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

Average Accuracy: 79.6% → 91.9%

Time: 31.4s

Precision: binary64

Cost: 20052

• Unsound rule application detected in e-graph. Results may not be sound.

• 37.5% of points produce a very large (infinite) output. You may want to add a precondition.

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_3 := \frac{\mathsf{fma}\left(t, a \cdot -4, t_1\right)}{c}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{-72}:\\ \;\;\;\;\frac{t_1 + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{+279}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

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 (/ (fma x (* 9.0 y) b) z))
        (t_2 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))
        (t_3 (/ (fma t (* a -4.0) t_1) c)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -2e+156)
       t_2
       (if (<= t_2 5e-72)
         (/ (+ t_1 (* t (* a -4.0))) c)
         (if (<= t_2 4e+279)
           t_2
           (if (<= t_2 INFINITY) t_3 (* -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 = fma(x, (9.0 * y), b) / z;
	double t_2 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double t_3 = fma(t, (a * -4.0), t_1) / c;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -2e+156) {
		tmp = t_2;
	} else if (t_2 <= 5e-72) {
		tmp = (t_1 + (t * (a * -4.0))) / c;
	} else if (t_2 <= 4e+279) {
		tmp = t_2;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = -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(fma(x, Float64(9.0 * y), b) / 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(fma(t, Float64(a * -4.0), t_1) / c)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -2e+156)
		tmp = t_2;
	elseif (t_2 <= 5e-72)
		tmp = Float64(Float64(t_1 + Float64(t * Float64(a * -4.0))) / c);
	elseif (t_2 <= 4e+279)
		tmp = t_2;
	elseif (t_2 <= Inf)
		tmp = t_3;
	else
		tmp = 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[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $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[(t * N[(a * -4.0), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -2e+156], t$95$2, If[LessEqual[t$95$2, 5e-72], N[(N[(t$95$1 + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, 4e+279], t$95$2, If[LessEqual[t$95$2, Infinity], t$95$3, N[(-4.0 * N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Target

Original	79.6%
Target	81.1%
Herbie	91.9%

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

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -inf.0 or 4.00000000000000023e279 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 80.0%

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

   2. Simplified 93.5%

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

      [Start] 80.0	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 82.3	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   if -inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -2e156 or 4.9999999999999996e-72 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 4.00000000000000023e279

   1. Initial program 99.5%

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

   if -2e156 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 4.9999999999999996e-72

   1. Initial program 82.4%

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

   2. Simplified 99.6%

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

      [Start] 82.4	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 99.7	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   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 0.0%

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

   2. Simplified 0.8%

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

      [Start] 0.0	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-*l* [=>] 0.0	\[ \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-*l* [=>] 0.8	\[ \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Taylor expanded in z around inf 49.7%

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

   4. Simplified 76.7%

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

      [Start] 49.7	\[ -4 \cdot \frac{a \cdot t}{c} \]
      *-commutative [=>] 49.7	\[ \color{blue}{\frac{a \cdot t}{c} \cdot -4} \]
      associate-/l* [=>] 76.7	\[ \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4 \]

   5. Applied egg-rr 76.6%

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

      [Start] 76.7	\[ \frac{a}{\frac{c}{t}} \cdot -4 \]
      clear-num [=>] 76.7	\[ \color{blue}{\frac{1}{\frac{\frac{c}{t}}{a}}} \cdot -4 \]
      associate-/r/ [=>] 76.5	\[ \color{blue}{\left(\frac{1}{\frac{c}{t}} \cdot a\right)} \cdot -4 \]
      clear-num [<=] 76.6	\[ \left(\color{blue}{\frac{t}{c}} \cdot a\right) \cdot -4 \]

3. Recombined 4 regimes into one program.

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -2 \cdot 10^{+156}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 5 \cdot 10^{-72}:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 4 \cdot 10^{+279}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	91.4%
Cost	13780

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 4 \cdot 10^{+279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 2
Accuracy	84.5%
Cost	5068

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{\frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 3
Accuracy	50.2%
Cost	2161

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_2 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ t_3 := \frac{\frac{b}{z}}{c}\\ t_4 := a \cdot \left(t \cdot \frac{-4}{c}\right)\\ t_5 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;y \leq -2.7 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-265}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-227}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-183}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-14}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+47}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+63}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+74}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+118} \lor \neg \left(y \leq 4.7 \cdot 10^{+147}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 4
Accuracy	50.7%
Cost	2028

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_2 := a \cdot \left(t \cdot \frac{-4}{c}\right)\\ t_3 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ t_4 := \frac{\frac{b}{z}}{c}\\ \mathbf{if}\;y \leq -1 \cdot 10^{-72}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-263}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-226}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-183}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-14}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+44}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+93}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Accuracy	49.1%
Cost	2028

\[\begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{+76}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -0.00011:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-77}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-229}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{-282}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-288}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-50}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 6
Accuracy	48.8%
Cost	2028

\[\begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{+76}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-5}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-79}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-173}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-229}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-287}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-50}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 7
Accuracy	49.1%
Cost	2028

\[\begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -8.2 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+75}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -0.000165:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-171}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-229}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;t \leq -4.25 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-286}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{-50}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 8
Accuracy	49.1%
Cost	2028

\[\begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -7.6 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+75}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-6}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-32}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-78}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-171}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-231}:\\ \;\;\;\;\frac{1}{z \cdot \frac{c}{b}}\\ \mathbf{elif}\;t \leq -7.8 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{z \cdot \left(0.1111111111111111 \cdot \frac{c}{y}\right)}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-281}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-49}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 9
Accuracy	56.3%
Cost	1761

\[\begin{array}{l} t_1 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{-75}:\\ \;\;\;\;\frac{y}{\frac{z}{x}} \cdot \frac{9}{c}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-263}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-227}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-182}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-13} \lor \neg \left(y \leq 2.25 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 10
Accuracy	70.7%
Cost	1233

\[\begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-62}:\\ \;\;\;\;\frac{y}{\frac{z}{x}} \cdot \frac{9}{c}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+46} \lor \neg \left(y \leq 4.1 \cdot 10^{+117}\right) \land y \leq 2.8 \cdot 10^{+148}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 11
Accuracy	71.0%
Cost	1233

\[\begin{array}{l} t_1 := b + 9 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{\frac{t_1}{z}}{c}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+44} \lor \neg \left(y \leq 3.8 \cdot 10^{+115}\right) \land y \leq 2 \cdot 10^{+148}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{z \cdot c}\\ \end{array} \]

Alternative 12
Accuracy	76.0%
Cost	1092

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -6.4 \cdot 10^{-68}:\\ \;\;\;\;\frac{t_1 + \frac{9 \cdot y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+34}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \end{array} \]

Alternative 13
Accuracy	50.1%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{-73} \lor \neg \left(z \leq 3 \cdot 10^{+32}\right):\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 14
Accuracy	50.1%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-74} \lor \neg \left(z \leq 2.5 \cdot 10^{+32}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 15
Accuracy	50.0%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-75}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \end{array} \]

Alternative 16
Accuracy	35.1%
Cost	320

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

Reproduce

herbie shell --seed 2023160 
(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)))