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

Average Accuracy: 67.5% → 89.7%

Time: 34.0s

Precision: binary64

Cost: 6352

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{\frac{9 \cdot y}{\frac{z}{x}} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+31}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+269}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))
        (t_2 (/ (+ (/ (* 9.0 y) (/ z x)) (* t (* a -4.0))) c)))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -1e-92)
       t_1
       (if (<= t_1 2e+31)
         (* (/ (+ b (- (* x (* 9.0 y)) (* (* z 4.0) (* t a)))) z) (/ 1.0 c))
         (if (<= t_1 5e+269) t_1 t_2))))))

C

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

↓

double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double t_2 = (((9.0 * y) / (z / x)) + (t * (a * -4.0))) / c;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -1e-92) {
		tmp = t_1;
	} else if (t_1 <= 2e+31) {
		tmp = ((b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / z) * (1.0 / c);
	} else if (t_1 <= 5e+269) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static 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);
}

↓

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double t_2 = (((9.0 * y) / (z / x)) + (t * (a * -4.0))) / c;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= -1e-92) {
		tmp = t_1;
	} else if (t_1 <= 2e+31) {
		tmp = ((b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / z) * (1.0 / c);
	} else if (t_1 <= 5e+269) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c):
	return ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)

↓

def code(x, y, z, t, a, b, c):
	t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c)
	t_2 = (((9.0 * y) / (z / x)) + (t * (a * -4.0))) / c
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= -1e-92:
		tmp = t_1
	elif t_1 <= 2e+31:
		tmp = ((b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / z) * (1.0 / c)
	elif t_1 <= 5e+269:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

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

↓

function code(x, y, z, t, a, b, c)
	t_1 = Float64(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	t_2 = Float64(Float64(Float64(Float64(9.0 * y) / Float64(z / x)) + Float64(t * Float64(a * -4.0))) / c)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -1e-92)
		tmp = t_1;
	elseif (t_1 <= 2e+31)
		tmp = Float64(Float64(Float64(b + Float64(Float64(x * Float64(9.0 * y)) - Float64(Float64(z * 4.0) * Float64(t * a)))) / z) * Float64(1.0 / c));
	elseif (t_1 <= 5e+269)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b, c)
	tmp = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
end

↓

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	t_2 = (((9.0 * y) / (z / x)) + (t * (a * -4.0))) / c;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= -1e-92)
		tmp = t_1;
	elseif (t_1 <= 2e+31)
		tmp = ((b + ((x * (9.0 * y)) - ((z * 4.0) * (t * a)))) / z) * (1.0 / c);
	elseif (t_1 <= 5e+269)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(N[(x * 9.0), $MachinePrecision] * y), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(9.0 * y), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -1e-92], t$95$1, If[LessEqual[t$95$1, 2e+31], N[(N[(N[(b + N[(N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision] - N[(N[(z * 4.0), $MachinePrecision] * N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+269], t$95$1, t$95$2]]]]]]

Target

Original	67.5%
Target	77.4%
Herbie	89.7%

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

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 5.0000000000000002e269 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 7.9%

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

   2. Simplified 61.2%

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

      [Start] 7.9	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 10.5	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Taylor expanded in x around inf 53.3%

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

   4. Simplified 66.3%

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

      [Start] 53.3	\[ \frac{9 \cdot \frac{y \cdot x}{z} + t \cdot \left(a \cdot -4\right)}{c} \]
      associate-/l* [=>] 66.4	\[ \frac{9 \cdot \color{blue}{\frac{y}{\frac{z}{x}}} + t \cdot \left(a \cdot -4\right)}{c} \]
      associate-*r/ [=>] 66.3	\[ \frac{\color{blue}{\frac{9 \cdot y}{\frac{z}{x}}} + t \cdot \left(a \cdot -4\right)}{c} \]

   if -inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -9.99999999999999988e-93 or 1.9999999999999999e31 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 5.0000000000000002e269

   1. Initial program 98.9%

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

   if -9.99999999999999988e-93 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 1.9999999999999999e31

   1. Initial program 75.8%

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

   2. Applied egg-rr 98.0%

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

      [Start] 75.8	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 98.0	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]
      div-inv [=>] 97.9	\[ \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z} \cdot \frac{1}{c}} \]
      associate-*l* [=>] 97.8	\[ \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z} \cdot \frac{1}{c} \]
      associate-*l* [=>] 98.0	\[ \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z} \cdot \frac{1}{c} \]

3. Recombined 3 regimes into one program.

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -\infty:\\ \;\;\;\;\frac{\frac{9 \cdot y}{\frac{z}{x}} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -1 \cdot 10^{-92}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 2 \cdot 10^{+31}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 5 \cdot 10^{+269}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{9 \cdot y}{\frac{z}{x}} + t \cdot \left(a \cdot -4\right)}{c}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	87.3%
Cost	6352

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_3 := \frac{\frac{9 \cdot y}{\frac{z}{x}} + t_1}{c}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-283}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{-158}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+269}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Accuracy	89.1%
Cost	6352

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{\frac{9 \cdot y}{\frac{z}{x}} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{-137}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{c}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+269}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	40.8%
Cost	2164

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := 9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ t_3 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{-127}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-232}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-236}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{1}{c} \cdot \frac{b}{z}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+64}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+89}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+190}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 4
Accuracy	41.0%
Cost	2164

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := 9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ t_3 := -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;a \leq -8.4 \cdot 10^{-128}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-232}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-236}:\\ \;\;\;\;\frac{x}{c} \cdot \frac{9 \cdot y}{z}\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.55 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{-32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+30}:\\ \;\;\;\;\frac{1}{c} \cdot \frac{b}{z}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+64}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.02 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+93}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;a \leq 10^{+191}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 5
Accuracy	41.7%
Cost	1901

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{-126}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq -5.1 \cdot 10^{-232}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{-236}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+30}:\\ \;\;\;\;\frac{1}{c} \cdot \frac{b}{z}\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+99} \lor \neg \left(a \leq 3.6 \cdot 10^{+190}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	41.8%
Cost	1637

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ t_2 := \frac{9}{\frac{z \cdot c}{x \cdot y}}\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{-126}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-242}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-128}:\\ \;\;\;\;9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+98} \lor \neg \left(a \leq 3.3 \cdot 10^{+190}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	41.7%
Cost	1637

\[\begin{array}{l} t_1 := \frac{\frac{b}{c}}{z}\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{-126}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-241}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-235}:\\ \;\;\;\;\frac{9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-128}:\\ \;\;\;\;9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-5}:\\ \;\;\;\;\frac{9}{\frac{z \cdot c}{x \cdot y}}\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+98} \lor \neg \left(a \leq 3.2 \cdot 10^{+190}\right):\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	70.2%
Cost	1488

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{\frac{9 \cdot y}{\frac{z}{x}} + t_1}{c}\\ t_3 := \frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+52}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+201}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	78.2%
Cost	1480

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{\frac{9 \cdot y}{\frac{z}{x}} + t_1}{c}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+65}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{+201}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Accuracy	67.2%
Cost	1233

\[\begin{array}{l} t_1 := \frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{if}\;z \leq -6.6 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{+168}:\\ \;\;\;\;\frac{x \cdot 9}{c \cdot \frac{z}{y}}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+75} \lor \neg \left(z \leq 1.15 \cdot 10^{+53}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 11
Accuracy	58.7%
Cost	1232

\[\begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{-126}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.25 \cdot 10^{+55}:\\ \;\;\;\;9 \cdot \frac{y}{c \cdot \frac{z}{x}}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+167}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 12
Accuracy	46.2%
Cost	713

\[\begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-38} \lor \neg \left(t \leq 3.5 \cdot 10^{-33}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 13
Accuracy	46.9%
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-38}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-92}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \end{array} \]

Alternative 14
Accuracy	32.5%
Cost	320

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

Alternative 15
Accuracy	32.7%
Cost	320

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

Reproduce

herbie shell --seed 2023151 
(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)))