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

Average Accuracy: 68.3% → 86.0%

Time: 41.4s

Precision: binary64

Cost: 12880

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

Math

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

↓

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{\frac{b}{z} + t_1}{c}\\ \mathbf{elif}\;t_2 \leq -8 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 10^{-166}:\\ \;\;\;\;\frac{t_1 + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{\frac{x}{\frac{c}{y}}}{z}, -4 \cdot \left(t \cdot \frac{a}{c}\right)\right)\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z t a b c)
 :precision binary64
 (let* ((t_1 (* t (* a -4.0)))
        (t_2 (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_2 (- INFINITY))
     (/ (+ (/ b z) t_1) c)
     (if (<= t_2 -8e+57)
       t_2
       (if (<= t_2 1e-166)
         (/ (+ t_1 (/ (+ b (* x (* 9.0 y))) z)) c)
         (if (<= t_2 INFINITY)
           t_2
           (+
            (/ b (* z c))
            (fma 9.0 (/ (/ x (/ c y)) z) (* -4.0 (* t (/ a 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 = t * (a * -4.0);
	double t_2 = ((((x * 9.0) * y) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = ((b / z) + t_1) / c;
	} else if (t_2 <= -8e+57) {
		tmp = t_2;
	} else if (t_2 <= 1e-166) {
		tmp = (t_1 + ((b + (x * (9.0 * y))) / z)) / c;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (b / (z * c)) + fma(9.0, ((x / (c / y)) / z), (-4.0 * (t * (a / 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(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))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(Float64(b / z) + t_1) / c);
	elseif (t_2 <= -8e+57)
		tmp = t_2;
	elseif (t_2 <= 1e-166)
		tmp = Float64(Float64(t_1 + Float64(Float64(b + Float64(x * Float64(9.0 * y))) / z)) / c);
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(b / Float64(z * c)) + fma(9.0, Float64(Float64(x / Float64(c / y)) / z), Float64(-4.0 * Float64(t * Float64(a / 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[(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]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(N[(b / z), $MachinePrecision] + t$95$1), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, -8e+57], t$95$2, If[LessEqual[t$95$2, 1e-166], N[(N[(t$95$1 + N[(N[(b + N[(x * N[(9.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$2, N[(N[(b / N[(z * c), $MachinePrecision]), $MachinePrecision] + N[(9.0 * N[(N[(x / N[(c / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(-4.0 * N[(t * N[(a / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Target

Original	68.3%
Target	77.6%
Herbie	86.0%

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

Derivation

1. Split input into 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

   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 64.3%

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

      [Start] 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-/r* [=>] 10.4	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Taylor expanded in x around 0 58.9%

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

   if -inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -8.00000000000000039e57 or 1.00000000000000004e-166 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < +inf.0

   1. Initial program 85.5%

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

   if -8.00000000000000039e57 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 1.00000000000000004e-166

   1. Initial program 76.3%

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

   2. Simplified 97.7%

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

      [Start] 76.3	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 96.9	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Applied egg-rr 97.7%

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

      [Start] 97.7	\[ \frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + t \cdot \left(a \cdot -4\right)}{c} \]
      fma-udef [=>] 97.7	\[ \frac{\frac{\color{blue}{x \cdot \left(9 \cdot y\right) + b}}{z} + t \cdot \left(a \cdot -4\right)}{c} \]

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

   1. 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 2.5%

      \[\leadsto \color{blue}{\frac{\left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}} \]
      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* [=>] 2.5	\[ \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Taylor expanded in x around 0 49.9%

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

   4. Simplified 76.9%

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

      [Start] 49.9	\[ \left(\frac{b}{c \cdot z} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c} \]
      associate--l+ [=>] 49.9	\[ \color{blue}{\frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]
      *-commutative [<=] 49.9	\[ \frac{b}{\color{blue}{z \cdot c}} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]
      cancel-sign-sub-inv [=>] 49.9	\[ \frac{b}{z \cdot c} + \color{blue}{\left(9 \cdot \frac{y \cdot x}{c \cdot z} + \left(-4\right) \cdot \frac{a \cdot t}{c}\right)} \]
      metadata-eval [=>] 49.9	\[ \frac{b}{z \cdot c} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} + \color{blue}{-4} \cdot \frac{a \cdot t}{c}\right) \]
      fma-def [=>] 49.9	\[ \frac{b}{z \cdot c} + \color{blue}{\mathsf{fma}\left(9, \frac{y \cdot x}{c \cdot z}, -4 \cdot \frac{a \cdot t}{c}\right)} \]
      associate-/r* [=>] 52.2	\[ \frac{b}{z \cdot c} + \mathsf{fma}\left(9, \color{blue}{\frac{\frac{y \cdot x}{c}}{z}}, -4 \cdot \frac{a \cdot t}{c}\right) \]
      *-commutative [<=] 52.2	\[ \frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{\frac{\color{blue}{x \cdot y}}{c}}{z}, -4 \cdot \frac{a \cdot t}{c}\right) \]
      associate-/l* [=>] 71.5	\[ \frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{\color{blue}{\frac{x}{\frac{c}{y}}}}{z}, -4 \cdot \frac{a \cdot t}{c}\right) \]
      *-commutative [=>] 71.5	\[ \frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{\frac{x}{\frac{c}{y}}}{z}, \color{blue}{\frac{a \cdot t}{c} \cdot -4}\right) \]
      associate-/l* [=>] 85.1	\[ \frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{\frac{x}{\frac{c}{y}}}{z}, \color{blue}{\frac{a}{\frac{c}{t}}} \cdot -4\right) \]
      associate-/r/ [=>] 76.9	\[ \frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{\frac{x}{\frac{c}{y}}}{z}, \color{blue}{\left(\frac{a}{c} \cdot t\right)} \cdot -4\right) \]

3. Recombined 4 regimes into one program.

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -\infty:\\ \;\;\;\;\frac{\frac{b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -8 \cdot 10^{+57}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 10^{-166}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq \infty:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c} + \mathsf{fma}\left(9, \frac{\frac{x}{\frac{c}{y}}}{z}, -4 \cdot \left(t \cdot \frac{a}{c}\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	85.1%
Cost	6352

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{\frac{b}{z} + t_1}{c}\\ \mathbf{elif}\;t_2 \leq -8 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 10^{-166}:\\ \;\;\;\;\frac{t_1 + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;t_2 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \end{array} \]

Alternative 2
Accuracy	68.1%
Cost	2016

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ t_2 := t_1 + -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ t_3 := t \cdot \left(a \cdot -4\right)\\ t_4 := \frac{t_3 + \frac{9 \cdot y}{\frac{z}{x}}}{c}\\ \mathbf{if}\;z \leq -1.02 \cdot 10^{+197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{+162}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{+66}:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+51}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-120}:\\ \;\;\;\;t_1 + -4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;z \leq 510000000000:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+108}:\\ \;\;\;\;\frac{\frac{b}{z} + t_3}{c}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 3
Accuracy	43.3%
Cost	1768

\[\begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ t_2 := -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{if}\;t \leq -1.14 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -76000:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-122}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-232}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-304}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	43.5%
Cost	1768

\[\begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ t_2 := -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ t_3 := 9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -70000:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-102}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-122}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -1.46 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-243}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-303}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-123}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	43.4%
Cost	1768

\[\begin{array}{l} t_1 := 9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ t_2 := -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -100000:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -1.11 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-101}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{z}}{c}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-123}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -1.32 \cdot 10^{-161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.6 \cdot 10^{-243}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-302}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-115}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	43.1%
Cost	1768

\[\begin{array}{l} t_1 := y \cdot \frac{9}{z \cdot \frac{c}{x}}\\ t_2 := -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{if}\;t \leq -2.15 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -75000:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -1.11 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-104}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{z}}{c}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-123}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.7 \cdot 10^{-243}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-301}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-107}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Accuracy	43.2%
Cost	1768

\[\begin{array}{l} t_1 := y \cdot \frac{9}{z \cdot \frac{c}{x}}\\ t_2 := -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -70000:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -1.11 \cdot 10^{-31}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;t \leq -1.06 \cdot 10^{-101}:\\ \;\;\;\;9 \cdot \frac{x \cdot \frac{y}{z}}{c}\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-123}:\\ \;\;\;\;\frac{\frac{a \cdot -4}{c}}{\frac{1}{t}}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-244}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-305}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;t \leq 2.85 \cdot 10^{-109}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Accuracy	53.4%
Cost	1760

\[\begin{array}{l} t_1 := -4 \cdot \left(a \cdot \frac{t}{c}\right)\\ t_2 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;t \leq -7 \cdot 10^{+288}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{+41}:\\ \;\;\;\;y \cdot \frac{9}{z \cdot \frac{c}{x}}\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+14}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-122}:\\ \;\;\;\;\frac{\frac{a \cdot -4}{c}}{\frac{1}{t}}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-165}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	66.6%
Cost	1492

\[\begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ t_2 := \frac{b}{z \cdot c}\\ t_3 := t_2 + -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;a \leq -9.2 \cdot 10^{-117}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-244}:\\ \;\;\;\;t_2 + -4 \cdot \frac{t \cdot a}{c}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-268}:\\ \;\;\;\;\frac{\frac{b}{z} + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Accuracy	85.4%
Cost	1481

\[\begin{array}{l} t_1 := x \cdot \left(9 \cdot y\right)\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+41} \lor \neg \left(z \leq 9.5 \cdot 10^{-64}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + t_1}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(t_1 - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 11
Accuracy	62.9%
Cost	1360

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c} + -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{if}\;x \leq -1.86 \cdot 10^{+273}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{+106}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 12
Accuracy	62.7%
Cost	1360

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ \mathbf{if}\;x \leq -1.85 \cdot 10^{+272}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{+209}:\\ \;\;\;\;t_1 + -4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+104}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{+42}:\\ \;\;\;\;t_1 + -4 \cdot \frac{t \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \left(\frac{y}{c} \cdot \frac{x}{z}\right)\\ \end{array} \]

Alternative 13
Accuracy	82.2%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{-129} \lor \neg \left(z \leq 4 \cdot 10^{-64}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b + x \cdot \left(9 \cdot y\right)}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 14
Accuracy	69.1%
Cost	1233

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+162}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-119} \lor \neg \left(z \leq 1050000000000\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 15
Accuracy	42.8%
Cost	977

\[\begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-211}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-24}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 9.6 \cdot 10^{+58} \lor \neg \left(a \leq 1.3 \cdot 10^{+75}\right):\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{c \cdot \frac{z}{b}}\\ \end{array} \]

Alternative 16
Accuracy	46.1%
Cost	712

\[\begin{array}{l} \mathbf{if}\;b \leq -5.8 \cdot 10^{+82}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+50}:\\ \;\;\;\;-4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 17
Accuracy	45.9%
Cost	712

\[\begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+101}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{+50}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 18
Accuracy	46.2%
Cost	712

\[\begin{array}{l} \mathbf{if}\;b \leq -8.5 \cdot 10^{+96}:\\ \;\;\;\;b \cdot \frac{1}{z \cdot c}\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+48}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 19
Accuracy	33.5%
Cost	584

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+158}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{+81}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 20
Accuracy	32.7%
Cost	320

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

Reproduce

herbie shell --seed 2023146 
(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)))