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

Average Accuracy: 42.9% → 55.1%

Time: 37.9s

Precision: binary64

Cost: 11212

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

Math

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

↓

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_3 := \frac{\frac{b}{z} + t_1}{c}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-309}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{-7}:\\ \;\;\;\;\frac{t_1 + \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}}{c}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+296}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

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 (* t (* a -4.0)))
        (t_2 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))
        (t_3 (/ (+ (/ b z) t_1) c)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -1e-309)
       t_2
       (if (<= t_2 4e-7)
         (/ (+ t_1 (/ (fma x (* 9.0 y) b) z)) c)
         (if (<= t_2 2e+296) t_2 t_3))))))

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 = t * (a * -4.0);
	double t_2 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double t_3 = ((b / z) + t_1) / c;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -1e-309) {
		tmp = t_2;
	} else if (t_2 <= 4e-7) {
		tmp = (t_1 + (fma(x, (9.0 * y), b) / z)) / c;
	} else if (t_2 <= 2e+296) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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(t * Float64(a * -4.0))
	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(Float64(b / z) + t_1) / c)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -1e-309)
		tmp = t_2;
	elseif (t_2 <= 4e-7)
		tmp = Float64(Float64(t_1 + Float64(fma(x, Float64(9.0 * y), b) / z)) / c);
	elseif (t_2 <= 2e+296)
		tmp = t_2;
	else
		tmp = t_3;
	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[(t * N[(a * -4.0), $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[(N[(b / z), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -1e-309], t$95$2, If[LessEqual[t$95$2, 4e-7], N[(N[(t$95$1 + N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, 2e+296], t$95$2, t$95$3]]]]]]]

Target

Original	42.9%
Target	48.8%
Herbie	55.1%

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

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -inf.0 or 1.99999999999999996e296 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 0.7%

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

   2. Simplified 23.9%

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

      [Start] 0.7	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 2.9	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Taylor expanded in x around 0 24.3%

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

   if -inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -1.000000000000002e-309 or 3.9999999999999998e-7 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 1.99999999999999996e296

   1. Initial program 99.4%

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

   if -1.000000000000002e-309 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 3.9999999999999998e-7

   1. Initial program 69.3%

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

   2. Simplified 99.7%

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

      [Start] 69.3	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 99.7	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -\infty:\\ \;\;\;\;\frac{\frac{b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -1 \cdot 10^{-309}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 4 \cdot 10^{-7}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 2 \cdot 10^{+296}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	54.3%
Cost	6354

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq -1 \cdot 10^{-309} \lor \neg \left(t_1 \leq 0\right) \land t_1 \leq 2 \cdot 10^{+296}\right):\\ \;\;\;\;\frac{\frac{b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	54.7%
Cost	6352

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{\frac{b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-309}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{-23}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{c}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+296}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	23.5%
Cost	1896

\[\begin{array}{l} t_1 := \frac{\frac{b}{z}}{c}\\ t_2 := \frac{\frac{b}{c}}{z}\\ t_3 := \frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+209}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{+145}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{+75}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-81}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-265}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-209}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{-44}:\\ \;\;\;\;9 \cdot \frac{x \cdot y}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 4
Accuracy	24.0%
Cost	1764

\[\begin{array}{l} t_1 := \frac{\frac{b}{z}}{c}\\ t_2 := \frac{\frac{b}{c}}{z}\\ t_3 := \frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+203}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{+76}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-258}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 6.4 \cdot 10^{-209}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ \end{array} \]

Alternative 5
Accuracy	23.4%
Cost	1764

\[\begin{array}{l} t_1 := \frac{\frac{b}{z}}{c}\\ t_2 := \frac{\frac{b}{c}}{z}\\ t_3 := \frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;x \leq -9.5 \cdot 10^{+196}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{+144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{+79}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-71}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-266}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-292}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.7 \cdot 10^{-209}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ \end{array} \]

Alternative 6
Accuracy	24.1%
Cost	1636

\[\begin{array}{l} t_1 := \frac{-4 \cdot \left(t \cdot a\right)}{c}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_3 := \frac{\frac{b}{z}}{c}\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{+224}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+103}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+85}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+19}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-162}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-260}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-295}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Accuracy	29.8%
Cost	1628

\[\begin{array}{l} t_1 := \frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ t_2 := \frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+207}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.26 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -9.8 \cdot 10^{-163}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-263}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-292}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-209}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	24.8%
Cost	1504

\[\begin{array}{l} t_1 := \frac{\frac{b}{z}}{c}\\ t_2 := \frac{\frac{b}{c}}{z}\\ t_3 := \frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{+204}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.55 \cdot 10^{+77}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-264}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-292}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 9
Accuracy	47.3%
Cost	1480

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{\frac{b}{z} + t_1}{c}\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{-13}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+28}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{+153}:\\ \;\;\;\;\frac{t_1 + \frac{\left(x \cdot 9\right) \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+169}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Accuracy	39.2%
Cost	1365

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-68}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+144}:\\ \;\;\;\;\frac{b + x \cdot \left(9 \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+221} \lor \neg \left(y \leq 10^{+256}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ \end{array} \]

Alternative 11
Accuracy	22.7%
Cost	1241

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+208}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-162}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-266} \lor \neg \left(x \leq -3.2 \cdot 10^{-294}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Accuracy	22.8%
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;x \leq -3.05 \cdot 10^{+203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.7 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-163}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-263}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot -4\right) \cdot \frac{t}{c}\\ \end{array} \]

Alternative 13
Accuracy	22.9%
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_3 := a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-162}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-261}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Accuracy	22.7%
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-74}:\\ \;\;\;\;a \cdot \left(t \cdot \frac{-4}{c}\right)\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-162}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq -1.7 \cdot 10^{-266}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Accuracy	22.6%
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_3 := \frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{if}\;x \leq -1.22 \cdot 10^{+196}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.25 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-162}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-263}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Accuracy	22.5%
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := \frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{if}\;x \leq -1.3 \cdot 10^{+197}:\\ \;\;\;\;\frac{t}{\frac{c}{a \cdot -4}}\\ \mathbf{elif}\;x \leq -3.25 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{-162}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-262}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 17
Accuracy	22.5%
Cost	1240

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := \frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+196}:\\ \;\;\;\;\frac{t}{\frac{c}{a \cdot -4}}\\ \mathbf{elif}\;x \leq -2.25 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-162}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-261}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.1 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 18
Accuracy	41.1%
Cost	1224

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{-64}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+78}:\\ \;\;\;\;\frac{\frac{b}{z} + t_1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \end{array} \]

Alternative 19
Accuracy	41.1%
Cost	1224

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{-64}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+75}:\\ \;\;\;\;\frac{\frac{b}{z} + t_1}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{\left(x \cdot 9\right) \cdot y}{z}}{c}\\ \end{array} \]

Alternative 20
Accuracy	19.9%
Cost	320

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

Alternative 21
Accuracy	20.0%
Cost	320

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

Reproduce

herbie shell --seed 2023157 
(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)))