AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1

Average Accuracy: 59.2% → 98.6%

Time: 19.8s

Precision: binary64

Cost: 2112

Math

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

↓

\[\begin{array}{l} t_1 := \left(x + t\right) + y\\ \frac{z - b}{\frac{t_1}{y}} + \left(\frac{z}{\frac{t_1}{x}} + \frac{t + y}{x + \left(t + y\right)} \cdot a\right) \end{array} \]

FPCore

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

↓

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x t) y)))
   (+
    (/ (- z b) (/ t_1 y))
    (+ (/ z (/ t_1 x)) (* (/ (+ t y) (+ x (+ t y))) a)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
}

↓

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	return ((z - b) / (t_1 / y)) + ((z / (t_1 / x)) + (((t + y) / (x + (t + y))) * a));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
end function

↓

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    t_1 = (x + t) + y
    code = ((z - b) / (t_1 / y)) + ((z / (t_1 / x)) + (((t + y) / (x + (t + y))) * a))
end function

Java

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

↓

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + t) + y;
	return ((z - b) / (t_1 / y)) + ((z / (t_1 / x)) + (((t + y) / (x + (t + y))) * a));
}

Python

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

↓

def code(x, y, z, t, a, b):
	t_1 = (x + t) + y
	return ((z - b) / (t_1 / y)) + ((z / (t_1 / x)) + (((t + y) / (x + (t + y))) * a))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
end

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + t) + y)
	return Float64(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(Float64(z / Float64(t_1 / x)) + Float64(Float64(Float64(t + y) / Float64(x + Float64(t + y))) * a)))
end

MATLAB

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

↓

function tmp = code(x, y, z, t, a, b)
	t_1 = (x + t) + y;
	tmp = ((z - b) / (t_1 / y)) + ((z / (t_1 / x)) + (((t + y) / (x + (t + y))) * a));
end

Wolfram

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

↓

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + t), $MachinePrecision] + y), $MachinePrecision]}, N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(N[(z / N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(t + y), $MachinePrecision] / N[(x + N[(t + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Target

Original	59.2%
Target	82.6%
Herbie	98.6%

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} < -3.5813117084150564 \cdot 10^{+153}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} < 1.2285964308315609 \cdot 10^{+82}:\\ \;\;\;\;\frac{1}{\frac{\left(x + t\right) + y}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Derivation

1. Initial program 59.2%

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

2. Simplified 59.2%

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

   [Start] 59.2	\[ \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
   sub-neg [=>] 59.2	\[ \frac{\color{blue}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) + \left(-y \cdot b\right)}}{\left(x + t\right) + y} \]
   +-commutative [=>] 59.2	\[ \frac{\color{blue}{\left(\left(t + y\right) \cdot a + \left(x + y\right) \cdot z\right)} + \left(-y \cdot b\right)}{\left(x + t\right) + y} \]
   associate-+l+ [=>] 59.2	\[ \frac{\color{blue}{\left(t + y\right) \cdot a + \left(\left(x + y\right) \cdot z + \left(-y \cdot b\right)\right)}}{\left(x + t\right) + y} \]
   fma-def [=>] 59.2	\[ \frac{\color{blue}{\mathsf{fma}\left(t + y, a, \left(x + y\right) \cdot z + \left(-y \cdot b\right)\right)}}{\left(x + t\right) + y} \]
   +-commutative [=>] 59.2	\[ \frac{\mathsf{fma}\left(\color{blue}{y + t}, a, \left(x + y\right) \cdot z + \left(-y \cdot b\right)\right)}{\left(x + t\right) + y} \]
   *-commutative [=>] 59.2	\[ \frac{\mathsf{fma}\left(y + t, a, \color{blue}{z \cdot \left(x + y\right)} + \left(-y \cdot b\right)\right)}{\left(x + t\right) + y} \]
   distribute-rgt-in [=>] 59.2	\[ \frac{\mathsf{fma}\left(y + t, a, \color{blue}{\left(x \cdot z + y \cdot z\right)} + \left(-y \cdot b\right)\right)}{\left(x + t\right) + y} \]
   associate-+l+ [=>] 59.2	\[ \frac{\mathsf{fma}\left(y + t, a, \color{blue}{x \cdot z + \left(y \cdot z + \left(-y \cdot b\right)\right)}\right)}{\left(x + t\right) + y} \]
   fma-def [=>] 59.2	\[ \frac{\mathsf{fma}\left(y + t, a, \color{blue}{\mathsf{fma}\left(x, z, y \cdot z + \left(-y \cdot b\right)\right)}\right)}{\left(x + t\right) + y} \]
   sub-neg [<=] 59.2	\[ \frac{\mathsf{fma}\left(y + t, a, \mathsf{fma}\left(x, z, \color{blue}{y \cdot z - y \cdot b}\right)\right)}{\left(x + t\right) + y} \]
   distribute-lft-out-- [=>] 59.2	\[ \frac{\mathsf{fma}\left(y + t, a, \mathsf{fma}\left(x, z, \color{blue}{y \cdot \left(z - b\right)}\right)\right)}{\left(x + t\right) + y} \]
   +-commutative [=>] 59.2	\[ \frac{\mathsf{fma}\left(y + t, a, \mathsf{fma}\left(x, z, y \cdot \left(z - b\right)\right)\right)}{\color{blue}{y + \left(x + t\right)}} \]

3. Taylor expanded in a around inf 59.2%

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

4. Simplified 98.6%

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

   [Start] 59.2	\[ \frac{\left(z - b\right) \cdot y}{y + \left(t + x\right)} + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
   associate-/l* [=>] 68.5	\[ \color{blue}{\frac{z - b}{\frac{y + \left(t + x\right)}{y}}} + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
   +-commutative [=>] 68.5	\[ \frac{z - b}{\frac{\color{blue}{\left(t + x\right) + y}}{y}} + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
   +-commutative [=>] 68.5	\[ \frac{z - b}{\frac{\color{blue}{\left(x + t\right)} + y}{y}} + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
   associate-/l* [=>] 78.4	\[ \frac{z - b}{\frac{\left(x + t\right) + y}{y}} + \left(\color{blue}{\frac{z}{\frac{y + \left(t + x\right)}{x}}} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
   +-commutative [=>] 78.4	\[ \frac{z - b}{\frac{\left(x + t\right) + y}{y}} + \left(\frac{z}{\frac{\color{blue}{\left(t + x\right) + y}}{x}} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
   +-commutative [=>] 78.4	\[ \frac{z - b}{\frac{\left(x + t\right) + y}{y}} + \left(\frac{z}{\frac{\color{blue}{\left(x + t\right)} + y}{x}} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
   associate-/l* [=>] 98.6	\[ \frac{z - b}{\frac{\left(x + t\right) + y}{y}} + \left(\frac{z}{\frac{\left(x + t\right) + y}{x}} + \color{blue}{\frac{a}{\frac{y + \left(t + x\right)}{y + t}}}\right) \]
   +-commutative [=>] 98.6	\[ \frac{z - b}{\frac{\left(x + t\right) + y}{y}} + \left(\frac{z}{\frac{\left(x + t\right) + y}{x}} + \frac{a}{\frac{\color{blue}{\left(t + x\right) + y}}{y + t}}\right) \]
   +-commutative [=>] 98.6	\[ \frac{z - b}{\frac{\left(x + t\right) + y}{y}} + \left(\frac{z}{\frac{\left(x + t\right) + y}{x}} + \frac{a}{\frac{\color{blue}{\left(x + t\right)} + y}{y + t}}\right) \]
   +-commutative [=>] 98.6	\[ \frac{z - b}{\frac{\left(x + t\right) + y}{y}} + \left(\frac{z}{\frac{\left(x + t\right) + y}{x}} + \frac{a}{\frac{\left(x + t\right) + y}{\color{blue}{t + y}}}\right) \]

5. Applied egg-rr 98.6%

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

6. Final simplification 98.6%

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

Alternatives

Alternative 1
Accuracy	95.9%
Cost	4297

\[\begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + \left(t + y\right) \cdot a\right) - b \cdot y}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 2 \cdot 10^{+239}\right):\\ \;\;\;\;\frac{z - b}{\frac{t_1}{y}} + \left(\frac{z}{\frac{t_1}{x}} + a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Accuracy	90.0%
Cost	4168

\[\begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + \left(t + y\right) \cdot a\right) - b \cdot y}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;z + \frac{y}{\frac{x + y}{a - b}}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+280}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{z}{\frac{t_1}{x}} + a\right) + y \cdot \frac{z - b}{t + y}\\ \end{array} \]

Alternative 3
Accuracy	89.8%
Cost	1865

\[\begin{array}{l} t_1 := \left(x + t\right) + y\\ t_2 := \frac{z - b}{\frac{t_1}{y}}\\ \mathbf{if}\;x \leq -5.8 \cdot 10^{+83} \lor \neg \left(x \leq 8 \cdot 10^{+151}\right):\\ \;\;\;\;t_2 + \left(z + \frac{t + y}{x + \left(t + y\right)} \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 + \left(\frac{z}{\frac{t_1}{x}} + a\right)\\ \end{array} \]

Alternative 4
Accuracy	76.6%
Cost	1746

\[\begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{-18} \lor \neg \left(t \leq 6.5 \cdot 10^{+25} \lor \neg \left(t \leq 1.5 \cdot 10^{+97}\right) \land t \leq 3.9 \cdot 10^{+149}\right):\\ \;\;\;\;\left(\frac{z}{\frac{\left(x + t\right) + y}{x}} + a\right) + y \cdot \frac{z - b}{t}\\ \mathbf{else}:\\ \;\;\;\;z + \frac{y}{\frac{x + y}{a - b}}\\ \end{array} \]

Alternative 5
Accuracy	63.0%
Cost	1628

\[\begin{array}{l} t_1 := z + \frac{y}{\frac{x + y}{a - b}}\\ t_2 := \left(t + y\right) \cdot \frac{a}{x + \left(t + y\right)}\\ \mathbf{if}\;a \leq -1.95 \cdot 10^{+177}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-209}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{-168}:\\ \;\;\;\;b \cdot \frac{-y}{\left(x + t\right) + y}\\ \mathbf{elif}\;a \leq 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+178}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 6
Accuracy	62.6%
Cost	1628

\[\begin{array}{l} t_1 := z + \frac{y}{\frac{x + y}{a - b}}\\ t_2 := \left(t + y\right) \cdot \frac{a}{x + \left(t + y\right)}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;a \leq -1.25 \cdot 10^{+177}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.45 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-209}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-169}:\\ \;\;\;\;\frac{t \cdot a + y \cdot t_3}{t + y}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+178}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Accuracy	84.2%
Cost	1609

\[\begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-37} \lor \neg \left(t \leq 7 \cdot 10^{-53}\right):\\ \;\;\;\;\left(\frac{z}{\frac{\left(x + t\right) + y}{x}} + a\right) + y \cdot \frac{z - b}{t + y}\\ \mathbf{else}:\\ \;\;\;\;z + \frac{y}{\frac{x + y}{a - b}}\\ \end{array} \]

Alternative 8
Accuracy	55.1%
Cost	1300

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := x + \left(t + y\right)\\ t_3 := \left(t + y\right) \cdot \frac{a}{t_2}\\ \mathbf{if}\;t \leq -3.1 \cdot 10^{+155}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{+108}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{t_2}\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+35}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.96 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{-143}:\\ \;\;\;\;b \cdot \frac{-y}{\left(x + t\right) + y}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+217}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 9
Accuracy	59.7%
Cost	1100

\[\begin{array}{l} t_1 := z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \mathbf{if}\;z \leq -6.7 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-157}:\\ \;\;\;\;\left(a - b\right) \cdot \frac{y}{x + y}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+100}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Accuracy	57.5%
Cost	972

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -3.6 \cdot 10^{+203}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-166}:\\ \;\;\;\;\left(a - b\right) \cdot \frac{y}{x + y}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 11
Accuracy	61.8%
Cost	841

\[\begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+75} \lor \neg \left(x \leq 2.8 \cdot 10^{+214}\right):\\ \;\;\;\;z + \frac{y}{\frac{x}{a - b}}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 12
Accuracy	56.4%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-196} \lor \neg \left(y \leq 5.5 \cdot 10^{-146}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \end{array} \]

Alternative 13
Accuracy	58.6%
Cost	584

\[\begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{+202}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+219}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 14
Accuracy	48.5%
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+145}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+100}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 15
Accuracy	45.5%
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+61}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+101}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 16
Accuracy	32.6%
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023122 
(FPCore (x y z t a b)
  :name "AI.Clustering.Hierarchical.Internal:ward from clustering-0.2.1"
  :precision binary64

  :herbie-target
  (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) -3.5813117084150564e+153) (- (+ z a) b) (if (< (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)) 1.2285964308315609e+82) (/ 1.0 (/ (+ (+ x t) y) (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)))) (- (+ z a) b)))

  (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))