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

Average Error: 26.5 → 0.8

Time: 25.7s

Precision: binary64

Cost: 5448

Math

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

↓

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right)\\ t_3 := \left(\left(x + y\right) \cdot \left(z \cdot \frac{1}{t_1}\right) + t_2\right) - \frac{y}{\frac{t_1}{b}}\\ t_4 := z \cdot \left(x + y\right)\\ t_5 := \frac{\left(t_4 + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_5 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_5 \leq 10^{+231}:\\ \;\;\;\;\left(t_2 + \frac{t_4}{t_1}\right) - \frac{y \cdot b}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

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 (+ y (+ x t)))
        (t_2 (* a (+ (/ y t_1) (/ t t_1))))
        (t_3 (- (+ (* (+ x y) (* z (/ 1.0 t_1))) t_2) (/ y (/ t_1 b))))
        (t_4 (* z (+ x y)))
        (t_5 (/ (- (+ t_4 (* a (+ y t))) (* y b)) t_1)))
   (if (<= t_5 (- INFINITY))
     t_3
     (if (<= t_5 1e+231) (- (+ t_2 (/ t_4 t_1)) (/ (* y b) t_1)) t_3))))

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 = y + (x + t);
	double t_2 = a * ((y / t_1) + (t / t_1));
	double t_3 = (((x + y) * (z * (1.0 / t_1))) + t_2) - (y / (t_1 / b));
	double t_4 = z * (x + y);
	double t_5 = ((t_4 + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if (t_5 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_5 <= 1e+231) {
		tmp = (t_2 + (t_4 / t_1)) - ((y * b) / t_1);
	} else {
		tmp = t_3;
	}
	return tmp;
}

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 = y + (x + t);
	double t_2 = a * ((y / t_1) + (t / t_1));
	double t_3 = (((x + y) * (z * (1.0 / t_1))) + t_2) - (y / (t_1 / b));
	double t_4 = z * (x + y);
	double t_5 = ((t_4 + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if (t_5 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_5 <= 1e+231) {
		tmp = (t_2 + (t_4 / t_1)) - ((y * b) / t_1);
	} else {
		tmp = t_3;
	}
	return tmp;
}

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 = y + (x + t)
	t_2 = a * ((y / t_1) + (t / t_1))
	t_3 = (((x + y) * (z * (1.0 / t_1))) + t_2) - (y / (t_1 / b))
	t_4 = z * (x + y)
	t_5 = ((t_4 + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if t_5 <= -math.inf:
		tmp = t_3
	elif t_5 <= 1e+231:
		tmp = (t_2 + (t_4 / t_1)) - ((y * b) / t_1)
	else:
		tmp = t_3
	return tmp

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(y + Float64(x + t))
	t_2 = Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1)))
	t_3 = Float64(Float64(Float64(Float64(x + y) * Float64(z * Float64(1.0 / t_1))) + t_2) - Float64(y / Float64(t_1 / b)))
	t_4 = Float64(z * Float64(x + y))
	t_5 = Float64(Float64(Float64(t_4 + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_5 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_5 <= 1e+231)
		tmp = Float64(Float64(t_2 + Float64(t_4 / t_1)) - Float64(Float64(y * b) / t_1));
	else
		tmp = t_3;
	end
	return tmp
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_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = a * ((y / t_1) + (t / t_1));
	t_3 = (((x + y) * (z * (1.0 / t_1))) + t_2) - (y / (t_1 / b));
	t_4 = z * (x + y);
	t_5 = ((t_4 + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if (t_5 <= -Inf)
		tmp = t_3;
	elseif (t_5 <= 1e+231)
		tmp = (t_2 + (t_4 / t_1)) - ((y * b) / t_1);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
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[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(x + y), $MachinePrecision] * N[(z * N[(1.0 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision] - N[(y / N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(N[(N[(t$95$4 + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$5, (-Infinity)], t$95$3, If[LessEqual[t$95$5, 1e+231], N[(N[(t$95$2 + N[(t$95$4 / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Target

Original	26.5
Target	11.0
Herbie	0.8

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -inf.0 or 1.0000000000000001e231 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 61.4

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

   2. Taylor expanded in a around 0 43.6

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

   3. Applied egg-rr 32.1

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

   4. Applied egg-rr 1.2

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e231

   1. Initial program 0.4

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

   2. Taylor expanded in a around 0 0.6

      \[\leadsto \color{blue}{\left(\frac{\left(y + x\right) \cdot z}{y + \left(t + x\right)} + a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right)\right) - \frac{y \cdot b}{y + \left(t + x\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 0.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;\left(\left(x + y\right) \cdot \left(z \cdot \frac{1}{y + \left(x + t\right)}\right) + a \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{t}{y + \left(x + t\right)}\right)\right) - \frac{y}{\frac{y + \left(x + t\right)}{b}}\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+231}:\\ \;\;\;\;\left(a \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{t}{y + \left(x + t\right)}\right) + \frac{z \cdot \left(x + y\right)}{y + \left(x + t\right)}\right) - \frac{y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(x + y\right) \cdot \left(z \cdot \frac{1}{y + \left(x + t\right)}\right) + a \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{t}{y + \left(x + t\right)}\right)\right) - \frac{y}{\frac{y + \left(x + t\right)}{b}}\\ \end{array} \]

Alternatives

Alternative 1
Error	3.4
Cost	5320

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(a + \left(x + y\right) \cdot \left(z \cdot \frac{1}{t_1}\right)\right) - \frac{y}{\frac{t_1}{b}}\\ t_3 := z \cdot \left(x + y\right)\\ t_4 := \frac{\left(t_3 + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_4 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_4 \leq 10^{+231}:\\ \;\;\;\;\left(a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right) + \frac{t_3}{t_1}\right) - \frac{y \cdot b}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	3.3
Cost	4552

\[\begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(z \cdot \left(x + y\right) + t_1\right) - y \cdot b}{t_2}\\ t_4 := \left(a + \left(x + y\right) \cdot \left(z \cdot \frac{1}{t_2}\right)\right) - \frac{y}{\frac{t_2}{b}}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_3 \leq 10^{+231}:\\ \;\;\;\;z \cdot \frac{x + y}{t_2} + \frac{t_1 - y \cdot b}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 3
Error	3.2
Cost	4424

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ t_3 := \left(a + \left(x + y\right) \cdot \left(z \cdot \frac{1}{t_1}\right)\right) - \frac{y}{\frac{t_1}{b}}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 10^{+231}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	7.7
Cost	4168

\[\begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 10^{+231}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	26.4
Cost	2284

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{a \cdot \left(y + t\right) - y \cdot b}{t_1}\\ t_3 := \left(z + a\right) - b\\ t_4 := \frac{y \cdot t_3}{t_1}\\ t_5 := z - z \cdot \frac{t}{x + y}\\ \mathbf{if}\;y \leq -1.5314145907679683 \cdot 10^{+87}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.8720003252778038 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.3704461280012734 \cdot 10^{-31}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -7.21119411225508 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.256062983275152 \cdot 10^{-153}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -4.146666450531246 \cdot 10^{-247}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq 8.99817972720879 \cdot 10^{-169}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 1.2802199895931109 \cdot 10^{-110}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 1.582657756925115 \cdot 10^{-68}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 4.6443070534256657 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.1799535592645347 \cdot 10^{+51}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	25.8
Cost	1888

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ t_3 := \frac{y \cdot t_2}{t_1}\\ \mathbf{if}\;y \leq -1.5314145907679683 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -0.0004444915510926359:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -5.643983027911088 \cdot 10^{-150}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 8.99817972720879 \cdot 10^{-169}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 1.2802199895931109 \cdot 10^{-110}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.1833489494978218 \cdot 10^{-85}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq 3.603678896707086 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.1799535592645347 \cdot 10^{+51}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	25.6
Cost	1872

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := t + \left(x + y\right)\\ \mathbf{if}\;y \leq -1.5314145907679683 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.8720003252778038 \cdot 10^{-9}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{t_2}\\ \mathbf{elif}\;y \leq -3.3704461280012734 \cdot 10^{-31}:\\ \;\;\;\;z - z \cdot \frac{t}{x + y}\\ \mathbf{elif}\;y \leq -4.146666450531246 \cdot 10^{-247}:\\ \;\;\;\;\frac{y + t}{\frac{t_3}{a}} - \frac{y \cdot b}{t_3}\\ \mathbf{elif}\;y \leq 8.99817972720879 \cdot 10^{-169}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 1.1799535592645347 \cdot 10^{+51}:\\ \;\;\;\;\frac{y \cdot t_1}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	27.9
Cost	1496

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{a}{\frac{t_1}{y + t}}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.361293534445588 \cdot 10^{+70}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.8720003252778038 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.3704461280012734 \cdot 10^{-31}:\\ \;\;\;\;z - z \cdot \frac{t}{x + y}\\ \mathbf{elif}\;y \leq -7.022938382899591 \cdot 10^{-301}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.2120864833441888 \cdot 10^{-253}:\\ \;\;\;\;z \cdot \frac{x + y}{t_1}\\ \mathbf{elif}\;y \leq 3.3483454214444316 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Error	29.6
Cost	1368

\[\begin{array}{l} t_1 := \frac{a}{\frac{x + t}{t}}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -154542.40248667053:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.256062983275152 \cdot 10^{-153}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -7.022938382899591 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.2120864833441888 \cdot 10^{-253}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;y \leq 1.1833489494978218 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5659553196028816 \cdot 10^{+118}:\\ \;\;\;\;\frac{y}{x + y} \cdot \left(a - b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	29.6
Cost	1368

\[\begin{array}{l} t_1 := \frac{a}{\frac{x + t}{t}}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -154542.40248667053:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.256062983275152 \cdot 10^{-153}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -7.022938382899591 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.2120864833441888 \cdot 10^{-253}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.1833489494978218 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5659553196028816 \cdot 10^{+118}:\\ \;\;\;\;\frac{y}{x + y} \cdot \left(a - b\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	25.4
Cost	1364

\[\begin{array}{l} t_1 := \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.361293534445588 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.8720003252778038 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.256062983275152 \cdot 10^{-153}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 8.99817972720879 \cdot 10^{-169}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 3.3483454214444316 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	28.5
Cost	1108

\[\begin{array}{l} t_1 := \frac{a}{\frac{x + t}{t}}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -154542.40248667053:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.256062983275152 \cdot 10^{-153}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -7.022938382899591 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.2120864833441888 \cdot 10^{-253}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;y \leq 3.3483454214444316 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	28.7
Cost	984

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -2.8172167520664615 \cdot 10^{+140}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.7179773896861078 \cdot 10^{-68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.975380127612113 \cdot 10^{-218}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 3.347685696017045 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6.670178134917259 \cdot 10^{+113}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 2.4417240058226224 \cdot 10^{+126}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 14
Error	29.8
Cost	980

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -154542.40248667053:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.256062983275152 \cdot 10^{-153}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -7.022938382899591 \cdot 10^{-301}:\\ \;\;\;\;t \cdot \frac{a}{x + t}\\ \mathbf{elif}\;y \leq 2.2120864833441888 \cdot 10^{-253}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;y \leq 3.3483454214444316 \cdot 10^{-16}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	33.3
Cost	720

\[\begin{array}{l} \mathbf{if}\;x \leq -1.496914480993222 \cdot 10^{+20}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 279955135177256.97:\\ \;\;\;\;a - b\\ \mathbf{elif}\;x \leq 6.670178134917259 \cdot 10^{+113}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 2.4417240058226224 \cdot 10^{+126}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 16
Error	35.8
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -1.496914480993222 \cdot 10^{+20}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.8333861350665838 \cdot 10^{-54}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 3.347685696017045 \cdot 10^{+69}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.7386130179678156 \cdot 10^{+138}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 17
Error	43.2
Cost	64

\[a \]

Reproduce

herbie shell --seed 2022300 
(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)))