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

Average Error: 26.2 → 7.0

Time: 27.9s

Precision: binary64

Cost: 4169

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+289}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

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 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+289))) (- (+ z a) b) t_1)))

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 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+289)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	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 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+289)) {
		tmp = (z + a) - b;
	} else {
		tmp = t_1;
	}
	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 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t))
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+289):
		tmp = (z + a) - b
	else:
		tmp = t_1
	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(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+289))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = t_1;
	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 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+289)))
		tmp = (z + a) - b;
	else
		tmp = t_1;
	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[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+289]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], t$95$1]]

Target

Original	26.2
Target	11.0
Herbie	7.0

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

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 5.00000000000000031e289 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 63.5

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

   2. Taylor expanded in y around inf 16.8

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000031e289

   1. Initial program 0.3

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

4. Final simplification 7.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+289}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error	30.9
Cost	2684

\[\begin{array}{l} t_1 := \frac{x \cdot z + t \cdot a}{x + t}\\ t_2 := \frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ t_3 := \frac{z - b}{\frac{y + \left(x + t\right)}{y}}\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+236}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{+207}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+187}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.75 \cdot 10^{+129}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+52}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{-243}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-257}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-198}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-133}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-127}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{-12}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \end{array} \]

Alternative 2
Error	30.5
Cost	2552

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := y \cdot \left(\left(a + \left(z - b\right)\right) \cdot \frac{1}{t_2}\right)\\ t_4 := \frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ t_5 := \frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{if}\;x \leq -3.8 \cdot 10^{+236}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -2.05 \cdot 10^{+207}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+185}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+162}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -6 \cdot 10^{+129}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+52}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-40}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 10^{-256}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{-161}:\\ \;\;\;\;\frac{z - b}{\frac{t_2}{y}}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-127}:\\ \;\;\;\;a + \left(\frac{z}{\frac{t}{x}} - \frac{a}{\frac{t}{x}}\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.55 \cdot 10^{+36}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+108}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \end{array} \]

Alternative 3
Error	24.2
Cost	2412

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{a \cdot \left(y + t\right) - y \cdot b}{t_1}\\ t_3 := \frac{z \cdot \left(x + y\right) - y \cdot b}{t_1}\\ t_4 := y \cdot \left(\left(a + \left(z - b\right)\right) \cdot \frac{1}{t_1}\right)\\ t_5 := t + \left(x + y\right)\\ \mathbf{if}\;y \leq -215000000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-59}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-84}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-137}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-193}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-226}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-136}:\\ \;\;\;\;z \cdot \frac{x + y}{t_5}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-39}:\\ \;\;\;\;\frac{x + y}{\frac{t_5}{z}}\\ \mathbf{elif}\;y \leq 10^{-5}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+99}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 4
Error	24.2
Cost	2016

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := t + \left(x + y\right)\\ t_3 := y \cdot \left(\left(a + \left(z - b\right)\right) \cdot \frac{1}{t_1}\right)\\ t_4 := \frac{a \cdot \left(y + t\right) - y \cdot b}{t_1}\\ \mathbf{if}\;y \leq -2250000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-157}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-227}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-136}:\\ \;\;\;\;z \cdot \frac{x + y}{t_2}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-88}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-39}:\\ \;\;\;\;\frac{x + y}{\frac{t_2}{z}}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-7}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+99}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Error	30.8
Cost	1696

\[\begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \frac{y}{\frac{t_1}{-b}}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;b \leq -3.6 \cdot 10^{+234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.05 \cdot 10^{+186}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_1}\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{-134}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-218}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \frac{x + y}{t_1}\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{+170}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{-y}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 6
Error	30.0
Cost	1432

\[\begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \frac{y}{\frac{t_1}{-b}}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;b \leq -3.6 \cdot 10^{+234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3 \cdot 10^{+185}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_1}\\ \mathbf{elif}\;b \leq -3.4 \cdot 10^{+129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-241}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+169}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{-y}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 7
Error	30.4
Cost	1432

\[\begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \frac{y}{\frac{t_1}{-b}}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;b \leq -3.6 \cdot 10^{+234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -7.6 \cdot 10^{+182}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_1}\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-220}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \frac{x + y}{t_1}\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{+169}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{-y}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 8
Error	29.3
Cost	1168

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := b \cdot \frac{-y}{y + \left(x + t\right)}\\ \mathbf{if}\;b \leq -6 \cdot 10^{+232}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.38 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	29.3
Cost	1168

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+232}:\\ \;\;\;\;\frac{y}{\frac{t + \left(x + y\right)}{-b}}\\ \mathbf{elif}\;b \leq 1.38 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.36 \cdot 10^{-108}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;b \leq 9.8 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \frac{-y}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 10
Error	27.1
Cost	1104

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a + x \cdot \frac{z - a}{t}\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.7 \cdot 10^{-155}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-225}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+218}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	27.0
Cost	976

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z \cdot \frac{x}{x + t}\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-297}:\\ \;\;\;\;\frac{y}{t} \cdot \left(z + \left(a - b\right)\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	26.8
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+228}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+116}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - \frac{t}{x}\right)\\ \end{array} \]

Alternative 13
Error	29.0
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-201}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-245}:\\ \;\;\;\;a \cdot \frac{t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 14
Error	28.9
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-158}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-230}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 15
Error	33.8
Cost	588

\[\begin{array}{l} \mathbf{if}\;b \leq -31000000000:\\ \;\;\;\;a - b\\ \mathbf{elif}\;b \leq 1.38 \cdot 10^{-241}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-108}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 16
Error	26.8
Cost	584

\[\begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{+226}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+116}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 17
Error	31.4
Cost	457

\[\begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-83} \lor \neg \left(t \leq 5.2 \cdot 10^{-57}\right):\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \]

Alternative 18
Error	31.6
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-166}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-171}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 19
Error	35.0
Cost	328

\[\begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{+22}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 11500000000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 20
Error	42.8
Cost	64

\[a \]

Reproduce

herbie shell --seed 2022364 
(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)))