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

Average Error: 26.7 → 5.8

Time: 24.7s

Precision: binary64

Cost: 4168

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := y + \left(t + x\right)\\ t_3 := \left(z + a \cdot \left(\frac{y}{t_2} + \frac{t}{t_2}\right)\right) - b\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+247}:\\ \;\;\;\;\frac{\left(z \cdot x + a \cdot t\right) + y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

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 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (+ y (+ t x)))
        (t_3 (- (+ z (* a (+ (/ y t_2) (/ t t_2)))) b)))
   (if (<= t_1 (- INFINITY))
     t_3
     (if (<= t_1 5e+247)
       (/ (+ (+ (* z x) (* a t)) (* y (- (+ z a) b))) (+ y (+ x t)))
       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 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = y + (t + x);
	double t_3 = (z + (a * ((y / t_2) + (t / t_2)))) - b;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_1 <= 5e+247) {
		tmp = (((z * x) + (a * t)) + (y * ((z + a) - b))) / (y + (x + t));
	} 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 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = y + (t + x);
	double t_3 = (z + (a * ((y / t_2) + (t / t_2)))) - b;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_1 <= 5e+247) {
		tmp = (((z * x) + (a * t)) + (y * ((z + a) - b))) / (y + (x + t));
	} 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 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
	t_2 = y + (t + x)
	t_3 = (z + (a * ((y / t_2) + (t / t_2)))) - b
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_3
	elif t_1 <= 5e+247:
		tmp = (((z * x) + (a * t)) + (y * ((z + a) - b))) / (y + (x + t))
	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(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_2 = Float64(y + Float64(t + x))
	t_3 = Float64(Float64(z + Float64(a * Float64(Float64(y / t_2) + Float64(t / t_2)))) - b)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_1 <= 5e+247)
		tmp = Float64(Float64(Float64(Float64(z * x) + Float64(a * t)) + Float64(y * Float64(Float64(z + a) - b))) / Float64(y + Float64(x + t)));
	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 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	t_2 = y + (t + x);
	t_3 = (z + (a * ((y / t_2) + (t / t_2)))) - b;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_3;
	elseif (t_1 <= 5e+247)
		tmp = (((z * x) + (a * t)) + (y * ((z + a) - b))) / (y + (x + t));
	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[(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]}, Block[{t$95$2 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z + N[(a * N[(N[(y / t$95$2), $MachinePrecision] + N[(t / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$3, If[LessEqual[t$95$1, 5e+247], N[(N[(N[(N[(z * x), $MachinePrecision] + N[(a * t), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Target

Original	26.7
Target	11.2
Herbie	5.8

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

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 5.00000000000000023e247 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 61.8

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

   2. Simplified 61.8

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

      [Start] 61.8	\[ \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
      rational_best-simplify-1 [=>] 61.8	\[ \frac{\left(\left(x + y\right) \cdot z + \color{blue}{\left(y + t\right)} \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
      rational_best-simplify-1 [=>] 61.8	\[ \frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{\color{blue}{y + \left(x + t\right)}} \]

   3. Taylor expanded in a around 0 43.2

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

   4. Taylor expanded in y around inf 23.4

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

   5. Taylor expanded in y around inf 13.1

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000023e247

   1. Initial program 0.3

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

   2. Simplified 0.3

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

      [Start] 0.3	\[ \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
      rational_best-simplify-1 [=>] 0.3	\[ \frac{\left(\left(x + y\right) \cdot z + \color{blue}{\left(y + t\right)} \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
      rational_best-simplify-1 [=>] 0.3	\[ \frac{\left(\left(x + y\right) \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b}{\color{blue}{y + \left(x + t\right)}} \]

   3. Taylor expanded in y around 0 0.3

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

   4. Simplified 0.3

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

      [Start] 0.3	\[ \frac{z \cdot x + \left(y \cdot \left(\left(a + z\right) - b\right) + a \cdot t\right)}{y + \left(x + t\right)} \]
      rational_best-simplify-1 [<=] 0.3	\[ \frac{z \cdot x + \color{blue}{\left(a \cdot t + y \cdot \left(\left(a + z\right) - b\right)\right)}}{y + \left(x + t\right)} \]
      rational_best-simplify-43 [=>] 0.3	\[ \frac{\color{blue}{y \cdot \left(\left(a + z\right) - b\right) + \left(a \cdot t + z \cdot x\right)}}{y + \left(x + t\right)} \]
      rational_best-simplify-1 [<=] 0.3	\[ \frac{y \cdot \left(\left(a + z\right) - b\right) + \color{blue}{\left(z \cdot x + a \cdot t\right)}}{y + \left(x + t\right)} \]
      rational_best-simplify-1 [=>] 0.3	\[ \frac{\color{blue}{\left(z \cdot x + a \cdot t\right) + y \cdot \left(\left(a + z\right) - b\right)}}{y + \left(x + t\right)} \]
      rational_best-simplify-1 [=>] 0.3	\[ \frac{\left(z \cdot x + a \cdot t\right) + y \cdot \left(\color{blue}{\left(z + a\right)} - b\right)}{y + \left(x + t\right)} \]

3. Recombined 2 regimes into one program.

4. Final simplification 5.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -\infty:\\ \;\;\;\;\left(z + a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right)\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 5 \cdot 10^{+247}:\\ \;\;\;\;\frac{\left(z \cdot x + a \cdot t\right) + y \cdot \left(\left(z + a\right) - b\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right)\right) - b\\ \end{array} \]

Alternatives

Alternative 1
Error	25.2
Cost	3596

\[\begin{array}{l} t_1 := \left(y + x\right) \cdot z\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{a \cdot \left(y + t\right) - y \cdot b}{t_2}\\ t_4 := \frac{z \cdot x + a \cdot t}{t + x}\\ t_5 := y + \left(t + x\right)\\ t_6 := \frac{y}{t_5}\\ t_7 := \frac{t_1}{t_5} + a\\ t_8 := \left(z + a \cdot \left(t_6 + \frac{t}{t_5}\right)\right) - b\\ t_9 := \left(\frac{x}{t_5} + t_6\right) \cdot z\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+233}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{+127}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+107}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{+83}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+66}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+63}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+54}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-27}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-139}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;z \leq -1.86 \cdot 10^{-280}:\\ \;\;\;\;\left(a + z\right) - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;z \leq 2.52 \cdot 10^{-264}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{-208}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-86}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-73}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-25}:\\ \;\;\;\;a + \frac{z \cdot x}{x + t}\\ \mathbf{elif}\;z \leq 7.7 \cdot 10^{-20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+28}:\\ \;\;\;\;\frac{t_1 - y \cdot b}{t_2}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+167}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{+267}:\\ \;\;\;\;t_9\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+268}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \]

Alternative 2
Error	26.1
Cost	2804

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{a \cdot \left(y + t\right) - y \cdot b}{t_1}\\ t_3 := y + \left(t + x\right)\\ t_4 := \frac{y}{t_3}\\ t_5 := \left(\frac{x}{t_3} + t_4\right) \cdot z\\ t_6 := a \cdot \left(t_4 + \frac{t}{t_3}\right)\\ t_7 := \left(y + x\right) \cdot z\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+233}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+127}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+64}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-24}:\\ \;\;\;\;\frac{t_7}{t_3} + a\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-30}:\\ \;\;\;\;z - \frac{y \cdot b}{t_3}\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-130}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-171}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;z \leq 1.08 \cdot 10^{-299}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-104}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-25}:\\ \;\;\;\;\frac{z \cdot x + a \cdot t}{t + x}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+28}:\\ \;\;\;\;\frac{t_7 - y \cdot b}{t_1}\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+169}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 3
Error	29.0
Cost	2152

\[\begin{array}{l} t_1 := \left(y + x\right) \cdot z\\ t_2 := a \cdot \left(y + t\right)\\ t_3 := y + \left(t + x\right)\\ t_4 := \frac{y}{t_3}\\ t_5 := \frac{t_1}{t_3} + a\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{+240}:\\ \;\;\;\;\left(\frac{x}{t_3} + t_4\right) \cdot z\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+102}:\\ \;\;\;\;\left(z + a \cdot \left(t_4 + \frac{t}{x}\right)\right) - b\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-38}:\\ \;\;\;\;\frac{z \cdot x + a \cdot t}{t + x}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-109}:\\ \;\;\;\;a \cdot \left(t_4 + \frac{t}{t_3}\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-125}:\\ \;\;\;\;z - \frac{y \cdot b}{t_3}\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{-298}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-84}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-21}:\\ \;\;\;\;\frac{t_1 - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+56}:\\ \;\;\;\;\left(\frac{t_2}{x} + z\right) - b\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+100}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;\frac{t_2}{t_3} + z\\ \end{array} \]

Alternative 4
Error	24.6
Cost	2020

\[\begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \left(z + a\right) - b\\ t_3 := \frac{a \cdot \left(y + t\right)}{t_1} + z\\ \mathbf{if}\;y \leq -2.35 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-29}:\\ \;\;\;\;a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right)\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-55}:\\ \;\;\;\;z - \frac{y \cdot b}{t_1}\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-109}:\\ \;\;\;\;\left(a + z\right) - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-225}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-253}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-148}:\\ \;\;\;\;\frac{z \cdot x + a \cdot t}{t + x}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-23}:\\ \;\;\;\;\frac{\left(y + x\right) \cdot z}{t_1} + a\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+132}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	26.4
Cost	1896

\[\begin{array}{l} t_1 := \frac{a \cdot t}{t + x} + z\\ t_2 := a + \frac{z \cdot x}{x + t}\\ t_3 := \left(z + a\right) - b\\ t_4 := z - \frac{y \cdot b}{y + \left(t + x\right)}\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+19}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-107}:\\ \;\;\;\;\left(a + z\right) - \frac{y \cdot b}{t}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-173}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-200}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-214}:\\ \;\;\;\;\frac{a \cdot t}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-231}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-288}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	22.7
Cost	1756

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(t + x\right)\\ t_3 := \frac{a \cdot \left(y + t\right)}{t_2} + z\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-109}:\\ \;\;\;\;\left(a + z\right) - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-225}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-253}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 10^{-148}:\\ \;\;\;\;\frac{z \cdot x + a \cdot t}{t + x}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-24}:\\ \;\;\;\;\frac{\left(y + x\right) \cdot z}{t_2} + a\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+132}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	22.9
Cost	1624

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)} + z\\ \mathbf{if}\;y \leq -1.32 \cdot 10^{+149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-110}:\\ \;\;\;\;\left(a + z\right) - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-226}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-253}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-262}:\\ \;\;\;\;\frac{z \cdot x + a \cdot t}{t + x}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+132}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	25.7
Cost	1500

\[\begin{array}{l} t_1 := a + \frac{z \cdot x}{x + t}\\ t_2 := \left(z + a\right) - b\\ t_3 := \frac{a \cdot t}{t + x} + z\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-110}:\\ \;\;\;\;\left(a + z\right) - \frac{y \cdot b}{t}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-229}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-149}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+148}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	23.4
Cost	1500

\[\begin{array}{l} t_1 := a + \frac{z \cdot x}{x + t}\\ t_2 := \left(z + a\right) - b\\ t_3 := \frac{a \cdot t}{t + x} + z\\ \mathbf{if}\;y \leq -2.35 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-111}:\\ \;\;\;\;\left(a + z\right) - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-226}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-231}:\\ \;\;\;\;z - \frac{y \cdot b}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	22.6
Cost	1364

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{z \cdot x + a \cdot t}{t + x}\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-111}:\\ \;\;\;\;\left(a + z\right) - \frac{y \cdot b}{y + t}\\ \mathbf{elif}\;y \leq -9.4 \cdot 10^{-225}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9.8 \cdot 10^{-256}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-37}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	31.1
Cost	1244

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+236}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-42}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-105}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-299}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a + z\\ \end{array} \]

Alternative 12
Error	30.9
Cost	1112

\[\begin{array}{l} t_1 := \frac{a \cdot t}{x} + z\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -2.05 \cdot 10^{+107}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -5.9 \cdot 10^{-126}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-283}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 13
Error	28.8
Cost	1108

\[\begin{array}{l} t_1 := \frac{a \cdot t}{x} + z\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{+236}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-301}:\\ \;\;\;\;a + \frac{z \cdot x}{x + t}\\ \mathbf{elif}\;x \leq 3.85 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	27.7
Cost	1104

\[\begin{array}{l} t_1 := \frac{a \cdot t}{t + x} + z\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+107}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -9.2 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-162}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a + \frac{z \cdot x}{x + t}\\ \end{array} \]

Alternative 15
Error	30.5
Cost	720

\[\begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+107}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -1.36 \cdot 10^{-121}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;t \leq -3.05 \cdot 10^{-304}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+194}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 16
Error	30.1
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+107}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+193}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 17
Error	36.1
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-42}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+144}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 18
Error	43.2
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023092 
(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)))