f64 a -4))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (*.f64 x 9) y) b)) z) (*.f64 t (*.f64 a -4))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 b (*.f64 (*.f64 x 9) y))) z) (*.f64 t (*.f64 a -4))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 t (*.f64 a (Rewrite<= metadata-eval (neg.f64 4))))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 t (Rewrite<= distribute-rgt-neg-in_binary64 (neg.f64 (*.f64 a 4))))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite=> distribute-rgt-neg-out_binary64 (neg.f64 (*.f64 t (*.f64 a 4))))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= distribute-lft-neg-out_binary64 (*.f64 (neg.f64 t) (*.f64 a 4)))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= cancel-sign-sub-inv_binary64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (*.f64 t (*.f64 a 4)))) 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 (*.f64 t a) 4))) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (/.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) z) (Rewrite<= *-commutative_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): 18 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): 18 points increase in error, 17 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): 26 points increase in error, 5 points decrease in error
      (/.f64 (Rewrite<= div-sub_binary64 (/.f64 (-.f64 (+.f64 b (*.f64 (*.f64 x 9) y)) (*.f64 (*.f64 (*.f64 z 4) t) a)) z)) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (/.f64 (Rewrite<= associate-+r-_binary64 (+.f64 b (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)))) z) c): 0 points increase in error, 0 points decrease in error
      (/.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b)) z) c): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r*_binary64 (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))): 51 points increase in error, 38 points decrease in error

   if 5e14 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 2.0000000000000001e300

   1. Initial program 0.5

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

   2. Applied egg-rr 3.5

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

   3. Simplified 0.9

      \[\leadsto \color{blue}{\left(-\left(b + \left(9 \cdot \left(y \cdot x\right) - \left(z \cdot \left(4 \cdot t\right)\right) \cdot a\right)\right)\right) \cdot \frac{\frac{1}{z}}{-c}} \]
      Proof
      (*.f64 (neg.f64 (+.f64 b (-.f64 (*.f64 9 (*.f64 y x)) (*.f64 (*.f64 z (*.f64 4 t)) a)))) (/.f64 (/.f64 1 z) (neg.f64 c))): 0 points increase in error, 0 points decrease in error
      (*.f64 (neg.f64 (+.f64 b (-.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 9 y) x)) (*.f64 (*.f64 z (*.f64 4 t)) a)))) (/.f64 (/.f64 1 z) (neg.f64 c))): 9 points increase in error, 3 points decrease in error
      (*.f64 (neg.f64 (+.f64 b (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 x (*.f64 9 y))) (*.f64 (*.f64 z (*.f64 4 t)) a)))) (/.f64 (/.f64 1 z) (neg.f64 c))): 0 points increase in error, 0 points decrease in error
      (*.f64 (neg.f64 (+.f64 b (-.f64 (*.f64 x (*.f64 9 y)) (Rewrite<= associate-*r*_binary64 (*.f64 z (*.f64 (*.f64 4 t) a)))))) (/.f64 (/.f64 1 z) (neg.f64 c))): 14 points increase in error, 21 points decrease in error
      (*.f64 (neg.f64 (Rewrite<= +-commutative_binary64 (+.f64 (-.f64 (*.f64 x (*.f64 9 y)) (*.f64 z (*.f64 (*.f64 4 t) a))) b))) (/.f64 (/.f64 1 z) (neg.f64 c))): 0 points increase in error, 0 points decrease in error
      (*.f64 (neg.f64 (+.f64 (-.f64 (*.f64 x (*.f64 9 y)) (*.f64 z (*.f64 (*.f64 4 t) a))) b)) (Rewrite<= associate-/r*_binary64 (/.f64 1 (*.f64 z (neg.f64 c))))): 22 points increase in error, 24 points decrease in error

   if 2.0000000000000001e300 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 62.4

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

   2. Simplified 54.9

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
      Proof
      (/.f64 (+.f64 (-.f64 (*.f64 x (*.f64 9 y)) (*.f64 (*.f64 z 4) (*.f64 t a))) b) (*.f64 z c)): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (-.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 x 9) y)) (*.f64 (*.f64 z 4) (*.f64 t a))) b) (*.f64 z c)): 6 points increase in error, 6 points decrease in error
      (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 z 4) t) a))) b) (*.f64 z c)): 24 points increase in error, 10 points decrease in error

   3. Taylor expanded in x around 0 30.2

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

   4. Simplified 7.2

      \[\leadsto \color{blue}{\frac{\frac{b}{c}}{z} + \left(9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right) - 4 \cdot \frac{a}{\frac{c}{t}}\right)} \]
      Proof
      (+.f64 (/.f64 (/.f64 b c) z) (-.f64 (*.f64 9 (*.f64 (/.f64 y c) (/.f64 x z))) (*.f64 4 (/.f64 a (/.f64 c t))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-/r*_binary64 (/.f64 b (*.f64 c z))) (-.f64 (*.f64 9 (*.f64 (/.f64 y c) (/.f64 x z))) (*.f64 4 (/.f64 a (/.f64 c t))))): 29 points increase in error, 19 points decrease in error
      (+.f64 (/.f64 b (*.f64 c z)) (-.f64 (*.f64 9 (Rewrite<= times-frac_binary64 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (/.f64 a (/.f64 c t))))): 38 points increase in error, 29 points decrease in error
      (+.f64 (/.f64 b (*.f64 c z)) (-.f64 (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z))) (*.f64 4 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 a t) c))))): 31 points increase in error, 24 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (/.f64 b (*.f64 c z)) (*.f64 9 (/.f64 (*.f64 y x) (*.f64 c z)))) (*.f64 4 (/.f64 (*.f64 a t) c)))): 0 points increase in error, 0 points decrease in error

   5. Applied egg-rr 7.3

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

4. Final simplification 6.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -1 \cdot 10^{+191}:\\ \;\;\;\;\frac{\frac{b}{c}}{z} + \left(9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right) + \frac{a}{\frac{c}{t}} \cdot -4\right)\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x \cdot 9, y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 2 \cdot 10^{+300}:\\ \;\;\;\;\left(b + \left(9 \cdot \left(x \cdot y\right) - a \cdot \left(z \cdot \left(4 \cdot t\right)\right)\right)\right) \cdot \frac{\frac{-1}{z}}{-c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z} + \left(9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right) + -4 \cdot \left(a \cdot \frac{t}{c}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	6.9
Cost	6868

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-47}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 2
Error	7.0
Cost	6868

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;\left(b + \left(9 \cdot \left(x \cdot y\right) - a \cdot \left(z \cdot \left(4 \cdot t\right)\right)\right)\right) \cdot \frac{\frac{-1}{z}}{-c}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 3
Error	6.4
Cost	5324

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{\frac{b}{c}}{z} + \left(9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right) + -4 \cdot \left(a \cdot \frac{t}{c}\right)\right)\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+191}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;\left(b + \left(9 \cdot \left(x \cdot y\right) - a \cdot \left(z \cdot \left(4 \cdot t\right)\right)\right)\right) \cdot \frac{\frac{-1}{z}}{-c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	6.3
Cost	5324

\[\begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_3 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;t_2 \leq -1 \cdot 10^{+191}:\\ \;\;\;\;t_3 + \left(t_1 + \frac{a}{\frac{c}{t}} \cdot -4\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+14}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+300}:\\ \;\;\;\;\left(b + \left(9 \cdot \left(x \cdot y\right) - a \cdot \left(z \cdot \left(4 \cdot t\right)\right)\right)\right) \cdot \frac{\frac{-1}{z}}{-c}\\ \mathbf{else}:\\ \;\;\;\;t_3 + \left(t_1 + -4 \cdot \left(a \cdot \frac{t}{c}\right)\right)\\ \end{array} \]

Alternative 5
Error	35.2
Cost	1768

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := y \cdot \frac{9}{z \cdot \frac{c}{x}}\\ \mathbf{if}\;t \leq -1050000:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-276}:\\ \;\;\;\;\frac{\frac{1}{c}}{\frac{z}{b}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-305}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-183}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-144}:\\ \;\;\;\;\frac{y}{c} \cdot \frac{9}{\frac{z}{x}}\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-87}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 6
Error	34.0
Cost	1632

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_2 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+258}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+139}:\\ \;\;\;\;9 \cdot \frac{\frac{x}{c}}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-56}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-235}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \end{array} \]

Alternative 7
Error	24.3
Cost	1496

\[\begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;x \leq -2.65 \cdot 10^{+256}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+139}:\\ \;\;\;\;9 \cdot \frac{\frac{x}{c}}{\frac{z}{y}}\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{+136}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-53}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \end{array} \]

Alternative 8
Error	12.9
Cost	1484

\[\begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b - x \cdot \left(y \cdot -9\right)}{z}}{c}\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-53}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq 58:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \end{array} \]

Alternative 9
Error	24.5
Cost	1364

\[\begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;x \leq -2.9 \cdot 10^{+183}:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;x \leq -5.1 \cdot 10^{+137}:\\ \;\;\;\;y \cdot \frac{9}{z \cdot \frac{c}{x}}\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{-53}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \end{array} \]

Alternative 10
Error	24.6
Cost	1364

\[\begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;x \leq -1.4 \cdot 10^{+182}:\\ \;\;\;\;\frac{\frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{+136}:\\ \;\;\;\;y \cdot \frac{9}{z \cdot \frac{c}{x}}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-53}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \end{array} \]

Alternative 11
Error	35.8
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_3 := \frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+97}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq -3.55 \cdot 10^{+28}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Error	35.9
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;z \leq -8.6 \cdot 10^{+148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{+96}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 13
Error	35.9
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+167}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;z \leq -1.46 \cdot 10^{+97}:\\ \;\;\;\;\frac{b}{c} \cdot \frac{1}{z}\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+29}:\\ \;\;\;\;\frac{a}{\frac{c}{t}} \cdot -4\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+14}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 14
Error	36.9
Cost	1240

\[\begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{-60}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-133}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-238}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-128}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-31}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+95}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 15
Error	36.3
Cost	1240

\[\begin{array}{l} t_1 := 9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{if}\;a \leq -8.6 \cdot 10^{-60}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-132}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-244}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-111}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+97}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 16
Error	36.7
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-60}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-133}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-238}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+95}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 17
Error	36.7
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -8.2 \cdot 10^{-60}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq -8.5 \cdot 10^{-133}:\\ \;\;\;\;\frac{1}{\frac{c}{\frac{b}{z}}}\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-238}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+95}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 18
Error	36.0
Cost	712

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	35.9
Cost	712

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+99}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 20
Error	43.9
Cost	452

\[\begin{array}{l} \mathbf{if}\;a \leq 1.66 \cdot 10^{-195}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 21
Error	43.3
Cost	320

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

Alternative 22
Error	43.6
Cost	320

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

Reproduce

herbie shell --seed 2022325 
(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)))