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

Average Error: 41.74% → 12.22%

Time: 27.0s

Precision: binary64

Cost: 4168

Math

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

↓

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;z + a \cdot \left(\frac{t}{t_1} + \frac{y}{t_1}\right)\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

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 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) t_1)))
   (if (<= t_2 (- INFINITY))
     (+ z (* a (+ (/ t t_1) (/ y t_1))))
     (if (<= t_2 5e+274) t_2 (- (+ z a) b)))))

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 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z + (a * ((t / t_1) + (y / t_1)));
	} else if (t_2 <= 5e+274) {
		tmp = t_2;
	} else {
		tmp = (z + a) - b;
	}
	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 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = z + (a * ((t / t_1) + (y / t_1)));
	} else if (t_2 <= 5e+274) {
		tmp = t_2;
	} else {
		tmp = (z + a) - b;
	}
	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 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = z + (a * ((t / t_1) + (y / t_1)))
	elif t_2 <= 5e+274:
		tmp = t_2
	else:
		tmp = (z + a) - b
	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(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z + Float64(a * Float64(Float64(t / t_1) + Float64(y / t_1))));
	elseif (t_2 <= 5e+274)
		tmp = t_2;
	else
		tmp = Float64(Float64(z + a) - b);
	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 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = z + (a * ((t / t_1) + (y / t_1)));
	elseif (t_2 <= 5e+274)
		tmp = t_2;
	else
		tmp = (z + a) - b;
	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[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(z + N[(a * N[(N[(t / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+274], t$95$2, N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]]]]]

Target

Original	41.74%
Target	17.22%
Herbie	12.22%

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

Derivation

1. Split input into 3 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

   1. Initial program 100

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

   2. Taylor expanded in a around 0 66.28

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

   3. Simplified 66.28

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

      [Start] 66.28	\[ \left(\frac{\left(y + x\right) \cdot z}{y + \left(t + x\right)} + a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right)\right) - \frac{y \cdot b}{y + \left(t + x\right)} \]
      +-commutative [=>] 66.28	\[ \color{blue}{\left(a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) + \frac{\left(y + x\right) \cdot z}{y + \left(t + x\right)}\right)} - \frac{y \cdot b}{y + \left(t + x\right)} \]
      associate--l+ [=>] 66.28	\[ \color{blue}{a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) + \left(\frac{\left(y + x\right) \cdot z}{y + \left(t + x\right)} - \frac{y \cdot b}{y + \left(t + x\right)}\right)} \]
      associate-+r+ [=>] 66.28	\[ a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) + \left(\frac{\left(y + x\right) \cdot z}{\color{blue}{\left(y + t\right) + x}} - \frac{y \cdot b}{y + \left(t + x\right)}\right) \]
      +-commutative [<=] 66.28	\[ a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) + \left(\frac{\left(y + x\right) \cdot z}{\color{blue}{x + \left(y + t\right)}} - \frac{y \cdot b}{y + \left(t + x\right)}\right) \]
      associate-+r+ [=>] 66.28	\[ a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) + \left(\frac{\left(y + x\right) \cdot z}{x + \left(y + t\right)} - \frac{y \cdot b}{\color{blue}{\left(y + t\right) + x}}\right) \]
      +-commutative [<=] 66.28	\[ a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) + \left(\frac{\left(y + x\right) \cdot z}{x + \left(y + t\right)} - \frac{y \cdot b}{\color{blue}{x + \left(y + t\right)}}\right) \]
      div-sub [<=] 66.28	\[ a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) + \color{blue}{\frac{\left(y + x\right) \cdot z - y \cdot b}{x + \left(y + t\right)}} \]
      +-commutative [=>] 66.28	\[ a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) + \frac{\left(y + x\right) \cdot z - y \cdot b}{\color{blue}{\left(y + t\right) + x}} \]
      associate-+r+ [<=] 66.28	\[ a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) + \frac{\left(y + x\right) \cdot z - y \cdot b}{\color{blue}{y + \left(t + x\right)}} \]
      *-commutative [=>] 66.28	\[ a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) + \frac{\color{blue}{z \cdot \left(y + x\right)} - y \cdot b}{y + \left(t + x\right)} \]

   4. Taylor expanded in x around inf 30.32

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 4.9999999999999998e274

   1. Initial program 0.53

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

   if 4.9999999999999998e274 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 97.35

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

   2. Taylor expanded in y around inf 26.81

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   3. Simplified 26.81

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

      [Start] 26.81	\[ \left(a + z\right) - b \]
      +-commutative [=>] 26.81	\[ \color{blue}{\left(z + a\right)} - b \]

3. Recombined 3 regimes into one program.

4. Final simplification 12.22

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty:\\ \;\;\;\;z + a \cdot \left(\frac{t}{y + \left(x + t\right)} + \frac{y}{y + \left(x + t\right)}\right)\\ \mathbf{elif}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+274}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternatives

Alternative 1
Error	29.64%
Cost	2072

\[\begin{array}{l} t_1 := a + \left(z \cdot \left(x + y\right) - y \cdot b\right) \cdot \frac{-1}{\left(-y\right) - \left(x + t\right)}\\ t_2 := y + \left(x + t\right)\\ t_3 := z + a \cdot \left(\frac{t}{t_2} + \frac{y}{t_2}\right)\\ t_4 := \frac{y}{y + t} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{+143}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-272}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 0.0058:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+41}:\\ \;\;\;\;\frac{x + y}{\frac{t_2}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 2
Error	24.12%
Cost	1873

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{y}{t_1}\\ t_3 := z + a \cdot \left(\frac{t}{t_1} + t_2\right)\\ \mathbf{if}\;a \leq -4 \cdot 10^{+144}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -8 \cdot 10^{+52}:\\ \;\;\;\;a + \left(z \cdot \left(x + y\right) - y \cdot b\right) \cdot \frac{-1}{\left(-y\right) - \left(x + t\right)}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-8} \lor \neg \left(a \leq 1.1 \cdot 10^{-39}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{z}{t_1} - b \cdot t_2\\ \end{array} \]

Alternative 3
Error	41.44%
Cost	1760

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ t_3 := z \cdot \frac{x + y}{t_1}\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-47}:\\ \;\;\;\;\frac{t \cdot a - y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-211}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-280}:\\ \;\;\;\;z + \frac{a}{\frac{x}{y + t}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \frac{y + t}{t_1}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-55}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + t} \cdot \left(a + \left(z - b\right)\right)\\ \end{array} \]

Alternative 4
Error	41.94%
Cost	1760

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -1 \cdot 10^{-8}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-49}:\\ \;\;\;\;\frac{t \cdot a - y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-84}:\\ \;\;\;\;z \cdot \frac{x + y}{t_1}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-213}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-281}:\\ \;\;\;\;z + \frac{a}{\frac{x}{y + t}}\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \frac{y + t}{t_1}\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-31}:\\ \;\;\;\;\frac{x \cdot z - y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq 1400000000000:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + t} \cdot \left(a + \left(z - b\right)\right)\\ \end{array} \]

Alternative 5
Error	41.48%
Cost	1760

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{-9}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-47}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-85}:\\ \;\;\;\;z \cdot \frac{x + y}{t_1}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-209}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-280}:\\ \;\;\;\;z + \frac{a}{\frac{x}{y + t}}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \frac{y + t}{t_1}\\ \mathbf{elif}\;y \leq 1.72 \cdot 10^{-28}:\\ \;\;\;\;\frac{x \cdot z - y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+17}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + t} \cdot \left(a + \left(z - b\right)\right)\\ \end{array} \]

Alternative 6
Error	42.03%
Cost	1628

\[\begin{array}{l} t_1 := a \cdot \frac{t}{y + \left(x + t\right)}\\ t_2 := z + \frac{a}{\frac{x}{y + t}}\\ t_3 := \frac{y}{y + t} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{if}\;y \leq -6.6 \cdot 10^{-36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4.7 \cdot 10^{-116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-142}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-279}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	31.35%
Cost	1612

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z + a \cdot \left(\frac{t}{t_1} + \frac{y}{t_1}\right)\\ \mathbf{if}\;a \leq -6 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-163}:\\ \;\;\;\;\frac{\left(y \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + t}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-89}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	41.34%
Cost	1496

\[\begin{array}{l} t_1 := a \cdot \frac{y + t}{y + \left(x + t\right)}\\ t_2 := \frac{y}{y + t} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-279}:\\ \;\;\;\;z + \frac{a}{\frac{x}{y + t}}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-34}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+20}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	40.86%
Cost	1496

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a \cdot \frac{y + t}{t_1}\\ t_3 := \frac{y}{y + t} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{-17}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-221}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-279}:\\ \;\;\;\;z + \frac{a}{\frac{x}{y + t}}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-55}:\\ \;\;\;\;z \cdot \frac{x + y}{t_1}\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+20}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	40.92%
Cost	1496

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{y}{y + t} \cdot \left(a + \left(z - b\right)\right)\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.78 \cdot 10^{-217}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-280}:\\ \;\;\;\;z + \frac{a}{\frac{x}{y + t}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-83}:\\ \;\;\;\;a \cdot \frac{y + t}{t_1}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-55}:\\ \;\;\;\;z \cdot \frac{x + y}{t_1}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+19}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	38.58%
Cost	1356

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+46}:\\ \;\;\;\;\frac{a}{\frac{t_2}{y + t}}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-88}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{t_2}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{t_2}\\ \end{array} \]

Alternative 12
Error	39.16%
Cost	1356

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{+77}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{-163}:\\ \;\;\;\;\frac{\left(y \cdot z + a \cdot \left(y + t\right)\right) - y \cdot b}{y + t}\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-87}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{t_1}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+56}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{t_1}\\ \end{array} \]

Alternative 13
Error	43.48%
Cost	1240

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.9 \cdot 10^{-221}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-248}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-140}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-87}:\\ \;\;\;\;\frac{a}{\frac{x}{y + t}}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \frac{y}{y + t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	45.58%
Cost	1240

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-221}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-280}:\\ \;\;\;\;\frac{x \cdot z}{x + t}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-140}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-88}:\\ \;\;\;\;\frac{a}{\frac{x}{y + t}}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \frac{y}{y + t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	42.11%
Cost	1236

\[\begin{array}{l} t_1 := a \cdot \frac{t}{y + \left(x + t\right)}\\ t_2 := \left(z + a\right) - b\\ t_3 := z + \frac{a}{\frac{x}{y + t}}\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{-143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-280}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-57}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	42.4%
Cost	1104

\[\begin{array}{l} \mathbf{if}\;t \leq -8.6 \cdot 10^{+173}:\\ \;\;\;\;a - x \cdot \frac{a}{t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+37}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+153}:\\ \;\;\;\;\frac{t}{\frac{x + t}{a}}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+174}:\\ \;\;\;\;y \cdot \frac{z - b}{y + t}\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 17
Error	50.74%
Cost	852

\[\begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-143}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{-220}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-279}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-214}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+150}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \]

Alternative 18
Error	41.15%
Cost	848

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-221}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-248}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-38}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Error	42.82%
Cost	841

\[\begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-142} \lor \neg \left(y \leq 4.2 \cdot 10^{-80}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{t}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 20
Error	50.07%
Cost	720

\[\begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-148}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-219}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-280}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-214}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 21
Error	56.69%
Cost	328

\[\begin{array}{l} \mathbf{if}\;t \leq -0.00066:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-95}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 22
Error	67.31%
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023121 
(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)))