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

Average Error: 31.95% → 12.01%

Time: 28.3s

Precision: binary64

Cost: 6352

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

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\frac{-4}{\frac{\frac{c}{t}}{a}}\\ \mathbf{elif}\;t_1 \leq -5 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c}\\ \mathbf{elif}\;t_1 \leq 10^{+294}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{c \cdot \frac{-0.25}{a}}\\ \end{array} \]

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 (/ (+ (- (* y (* x 9.0)) (* (* (* z 4.0) t) a)) b) (* z c))))
   (if (<= t_1 (- INFINITY))
     (/ -4.0 (/ (/ c t) a))
     (if (<= t_1 -5e-128)
       t_1
       (if (<= t_1 0.0)
         (/ (+ (* -4.0 (* t a)) (/ (- b (* y (* x -9.0))) z)) c)
         (if (<= t_1 1e+294) t_1 (/ t (* c (/ -0.25 a)))))))))

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 = (((y * (x * 9.0)) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = -4.0 / ((c / t) / a);
	} else if (t_1 <= -5e-128) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * (t * a)) + ((b - (y * (x * -9.0))) / z)) / c;
	} else if (t_1 <= 1e+294) {
		tmp = t_1;
	} else {
		tmp = t / (c * (-0.25 / a));
	}
	return tmp;
}

Java

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

↓

public static double code(double x, double y, double z, double t, double a, double b, double c) {
	double t_1 = (((y * (x * 9.0)) - (((z * 4.0) * t) * a)) + b) / (z * c);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = -4.0 / ((c / t) / a);
	} else if (t_1 <= -5e-128) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = ((-4.0 * (t * a)) + ((b - (y * (x * -9.0))) / z)) / c;
	} else if (t_1 <= 1e+294) {
		tmp = t_1;
	} else {
		tmp = t / (c * (-0.25 / a));
	}
	return tmp;
}

Python

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

↓

def code(x, y, z, t, a, b, c):
	t_1 = (((y * (x * 9.0)) - (((z * 4.0) * t) * a)) + b) / (z * c)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = -4.0 / ((c / t) / a)
	elif t_1 <= -5e-128:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = ((-4.0 * (t * a)) + ((b - (y * (x * -9.0))) / z)) / c
	elif t_1 <= 1e+294:
		tmp = t_1
	else:
		tmp = t / (c * (-0.25 / a))
	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(y * Float64(x * 9.0)) - Float64(Float64(Float64(z * 4.0) * t) * a)) + b) / Float64(z * c))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(-4.0 / Float64(Float64(c / t) / a));
	elseif (t_1 <= -5e-128)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(Float64(Float64(-4.0 * Float64(t * a)) + Float64(Float64(b - Float64(y * Float64(x * -9.0))) / z)) / c);
	elseif (t_1 <= 1e+294)
		tmp = t_1;
	else
		tmp = Float64(t / Float64(c * Float64(-0.25 / a)));
	end
	return tmp
end

MATLAB

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

↓

function tmp_2 = code(x, y, z, t, a, b, c)
	t_1 = (((y * (x * 9.0)) - (((z * 4.0) * t) * a)) + b) / (z * c);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = -4.0 / ((c / t) / a);
	elseif (t_1 <= -5e-128)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = ((-4.0 * (t * a)) + ((b - (y * (x * -9.0))) / z)) / c;
	elseif (t_1 <= 1e+294)
		tmp = t_1;
	else
		tmp = t / (c * (-0.25 / a));
	end
	tmp_2 = tmp;
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_, b_, c_] := Block[{t$95$1 = N[(N[(N[(N[(y * N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(z * 4.0), $MachinePrecision] * t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + b), $MachinePrecision] / N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(-4.0 / N[(N[(c / t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -5e-128], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(N[(-4.0 * N[(t * a), $MachinePrecision]), $MachinePrecision] + N[(N[(b - N[(y * N[(x * -9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / c), $MachinePrecision], If[LessEqual[t$95$1, 1e+294], t$95$1, N[(t / N[(c * N[(-0.25 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	31.95%
Target	23.29%
Herbie	12.01%

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

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 100

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

   2. Simplified 38.55

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

      [Start] 100	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 89.09	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Taylor expanded in a around inf 50.72

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

   4. Applied egg-rr 48.72

      \[\leadsto \color{blue}{\frac{t}{c} \cdot \frac{a}{-0.25}} \]

   5. Applied egg-rr 47.85

      \[\leadsto \color{blue}{\frac{-4}{\frac{\frac{c}{t}}{a}}} \]

   if -inf.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < -5.0000000000000001e-128 or 0.0 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 1.00000000000000007e294

   1. Initial program 1.13

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

   if -5.0000000000000001e-128 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c)) < 0.0

   1. Initial program 45.95

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

   2. Simplified 1.42

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

      [Start] 45.95	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 2.02	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Taylor expanded in c around 0 1.32

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

   4. Taylor expanded in z around -inf 1.34

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

   5. Simplified 1.34

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

      [Start] 1.34	\[ \frac{-1 \cdot \frac{-9 \cdot \left(y \cdot x\right) + -1 \cdot b}{z} + -4 \cdot \left(a \cdot t\right)}{c} \]
      +-commutative [=>] 1.34	\[ \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) + -1 \cdot \frac{-9 \cdot \left(y \cdot x\right) + -1 \cdot b}{z}}}{c} \]
      mul-1-neg [=>] 1.34	\[ \frac{-4 \cdot \left(a \cdot t\right) + \color{blue}{\left(-\frac{-9 \cdot \left(y \cdot x\right) + -1 \cdot b}{z}\right)}}{c} \]
      unsub-neg [=>] 1.34	\[ \frac{\color{blue}{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \left(y \cdot x\right) + -1 \cdot b}{z}}}{c} \]
      mul-1-neg [=>] 1.34	\[ \frac{-4 \cdot \left(a \cdot t\right) - \frac{-9 \cdot \left(y \cdot x\right) + \color{blue}{\left(-b\right)}}{z}}{c} \]
      unsub-neg [=>] 1.34	\[ \frac{-4 \cdot \left(a \cdot t\right) - \frac{\color{blue}{-9 \cdot \left(y \cdot x\right) - b}}{z}}{c} \]
      *-commutative [=>] 1.34	\[ \frac{-4 \cdot \left(a \cdot t\right) - \frac{\color{blue}{\left(y \cdot x\right) \cdot -9} - b}{z}}{c} \]
      associate-*l* [=>] 1.34	\[ \frac{-4 \cdot \left(a \cdot t\right) - \frac{\color{blue}{y \cdot \left(x \cdot -9\right)} - b}{z}}{c} \]

   if 1.00000000000000007e294 < (/.f64 (+.f64 (-.f64 (*.f64 (*.f64 x 9) y) (*.f64 (*.f64 (*.f64 z 4) t) a)) b) (*.f64 z c))

   1. Initial program 95.26

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

   2. Simplified 41.14

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

      [Start] 95.26	\[ \frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \]
      associate-/r* [=>] 92.62	\[ \color{blue}{\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}} \]

   3. Taylor expanded in a around inf 49.57

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

   4. Applied egg-rr 39.55

      \[\leadsto \color{blue}{\frac{t}{c} \cdot \frac{a}{-0.25}} \]

   5. Applied egg-rr 41.16

      \[\leadsto \color{blue}{\frac{t}{c \cdot \frac{-0.25}{a}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 12.01

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -\infty:\\ \;\;\;\;\frac{-4}{\frac{\frac{c}{t}}{a}}\\ \mathbf{elif}\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq -5 \cdot 10^{-128}:\\ \;\;\;\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 0:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c}\\ \mathbf{elif}\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \leq 10^{+294}:\\ \;\;\;\;\frac{\left(y \cdot \left(x \cdot 9\right) - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{c \cdot \frac{-0.25}{a}}\\ \end{array} \]

Alternatives

Alternative 1
Error	44.41%
Cost	2156

\[\begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ t_2 := \frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ t_3 := \frac{y}{\frac{z}{x} \cdot \frac{c}{9}}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{-30}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-74}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-131}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -5.1 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 11500000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+191}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+223}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{c}}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+252}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	45.28%
Cost	2156

\[\begin{array}{l} t_1 := \frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ t_2 := \frac{-4 \cdot \left(t \cdot a\right) + \frac{b}{z}}{c}\\ t_3 := \frac{y}{\frac{z}{x} \cdot \frac{c}{9}}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{-30}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.08 \cdot 10^{-131}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{-253}:\\ \;\;\;\;\frac{b + -4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1100000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.92 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+223}:\\ \;\;\;\;\frac{9 \cdot \frac{y}{c}}{\frac{z}{x}}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+251}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 3
Error	23.18%
Cost	1880

\[\begin{array}{l} t_1 := \frac{-4 \cdot \left(t \cdot a\right) + \frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c}\\ t_2 := \frac{b + \left(x \cdot \left(9 \cdot y\right) + \left(t \cdot a\right) \cdot \left(z \cdot -4\right)\right)}{z \cdot c}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+178}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{+36}:\\ \;\;\;\;\frac{a \cdot \left(t \cdot -4\right) + \frac{b + 9 \cdot \left(x \cdot y\right)}{z}}{c}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-232}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-226}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a \cdot -4}{\frac{c}{t}}\\ \end{array} \]

Alternative 4
Error	57.22%
Cost	1764

\[\begin{array}{l} t_1 := \frac{y}{\frac{z}{x} \cdot \frac{c}{9}}\\ t_2 := -4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{if}\;a \leq -2.85 \cdot 10^{-96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-257}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-95}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-42}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+78}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{c}{a \cdot -4}}\\ \end{array} \]

Alternative 5
Error	57.18%
Cost	1764

\[\begin{array}{l} t_1 := -4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{if}\;a \leq -2.85 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-238}:\\ \;\;\;\;\frac{y}{\frac{z}{x} \cdot \frac{c}{9}}\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-257}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-97}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-43}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+77}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{+127}:\\ \;\;\;\;\frac{9 \cdot y}{c \cdot \frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{c}{a \cdot -4}}\\ \end{array} \]

Alternative 6
Error	56.3%
Cost	1636

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ t_2 := -4 \cdot \frac{t}{\frac{c}{a}}\\ t_3 := 9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{-96}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+62}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+78}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+118}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{c}{a \cdot -4}}\\ \end{array} \]

Alternative 7
Error	56.06%
Cost	1636

\[\begin{array}{l} t_1 := \frac{b}{z \cdot c}\\ t_2 := -4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-97}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-42}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 7.2 \cdot 10^{+61}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+78}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+116}:\\ \;\;\;\;\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{c}{a \cdot -4}}\\ \end{array} \]

Alternative 8
Error	19.3%
Cost	1617

\[\begin{array}{l} t_1 := b + 9 \cdot \left(x \cdot y\right)\\ t_2 := \frac{a \cdot \left(t \cdot -4\right) + \frac{t_1}{z}}{c}\\ \mathbf{if}\;z \leq -5 \cdot 10^{-129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-191}:\\ \;\;\;\;\frac{b + -4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-258} \lor \neg \left(z \leq 5.1 \cdot 10^{-67}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{z \cdot c}\\ \end{array} \]

Alternative 9
Error	19.42%
Cost	1616

\[\begin{array}{l} t_1 := b + 9 \cdot \left(x \cdot y\right)\\ t_2 := \frac{a \cdot \left(t \cdot -4\right) + \frac{t_1}{z}}{c}\\ \mathbf{if}\;z \leq -2 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-193}:\\ \;\;\;\;\frac{b + -4 \cdot \left(a \cdot \left(z \cdot t\right)\right)}{z \cdot c}\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-261}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-67}:\\ \;\;\;\;\frac{t_1}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{-4 \cdot \left(t \cdot a\right) + \frac{b - y \cdot \left(x \cdot -9\right)}{z}}{c}\\ \end{array} \]

Alternative 10
Error	42.84%
Cost	1233

\[\begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+149}:\\ \;\;\;\;-4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{+91}:\\ \;\;\;\;9 \cdot \left(\frac{x}{c} \cdot \frac{y}{z}\right)\\ \mathbf{elif}\;t \leq -1.56 \cdot 10^{+19} \lor \neg \left(t \leq 1.08 \cdot 10^{-29}\right):\\ \;\;\;\;\frac{-4}{\frac{\frac{c}{t}}{a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{b + 9 \cdot \left(x \cdot y\right)}{z \cdot c}\\ \end{array} \]

Alternative 11
Error	57.63%
Cost	977

\[\begin{array}{l} t_1 := \left(t \cdot a\right) \cdot \frac{-4}{c}\\ \mathbf{if}\;a \leq -5 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{-43}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+41} \lor \neg \left(a \leq 2.2 \cdot 10^{+100}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 12
Error	54.05%
Cost	977

\[\begin{array}{l} t_1 := \frac{t}{c} \cdot \frac{a}{-0.25}\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-42}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+41} \lor \neg \left(a \leq 6.6 \cdot 10^{+98}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 13
Error	54.31%
Cost	977

\[\begin{array}{l} t_1 := -4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{if}\;a \leq -1.2 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-43}:\\ \;\;\;\;\frac{b}{z \cdot c}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{+41} \lor \neg \left(a \leq 2.2 \cdot 10^{+100}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 14
Error	54.22%
Cost	977

\[\begin{array}{l} t_1 := -4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{if}\;a \leq -7.5 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{-43}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+41} \lor \neg \left(a \leq 2.2 \cdot 10^{+100}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 15
Error	54.24%
Cost	976

\[\begin{array}{l} t_1 := -4 \cdot \frac{t}{\frac{c}{a}}\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \frac{\frac{1}{z}}{c}\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+100}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{c \cdot \frac{-0.25}{a}}\\ \end{array} \]

Alternative 16
Error	65.18%
Cost	585

\[\begin{array}{l} \mathbf{if}\;c \leq -1500000000000 \lor \neg \left(c \leq 3.9 \cdot 10^{-79}\right):\\ \;\;\;\;\frac{\frac{b}{c}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c}\\ \end{array} \]

Alternative 17
Error	67.49%
Cost	320

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

Reproduce

herbie shell --seed 2023089 
(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)))