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

Percentage Accurate: 79.4% → 89.1%

Time: 15.6s

Precision: binary64

Cost: 13896

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

• 37.5% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+76}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot \frac{x}{z}\right) + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-48}:\\ \;\;\;\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \end{array} \end{array} \]

FPCore

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

↓

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a b c)
 :precision binary64
 (if (<= z -2.6e+76)
   (/ (+ (* 9.0 (* y (/ x z))) (* t (* a -4.0))) c)
   (if (<= z 1.32e-48)
     (/ (+ (- (* y (* 9.0 x)) (* a (* t (* z 4.0)))) b) (* z c))
     (/ (fma t (* a -4.0) (/ (fma x (* 9.0 y) b) z)) 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);
}

↓

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a, double b, double c) {
	double tmp;
	if (z <= -2.6e+76) {
		tmp = ((9.0 * (y * (x / z))) + (t * (a * -4.0))) / c;
	} else if (z <= 1.32e-48) {
		tmp = (((y * (9.0 * x)) - (a * (t * (z * 4.0)))) + b) / (z * c);
	} else {
		tmp = fma(t, (a * -4.0), (fma(x, (9.0 * y), b) / z)) / 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

↓

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a, b, c)
	tmp = 0.0
	if (z <= -2.6e+76)
		tmp = Float64(Float64(Float64(9.0 * Float64(y * Float64(x / z))) + Float64(t * Float64(a * -4.0))) / c);
	elseif (z <= 1.32e-48)
		tmp = Float64(Float64(Float64(Float64(y * Float64(9.0 * x)) - Float64(a * Float64(t * Float64(z * 4.0)))) + b) / Float64(z * c));
	else
		tmp = Float64(fma(t, Float64(a * -4.0), Float64(fma(x, Float64(9.0 * y), b) / z)) / 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]

↓

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_, c_] := If[LessEqual[z, -2.6e+76], N[(N[(N[(9.0 * N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(a * -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[z, 1.32e-48], N[(N[(N[(N[(y * N[(9.0 * x), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t * N[(z * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(a * -4.0), $MachinePrecision] + N[(N[(x * N[(9.0 * y), $MachinePrecision] + b), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision]]]

Target

Original	79.4%
Target	80.6%
Herbie	89.1%

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

Derivation

1. Split input into 3 regimes

2. if z < -2.5999999999999999e76

   1. Initial program 49.0%

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

   2. Simplified 70.2%

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

      [Start] 49.0%	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 52.1%	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Taylor expanded in x around inf 61.7%

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

   4. Simplified 81.9%

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

      [Start] 61.7%	\[ \frac{9 \cdot \frac{y \cdot x}{z} + t \cdot \left(a \cdot -4\right)}{c} \]
      associate-/l* [=>] 81.9%	\[ \frac{9 \cdot \color{blue}{\frac{y}{\frac{z}{x}}} + t \cdot \left(a \cdot -4\right)}{c} \]

   5. Taylor expanded in y around 0 61.7%

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

   6. Simplified 81.9%

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

      [Start] 61.7%	\[ \frac{9 \cdot \frac{y \cdot x}{z} + t \cdot \left(a \cdot -4\right)}{c} \]
      associate-/l* [=>] 81.9%	\[ \frac{9 \cdot \color{blue}{\frac{y}{\frac{z}{x}}} + t \cdot \left(a \cdot -4\right)}{c} \]
      *-rgt-identity [<=] 81.9%	\[ \frac{9 \cdot \frac{\color{blue}{y \cdot 1}}{\frac{z}{x}} + t \cdot \left(a \cdot -4\right)}{c} \]
      associate-*r/ [<=] 81.9%	\[ \frac{9 \cdot \color{blue}{\left(y \cdot \frac{1}{\frac{z}{x}}\right)} + t \cdot \left(a \cdot -4\right)}{c} \]
      associate-/r/ [=>] 81.9%	\[ \frac{9 \cdot \left(y \cdot \color{blue}{\left(\frac{1}{z} \cdot x\right)}\right) + t \cdot \left(a \cdot -4\right)}{c} \]
      associate-*l/ [=>] 81.9%	\[ \frac{9 \cdot \left(y \cdot \color{blue}{\frac{1 \cdot x}{z}}\right) + t \cdot \left(a \cdot -4\right)}{c} \]
      *-lft-identity [=>] 81.9%	\[ \frac{9 \cdot \left(y \cdot \frac{\color{blue}{x}}{z}\right) + t \cdot \left(a \cdot -4\right)}{c} \]

   if -2.5999999999999999e76 < z < 1.32e-48

   1. Initial program 95.5%

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

   if 1.32e-48 < z

   1. Initial program 73.9%

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

   2. Simplified 93.3%

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

      [Start] 73.9%	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 80.7%	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

3. Recombined 3 regimes into one program.

4. Final simplification 92.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+76}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot \frac{x}{z}\right) + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-48}:\\ \;\;\;\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	89.1%
Cost	13896

\[\begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+76}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot \frac{x}{z}\right) + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-48}:\\ \;\;\;\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, a \cdot -4, \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}\right)}{c}\\ \end{array} \]

Alternative 2
Accuracy	89.1%
Cost	7624

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -1.26 \cdot 10^{+78}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot \frac{x}{z}\right) + t_1}{c}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-48}:\\ \;\;\;\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{\mathsf{fma}\left(x, 9 \cdot y, b\right)}{z}}{c}\\ \end{array} \]

Alternative 3
Accuracy	86.1%
Cost	1609

\[\begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+76} \lor \neg \left(z \leq 2.4 \cdot 10^{+200}\right):\\ \;\;\;\;\frac{9 \cdot \left(y \cdot \frac{x}{z}\right) + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(b + \left(x \cdot \left(9 \cdot y\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right)\right) \cdot \frac{1}{z \cdot c}\\ \end{array} \]

Alternative 4
Accuracy	85.3%
Cost	1481

\[\begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+78} \lor \neg \left(z \leq 2.4 \cdot 10^{+200}\right):\\ \;\;\;\;\frac{9 \cdot \left(y \cdot \frac{x}{z}\right) + t \cdot \left(a \cdot -4\right)}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + \left(x \cdot \left(9 \cdot y\right) - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right)}{z \cdot c}\\ \end{array} \]

Alternative 5
Accuracy	86.1%
Cost	1480

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{+75}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot \frac{x}{z}\right) + t_1}{c}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+175}:\\ \;\;\;\;\frac{\left(y \cdot \left(9 \cdot x\right) - a \cdot \left(t \cdot \left(z \cdot 4\right)\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1 + \frac{9 \cdot \left(y \cdot x\right)}{z}}{c}\\ \end{array} \]

Alternative 6
Accuracy	73.9%
Cost	1356

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ t_2 := \frac{9 \cdot \left(y \cdot \frac{x}{z}\right) + t_1}{c}\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+91}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+193}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Accuracy	74.0%
Cost	1356

\[\begin{array}{l} t_1 := t \cdot \left(a \cdot -4\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{-24}:\\ \;\;\;\;\frac{t_1 + 9 \cdot \frac{y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+94}:\\ \;\;\;\;\frac{t_1 + \frac{b}{z}}{c}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+192}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot \frac{x}{z}\right) + t_1}{c}\\ \end{array} \]

Alternative 8
Accuracy	50.2%
Cost	1108

\[\begin{array}{l} t_1 := 9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ t_2 := -4 \cdot \frac{t}{\frac{c}{a}}\\ t_3 := \frac{b}{z \cdot c}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-296}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-93}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	50.1%
Cost	1108

\[\begin{array}{l} t_1 := -4 \cdot \frac{t}{\frac{c}{a}}\\ t_2 := \frac{b}{z \cdot c}\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{-46}:\\ \;\;\;\;9 \cdot \frac{y}{\frac{z \cdot c}{x}}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 10^{-191}:\\ \;\;\;\;9 \cdot \frac{\frac{y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Accuracy	49.8%
Cost	1108

\[\begin{array}{l} t_1 := -4 \cdot \frac{t}{\frac{c}{a}}\\ t_2 := \frac{b}{z \cdot c}\\ \mathbf{if}\;t \leq -4.2 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-46}:\\ \;\;\;\;\frac{9 \cdot \left(y \cdot \frac{x}{z}\right)}{c}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.75 \cdot 10^{-191}:\\ \;\;\;\;9 \cdot \frac{\frac{y}{\frac{z}{x}}}{c}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-93}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Accuracy	76.1%
Cost	969

\[\begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+41} \lor \neg \left(z \leq 1.4 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{t \cdot \left(a \cdot -4\right) + \frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \end{array} \]

Alternative 12
Accuracy	67.6%
Cost	968

\[\begin{array}{l} \mathbf{if}\;t \leq -1.52 \cdot 10^{+106}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq 10^{-36}:\\ \;\;\;\;\frac{b + 9 \cdot \left(y \cdot x\right)}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t \cdot -4}{c}\\ \end{array} \]

Alternative 13
Accuracy	49.8%
Cost	844

\[\begin{array}{l} t_1 := -4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{if}\;t \leq -7 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.1 \cdot 10^{-45}:\\ \;\;\;\;9 \cdot \left(\frac{y}{z} \cdot \frac{x}{c}\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-93}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Accuracy	49.6%
Cost	713

\[\begin{array}{l} \mathbf{if}\;t \leq -2.55 \cdot 10^{+105} \lor \neg \left(t \leq 1.9 \cdot 10^{-93}\right):\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \end{array} \]

Alternative 15
Accuracy	49.5%
Cost	712

\[\begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+105}:\\ \;\;\;\;-4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-94}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array} \]

Alternative 16
Accuracy	34.6%
Cost	320

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

Reproduce

herbie shell --seed 2023167 
(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)))