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

Average Accuracy: 68.0% → 94.8%

Time: 35.7s

Precision: binary64

Cost: 17484

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{\frac{b}{c}}{z} + \left(\frac{x}{\frac{c}{y} \cdot \left(z \cdot 0.1111111111111111\right)} + \left(a \cdot \frac{t}{c}\right) \cdot -4\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 100000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{elif}\;t_1 \leq 10^{+303}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

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
         (+
          (/ (/ b c) z)
          (+
           (/ x (* (/ c y) (* z 0.1111111111111111)))
           (* (* a (/ t c)) -4.0)))))
   (if (<= t_1 (- INFINITY))
     t_2
     (if (<= t_1 -2e+37)
       t_1
       (if (<= t_1 100000000000.0)
         (/ (fma t (* a -4.0) (/ (fma x (* 9.0 y) b) z)) c)
         (if (<= t_1 1e+303) 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 = ((b / c) / z) + ((x / ((c / y) * (z * 0.1111111111111111))) + ((a * (t / c)) * -4.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= -2e+37) {
		tmp = t_1;
	} else if (t_1 <= 100000000000.0) {
		tmp = fma(t, (a * -4.0), (fma(x, (9.0 * y), b) / z)) / c;
	} else if (t_1 <= 1e+303) {
		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(b / c) / z) + Float64(Float64(x / Float64(Float64(c / y) * Float64(z * 0.1111111111111111))) + Float64(Float64(a * Float64(t / c)) * -4.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= -2e+37)
		tmp = t_1;
	elseif (t_1 <= 100000000000.0)
		tmp = Float64(fma(t, Float64(a * -4.0), Float64(fma(x, Float64(9.0 * y), b) / z)) / c);
	elseif (t_1 <= 1e+303)
		tmp = t_1;
	else
		tmp = t_2;
	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[(N[(b / c), $MachinePrecision] / z), $MachinePrecision] + N[(N[(x / N[(N[(c / y), $MachinePrecision] * N[(z * 0.1111111111111111), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(t / c), $MachinePrecision]), $MachinePrecision] * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, -2e+37], t$95$1, If[LessEqual[t$95$1, 100000000000.0], 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, 1e+303], t$95$1, t$95$2]]]]]]

Target

Original	68.0%
Target	76.9%
Herbie	94.8%

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

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 1e303 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 0.9%

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

   2. Simplified 15.1%

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

      [Start] 0.9	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-*l* [=>] 1.1	\[ \frac{\left(\color{blue}{x \cdot \left(9 \cdot y\right)} - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-*l* [=>] 15.1	\[ \frac{\left(x \cdot \left(9 \cdot y\right) - \color{blue}{\left(z \cdot 4\right) \cdot \left(t \cdot a\right)}\right) + b}{z \cdot c} \]

   3. Taylor expanded in x around 0 52.0%

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

   4. Simplified 74.9%

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

      [Start] 52.0	\[ \left(\frac{b}{c \cdot z} + 9 \cdot \frac{y \cdot x}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c} \]
      associate--l+ [=>] 52.0	\[ \color{blue}{\frac{b}{c \cdot z} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right)} \]
      associate-/r* [=>] 49.8	\[ \color{blue}{\frac{\frac{b}{c}}{z}} + \left(9 \cdot \frac{y \cdot x}{c \cdot z} - 4 \cdot \frac{a \cdot t}{c}\right) \]
      *-commutative [<=] 49.8	\[ \frac{\frac{b}{c}}{z} + \left(9 \cdot \frac{y \cdot x}{\color{blue}{z \cdot c}} - 4 \cdot \frac{a \cdot t}{c}\right) \]
      associate-*r/ [=>] 49.7	\[ \frac{\frac{b}{c}}{z} + \left(\color{blue}{\frac{9 \cdot \left(y \cdot x\right)}{z \cdot c}} - 4 \cdot \frac{a \cdot t}{c}\right) \]
      associate-*r* [=>] 49.7	\[ \frac{\frac{b}{c}}{z} + \left(\frac{\color{blue}{\left(9 \cdot y\right) \cdot x}}{z \cdot c} - 4 \cdot \frac{a \cdot t}{c}\right) \]
      *-commutative [<=] 49.7	\[ \frac{\frac{b}{c}}{z} + \left(\frac{\color{blue}{x \cdot \left(9 \cdot y\right)}}{z \cdot c} - 4 \cdot \frac{a \cdot t}{c}\right) \]
      associate-/l* [=>] 64.4	\[ \frac{\frac{b}{c}}{z} + \left(\color{blue}{\frac{x}{\frac{z \cdot c}{9 \cdot y}}} - 4 \cdot \frac{a \cdot t}{c}\right) \]
      associate-/l* [=>] 74.9	\[ \frac{\frac{b}{c}}{z} + \left(\frac{x}{\frac{z \cdot c}{9 \cdot y}} - 4 \cdot \color{blue}{\frac{a}{\frac{c}{t}}}\right) \]

   5. Applied egg-rr 74.5%

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

      [Start] 74.9	\[ \frac{\frac{b}{c}}{z} + \left(\frac{x}{\frac{z \cdot c}{9 \cdot y}} - 4 \cdot \frac{a}{\frac{c}{t}}\right) \]
      div-inv [=>] 74.3	\[ \frac{\frac{b}{c}}{z} + \left(\frac{x}{\frac{z \cdot c}{9 \cdot y}} - 4 \cdot \color{blue}{\left(a \cdot \frac{1}{\frac{c}{t}}\right)}\right) \]
      *-commutative [=>] 74.3	\[ \frac{\frac{b}{c}}{z} + \left(\frac{x}{\frac{z \cdot c}{9 \cdot y}} - 4 \cdot \color{blue}{\left(\frac{1}{\frac{c}{t}} \cdot a\right)}\right) \]
      clear-num [<=] 74.5	\[ \frac{\frac{b}{c}}{z} + \left(\frac{x}{\frac{z \cdot c}{9 \cdot y}} - 4 \cdot \left(\color{blue}{\frac{t}{c}} \cdot a\right)\right) \]

   6. Applied egg-rr 83.5%

      \[\leadsto \frac{\frac{b}{c}}{z} + \left(\frac{x}{\color{blue}{\frac{c}{y} \cdot \left(z \cdot 0.1111111111111111\right)}} - 4 \cdot \left(\frac{t}{c} \cdot a\right)\right) \]
      Proof

      [Start] 74.5	\[ \frac{\frac{b}{c}}{z} + \left(\frac{x}{\frac{z \cdot c}{9 \cdot y}} - 4 \cdot \left(\frac{t}{c} \cdot a\right)\right) \]
      times-frac [=>] 83.6	\[ \frac{\frac{b}{c}}{z} + \left(\frac{x}{\color{blue}{\frac{z}{9} \cdot \frac{c}{y}}} - 4 \cdot \left(\frac{t}{c} \cdot a\right)\right) \]
      *-commutative [=>] 83.6	\[ \frac{\frac{b}{c}}{z} + \left(\frac{x}{\color{blue}{\frac{c}{y} \cdot \frac{z}{9}}} - 4 \cdot \left(\frac{t}{c} \cdot a\right)\right) \]
      div-inv [=>] 83.5	\[ \frac{\frac{b}{c}}{z} + \left(\frac{x}{\frac{c}{y} \cdot \color{blue}{\left(z \cdot \frac{1}{9}\right)}} - 4 \cdot \left(\frac{t}{c} \cdot a\right)\right) \]
      metadata-eval [=>] 83.5	\[ \frac{\frac{b}{c}}{z} + \left(\frac{x}{\frac{c}{y} \cdot \left(z \cdot \color{blue}{0.1111111111111111}\right)} - 4 \cdot \left(\frac{t}{c} \cdot a\right)\right) \]

   if -inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -1.99999999999999991e37 or 1e11 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 1e303

   1. Initial program 99.0%

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

   if -1.99999999999999991e37 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 1e11

   1. Initial program 80.7%

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

   2. Simplified 98.4%

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

      [Start] 80.7	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 98.0	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -\infty:\\ \;\;\;\;\frac{\frac{b}{c}}{z} + \left(\frac{x}{\frac{c}{y} \cdot \left(z \cdot 0.1111111111111111\right)} + \left(a \cdot \frac{t}{c}\right) \cdot -4\right)\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -2 \cdot 10^{+37}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 100000000000:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 10^{+303}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{c}}{z} + \left(\frac{x}{\frac{c}{y} \cdot \left(z \cdot 0.1111111111111111\right)} + \left(a \cdot \frac{t}{c}\right) \cdot -4\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	94.9%
Cost	11212

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{\frac{b}{c}}{z} + \left(\frac{x}{\frac{c}{y} \cdot \left(z \cdot 0.1111111111111111\right)} + \left(a \cdot \frac{t}{c}\right) \cdot -4\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 100000000000:\\ \;\;\;\;\frac{\frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z} + a \cdot \left(t \cdot -4\right)}{c}\\ \mathbf{elif}\;t_1 \leq 10^{+303}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Accuracy	94.8%
Cost	6608

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := \frac{\frac{b}{c}}{z} + \left(\frac{x}{\frac{c}{y} \cdot \left(z \cdot 0.1111111111111111\right)} + \left(a \cdot \frac{t}{c}\right) \cdot -4\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 100000000000:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t_1 \leq 10^{+303}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	88.4%
Cost	6352

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{t_2 + \left(9 \cdot y\right) \cdot \frac{x}{z}}{c}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{-190}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 10^{-183}:\\ \;\;\;\;\frac{1}{c} \cdot \frac{b + -4 \cdot \left(z \cdot \left(t \cdot a\right)\right)}{z}\\ \mathbf{elif}\;t_1 \leq 10^{+308}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2 + y \cdot \frac{9}{\frac{z}{x}}}{c}\\ \end{array} \]

Alternative 4
Accuracy	90.5%
Cost	6352

\[\begin{array}{l} t_1 := \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ t_2 := a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{t_2 + \left(9 \cdot y\right) \cdot \frac{x}{z}}{c}\\ \mathbf{elif}\;t_1 \leq -2 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 100000000000:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)\right)}{z} \cdot \frac{1}{c}\\ \mathbf{elif}\;t_1 \leq 10^{+308}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2 + y \cdot \frac{9}{\frac{z}{x}}}{c}\\ \end{array} \]

Alternative 5
Accuracy	49.9%
Cost	2420

\[\begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ t_2 := t \cdot \frac{a \cdot -4}{c}\\ \mathbf{if}\;x \leq -2.15 \cdot 10^{+243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+195}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \mathbf{elif}\;x \leq -8.4 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{+136}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq -3900000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -200:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-162}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-238}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-296}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-259}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-246}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-136}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;x \leq 0.00045:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \end{array} \]

Alternative 6
Accuracy	70.6%
Cost	2272

\[\begin{array}{l} t_1 := t \cdot \frac{a \cdot -4}{c}\\ t_2 := \frac{b + \left(x \cdot \left(9 \cdot y\right) + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)\right)}{z \cdot c}\\ t_3 := a \cdot \left(t \cdot -4\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{-16}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+57}:\\ \;\;\;\;\frac{t_3 + \left(9 \cdot y\right) \cdot \frac{x}{z}}{c}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+189}:\\ \;\;\;\;\frac{t_3 + y \cdot \frac{9}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+279}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 7
Accuracy	42.3%
Cost	2160

\[\begin{array}{l} t_1 := \frac{t \cdot -4}{\frac{c}{a}}\\ t_2 := 9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ t_3 := \frac{b}{z \cdot c}\\ \mathbf{if}\;x \leq -1.62 \cdot 10^{+153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{+135}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq -4.9 \cdot 10^{+117}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6.2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-28}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{-162}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.6 \cdot 10^{-238}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-294}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-259}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-239}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Accuracy	42.4%
Cost	2160

\[\begin{array}{l} t_1 := \frac{t \cdot -4}{\frac{c}{a}}\\ t_2 := \frac{b}{z \cdot c}\\ \mathbf{if}\;x \leq -5.9 \cdot 10^{+153}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{+135}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -58:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-238}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-295}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-259}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-247}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{x}{z \cdot \frac{c}{y}}\\ \end{array} \]

Alternative 9
Accuracy	42.6%
Cost	2160

\[\begin{array}{l} t_1 := \frac{t \cdot -4}{\frac{c}{a}}\\ t_2 := \frac{b}{z \cdot c}\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{+160}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{+135}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.8:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-238}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-295}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;x \leq 1.06 \cdot 10^{-238}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \end{array} \]

Alternative 10
Accuracy	42.2%
Cost	2160

\[\begin{array}{l} t_1 := \frac{t \cdot -4}{\frac{c}{a}}\\ t_2 := \frac{b}{z \cdot c}\\ \mathbf{if}\;x \leq -4.05 \cdot 10^{+155}:\\ \;\;\;\;9 \cdot \left(x \cdot \frac{\frac{y}{c}}{z}\right)\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+135}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -42:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-238}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-295}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-259}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-248}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{9 \cdot y}{c}\\ \end{array} \]

Alternative 11
Accuracy	62.9%
Cost	1892

\[\begin{array}{l} t_1 := \frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ t_2 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{-16}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-181}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-61}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+60}:\\ \;\;\;\;\frac{y \cdot \frac{9}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+244}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 12
Accuracy	42.2%
Cost	1764

\[\begin{array}{l} t_1 := 9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+128}:\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-149}:\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-242}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-21}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+143}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+179}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \end{array} \]

Alternative 13
Accuracy	63.3%
Cost	1760

\[\begin{array}{l} t_1 := -4 \cdot \frac{t \cdot a}{c} + \frac{b}{z \cdot c}\\ t_2 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-138}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;y \leq 115000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{+95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+248}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+250}:\\ \;\;\;\;t \cdot \frac{a \cdot -4}{c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Accuracy	65.3%
Cost	1756

\[\begin{array}{l} t_1 := -4 \cdot \frac{t \cdot a}{c} + \frac{b}{z \cdot c}\\ t_2 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{if}\;x \leq -2 \cdot 10^{+244}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{+137}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + 9 \cdot \frac{x \cdot y}{z}}{c}\\ \mathbf{elif}\;x \leq -2.9:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-281}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \end{array} \]

Alternative 15
Accuracy	66.2%
Cost	1624

\[\begin{array}{l} t_1 := -4 \cdot \frac{t \cdot a}{c} + \frac{b}{z \cdot c}\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+139}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + y \cdot \frac{9}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;x \leq -5.5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-282}:\\ \;\;\;\;\frac{\frac{b}{z} + -4 \cdot \left(t \cdot a\right)}{c}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;9 \cdot \frac{y}{z \cdot \frac{c}{x}}\\ \end{array} \]

Alternative 16
Accuracy	46.5%
Cost	1108

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ t_2 := -4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{-25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-181}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Accuracy	46.7%
Cost	1108

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ t_2 := a \cdot \frac{t \cdot -4}{c}\\ \mathbf{if}\;a \leq -2.8 \cdot 10^{-26}:\\ \;\;\;\;-4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-185}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Accuracy	46.6%
Cost	1108

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ t_2 := a \cdot \frac{t \cdot -4}{c}\\ \mathbf{if}\;a \leq -1.85 \cdot 10^{-35}:\\ \;\;\;\;\frac{t \cdot -4}{\frac{c}{a}}\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-125}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.6 \cdot 10^{-182}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 8.1 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Accuracy	32.4%
Cost	320

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

Reproduce

herbie shell --seed 2023138 
(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)))