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

Average Accuracy: 78.5% → 92.0%

Time: 27.6s

Precision: binary64

Cost: 17484

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

• 36.7% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{+307}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z} + \left(t \cdot \left(a \cdot -4\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)\right)\right) \cdot \frac{1}{c}\\ \end{array} \]

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 (/ (fma t (* a -4.0) (/ (fma x (* 9.0 y) b) z)) c)))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -5e+141)
       t_1
       (if (<= t_1 1e+61)
         t_2
         (if (<= t_1 1e+307)
           t_1
           (*
            (+ (/ b z) (+ (* t (* a -4.0)) (* 9.0 (* x (/ y z)))))
            (/ 1.0 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 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double t_2 = fma(t, (a * -4.0), (fma(x, (9.0 * y), b) / z)) / c;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -5e+141) {
		tmp = t_1;
	} else if (t_1 <= 1e+61) {
		tmp = t_2;
	} else if (t_1 <= 1e+307) {
		tmp = t_1;
	} else {
		tmp = ((b / z) + ((t * (a * -4.0)) + (9.0 * (x * (y / z))))) * (1.0 / 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(Float64(Float64(Float64(Float64(x * 9.0) * y) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	t_2 = Float64(fma(t, Float64(a * -4.0), Float64(fma(x, Float64(9.0 * y), b) / z)) / c)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -5e+141)
		tmp = t_1;
	elseif (t_1 <= 1e+61)
		tmp = t_2;
	elseif (t_1 <= 1e+307)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(b / z) + Float64(Float64(t * Float64(a * -4.0)) + Float64(9.0 * Float64(x * Float64(y / z))))) * Float64(1.0 / 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[(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[(t * N[(a * -4.0), $MachinePrecision] + N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -5e+141], t$95$1, If[LessEqual[t$95$1, 1e+61], t$95$2, If[LessEqual[t$95$1, 1e+307], t$95$1, N[(N[(N[(b / z), $MachinePrecision] + N[(N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	78.5%
Target	79.9%
Herbie	92.0%

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

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 -5.00000000000000025e141 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 9.99999999999999949e60

   1. Initial program 77.8%

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

   2. Simplified 95.0%

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

      [Start] 77.8	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 91.6	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   if -inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -5.00000000000000025e141 or 9.99999999999999949e60 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 9.99999999999999986e306

   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 9.99999999999999986e306 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 61.2%

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

   2. Applied egg-rr 72.8%

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

      [Start] 61.2	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 68.5	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]
      div-inv [=>] 68.5	\[ \color{blue}{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z} \cdot \frac{1}{c}} \]
      associate-*l* [=>] 68.5	\[ \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z} \cdot \frac{1}{c} \]
      associate-*l* [=>] 72.8	\[ \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z} \cdot \frac{1}{c} \]

   3. Taylor expanded in x around 0 79.7%

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

   4. Simplified 88.3%

      \[\leadsto \color{blue}{\left(\frac{b}{z} + \mathsf{fma}\left(9, \frac{y}{z} \cdot x, t \cdot \left(a \cdot -4\right)\right)\right)} \cdot \frac{1}{c} \]
      Step-by-step derivation

      [Start] 79.7	\[ \left(\left(\frac{b}{z} + 9 \cdot \frac{y \cdot x}{z}\right) - 4 \cdot \left(a \cdot t\right)\right) \cdot \frac{1}{c} \]
      associate--l+ [=>] 79.7	\[ \color{blue}{\left(\frac{b}{z} + \left(9 \cdot \frac{y \cdot x}{z} - 4 \cdot \left(a \cdot t\right)\right)\right)} \cdot \frac{1}{c} \]
      fma-neg [=>] 79.7	\[ \left(\frac{b}{z} + \color{blue}{\mathsf{fma}\left(9, \frac{y \cdot x}{z}, -4 \cdot \left(a \cdot t\right)\right)}\right) \cdot \frac{1}{c} \]
      associate-/l* [=>] 86.8	\[ \left(\frac{b}{z} + \mathsf{fma}\left(9, \color{blue}{\frac{y}{\frac{z}{x}}}, -4 \cdot \left(a \cdot t\right)\right)\right) \cdot \frac{1}{c} \]
      associate-/r/ [=>] 88.3	\[ \left(\frac{b}{z} + \mathsf{fma}\left(9, \color{blue}{\frac{y}{z} \cdot x}, -4 \cdot \left(a \cdot t\right)\right)\right) \cdot \frac{1}{c} \]
      distribute-lft-neg-in [=>] 88.3	\[ \left(\frac{b}{z} + \mathsf{fma}\left(9, \frac{y}{z} \cdot x, \color{blue}{\left(-4\right) \cdot \left(a \cdot t\right)}\right)\right) \cdot \frac{1}{c} \]
      metadata-eval [=>] 88.3	\[ \left(\frac{b}{z} + \mathsf{fma}\left(9, \frac{y}{z} \cdot x, \color{blue}{-4} \cdot \left(a \cdot t\right)\right)\right) \cdot \frac{1}{c} \]
      *-commutative [=>] 88.3	\[ \left(\frac{b}{z} + \mathsf{fma}\left(9, \frac{y}{z} \cdot x, \color{blue}{\left(a \cdot t\right) \cdot -4}\right)\right) \cdot \frac{1}{c} \]
      *-commutative [=>] 88.3	\[ \left(\frac{b}{z} + \mathsf{fma}\left(9, \frac{y}{z} \cdot x, \color{blue}{\left(t \cdot a\right)} \cdot -4\right)\right) \cdot \frac{1}{c} \]
      associate-*l* [=>] 88.3	\[ \left(\frac{b}{z} + \mathsf{fma}\left(9, \frac{y}{z} \cdot x, \color{blue}{t \cdot \left(a \cdot -4\right)}\right)\right) \cdot \frac{1}{c} \]

   5. Applied egg-rr 88.3%

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

      [Start] 88.3	\[ \left(\frac{b}{z} + \mathsf{fma}\left(9, \frac{y}{z} \cdot x, t \cdot \left(a \cdot -4\right)\right)\right) \cdot \frac{1}{c} \]
      fma-udef [=>] 88.3	\[ \left(\frac{b}{z} + \color{blue}{\left(9 \cdot \left(\frac{y}{z} \cdot x\right) + t \cdot \left(a \cdot -4\right)\right)}\right) \cdot \frac{1}{c} \]
      +-commutative [=>] 88.3	\[ \left(\frac{b}{z} + \color{blue}{\left(t \cdot \left(a \cdot -4\right) + 9 \cdot \left(\frac{y}{z} \cdot x\right)\right)}\right) \cdot \frac{1}{c} \]

3. Recombined 3 regimes into one program.

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -\infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -5 \cdot 10^{+141}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 10^{+61}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 10^{+307}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z} + \left(t \cdot \left(a \cdot -4\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)\right)\right) \cdot \frac{1}{c}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	91.7%
Cost	11212

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_3 := \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t_1}{c}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq -5 \cdot 10^{+141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 10^{+61}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 10^{+307}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z} + \left(t_1 + 9 \cdot \left(x \cdot \frac{y}{z}\right)\right)\right) \cdot \frac{1}{c}\\ \end{array} \]

Alternative 2
Accuracy	91.3%
Cost	6482

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq -1 \cdot 10^{+32} \lor \neg \left(t_1 \leq 10^{+61}\right) \land t_1 \leq 10^{+307}\right):\\ \;\;\;\;\left(\frac{b}{z} + \left(t \cdot \left(a \cdot -4\right) + 9 \cdot \left(x \cdot \frac{y}{z}\right)\right)\right) \cdot \frac{1}{c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	48.1%
Cost	1764

\[\begin{array}{l} t_1 := 9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -8 \cdot 10^{+153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{+127}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{-245}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-306}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{-240}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-62}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq 4.15 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 4
Accuracy	48.4%
Cost	1764

\[\begin{array}{l} t_1 := 9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{+127}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-245}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-305}:\\ \;\;\;\;x \cdot \frac{9}{\frac{z}{\frac{y}{c}}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-242}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-67}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 5
Accuracy	48.3%
Cost	1764

\[\begin{array}{l} t_1 := 9 \cdot \frac{x \cdot \frac{y}{c}}{z}\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{+127}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{-245}:\\ \;\;\;\;\frac{b}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t \leq -3 \cdot 10^{-306}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-241}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-70}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-39}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 6
Accuracy	74.3%
Cost	1488

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{\frac{b}{z} + t_1}{c}\\ t_3 := \frac{t_1 + \frac{9 \cdot y}{\frac{z}{x}}}{c}\\ \mathbf{if}\;b \leq -5.1 \cdot 10^{-9}:\\ \;\;\;\;\frac{1}{c} \cdot \left(\frac{b}{z} + -4 \cdot \left(t \cdot a\right)\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-113}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 5 \cdot 10^{+40}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+69}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Accuracy	84.6%
Cost	1480

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+115}:\\ \;\;\;\;\frac{\frac{b}{z} + t_1}{c}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+167}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{9 \cdot y}{\frac{z}{x}}}{c}\\ \end{array} \]

Alternative 8
Accuracy	85.8%
Cost	1480

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -1.65 \cdot 10^{+118}:\\ \;\;\;\;\frac{\frac{b}{z} + t_1}{c}\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+109}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{9 \cdot y}{\frac{z}{x}}}{c}\\ \end{array} \]

Alternative 9
Accuracy	48.3%
Cost	1373

\[\begin{array}{l} t_1 := 9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{-140}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-123}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+80} \lor \neg \left(a \leq 1.4 \cdot 10^{+185}\right) \land a \leq 1.12 \cdot 10^{+198}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 10
Accuracy	47.6%
Cost	1242

\[\begin{array}{l} t_1 := t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \mathbf{if}\;a \leq -2.25 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+54} \lor \neg \left(a \leq 6.6 \cdot 10^{+80}\right) \land \left(a \leq 1.4 \cdot 10^{+185} \lor \neg \left(a \leq 1.12 \cdot 10^{+198}\right)\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 11
Accuracy	47.0%
Cost	1242

\[\begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-158}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{+53} \lor \neg \left(a \leq 8 \cdot 10^{+80} \lor \neg \left(a \leq 1.2 \cdot 10^{+185}\right) \land a \leq 1.12 \cdot 10^{+198}\right):\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 12
Accuracy	46.4%
Cost	1240

\[\begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{+127}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-240}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-116}:\\ \;\;\;\;\frac{-4}{\frac{c}{t \cdot a}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 13
Accuracy	46.4%
Cost	1240

\[\begin{array}{l} t_1 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;t \leq -7 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7.6 \cdot 10^{+127}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-239}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-116}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;t \leq 8.9 \cdot 10^{-38}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-4 \cdot \frac{a}{c}\right)\\ \end{array} \]

Alternative 14
Accuracy	67.5%
Cost	1232

\[\begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+86}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+94}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+107}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right)}{c}\\ \end{array} \]

Alternative 15
Accuracy	74.8%
Cost	969

\[\begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{-16} \lor \neg \left(z \leq 8 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{\frac{b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 16
Accuracy	34.9%
Cost	585

\[\begin{array}{l} \mathbf{if}\;b \leq -5 \cdot 10^{-180} \lor \neg \left(b \leq 8.6 \cdot 10^{+150}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 17
Accuracy	33.9%
Cost	584

\[\begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{-170}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+268}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \end{array} \]

Alternative 18
Accuracy	34.4%
Cost	320

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

Reproduce

herbie shell --seed 2023159 
(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)))