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

Average Error: 27.3 → 0.4

Time: 25.6s

Precision: binary64

Cost: 4937

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \left(y + t\right) \cdot a\\ t_4 := \frac{\left(t_3 + z \cdot \left(x + y\right)\right) - y \cdot b}{t_2}\\ \mathbf{if}\;t_4 \leq -\infty \lor \neg \left(t_4 \leq 2 \cdot 10^{+304}\right):\\ \;\;\;\;\left(\left(y + t\right) \cdot \frac{a}{t_1} + \frac{z}{\frac{t_1}{x + y}}\right) - \frac{y}{\frac{t_1}{b}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{t_2} + \frac{y}{t_2}\right) + \frac{t_3 - y \cdot b}{t_2}\\ \end{array} \]

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 t)))
        (t_2 (+ y (+ x t)))
        (t_3 (* (+ y t) a))
        (t_4 (/ (- (+ t_3 (* z (+ x y))) (* y b)) t_2)))
   (if (or (<= t_4 (- INFINITY)) (not (<= t_4 2e+304)))
     (- (+ (* (+ y t) (/ a t_1)) (/ z (/ t_1 (+ x y)))) (/ y (/ t_1 b)))
     (+ (* z (+ (/ x t_2) (/ y t_2))) (/ (- t_3 (* y b)) t_2)))))

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 + t);
	double t_2 = y + (x + t);
	double t_3 = (y + t) * a;
	double t_4 = ((t_3 + (z * (x + y))) - (y * b)) / t_2;
	double tmp;
	if ((t_4 <= -((double) INFINITY)) || !(t_4 <= 2e+304)) {
		tmp = (((y + t) * (a / t_1)) + (z / (t_1 / (x + y)))) - (y / (t_1 / b));
	} else {
		tmp = (z * ((x / t_2) + (y / t_2))) + ((t_3 - (y * b)) / t_2);
	}
	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 + t);
	double t_2 = y + (x + t);
	double t_3 = (y + t) * a;
	double t_4 = ((t_3 + (z * (x + y))) - (y * b)) / t_2;
	double tmp;
	if ((t_4 <= -Double.POSITIVE_INFINITY) || !(t_4 <= 2e+304)) {
		tmp = (((y + t) * (a / t_1)) + (z / (t_1 / (x + y)))) - (y / (t_1 / b));
	} else {
		tmp = (z * ((x / t_2) + (y / t_2))) + ((t_3 - (y * b)) / t_2);
	}
	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 + t)
	t_2 = y + (x + t)
	t_3 = (y + t) * a
	t_4 = ((t_3 + (z * (x + y))) - (y * b)) / t_2
	tmp = 0
	if (t_4 <= -math.inf) or not (t_4 <= 2e+304):
		tmp = (((y + t) * (a / t_1)) + (z / (t_1 / (x + y)))) - (y / (t_1 / b))
	else:
		tmp = (z * ((x / t_2) + (y / t_2))) + ((t_3 - (y * b)) / t_2)
	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(x + Float64(y + t))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(y + t) * a)
	t_4 = Float64(Float64(Float64(t_3 + Float64(z * Float64(x + y))) - Float64(y * b)) / t_2)
	tmp = 0.0
	if ((t_4 <= Float64(-Inf)) || !(t_4 <= 2e+304))
		tmp = Float64(Float64(Float64(Float64(y + t) * Float64(a / t_1)) + Float64(z / Float64(t_1 / Float64(x + y)))) - Float64(y / Float64(t_1 / b)));
	else
		tmp = Float64(Float64(z * Float64(Float64(x / t_2) + Float64(y / t_2))) + Float64(Float64(t_3 - Float64(y * b)) / t_2));
	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 + t);
	t_2 = y + (x + t);
	t_3 = (y + t) * a;
	t_4 = ((t_3 + (z * (x + y))) - (y * b)) / t_2;
	tmp = 0.0;
	if ((t_4 <= -Inf) || ~((t_4 <= 2e+304)))
		tmp = (((y + t) * (a / t_1)) + (z / (t_1 / (x + y)))) - (y / (t_1 / b));
	else
		tmp = (z * ((x / t_2) + (y / t_2))) + ((t_3 - (y * b)) / t_2);
	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[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[(t$95$3 + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$4, (-Infinity)], N[Not[LessEqual[t$95$4, 2e+304]], $MachinePrecision]], N[(N[(N[(N[(y + t), $MachinePrecision] * N[(a / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(N[(x / t$95$2), $MachinePrecision] + N[(y / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$3 - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	27.3
Target	11.5
Herbie	0.4

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

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 1.9999999999999999e304 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 63.8

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

   2. Simplified 63.8

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y + t, a, \mathsf{fma}\left(x, z, y \cdot \left(z - b\right)\right)\right)}{y + \left(x + t\right)}} \]
      Proof
      (/.f64 (fma.f64 (+.f64 y t) a (fma.f64 x z (*.f64 y (-.f64 z b)))) (+.f64 y (+.f64 x t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (Rewrite<= +-commutative_binary64 (+.f64 t y)) a (fma.f64 x z (*.f64 y (-.f64 z b)))) (+.f64 y (+.f64 x t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (+.f64 t y) a (fma.f64 x z (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 y z) (*.f64 y b))))) (+.f64 y (+.f64 x t))): 0 points increase in error, 13 points decrease in error
      (/.f64 (fma.f64 (+.f64 t y) a (fma.f64 x z (Rewrite=> sub-neg_binary64 (+.f64 (*.f64 y z) (neg.f64 (*.f64 y b)))))) (+.f64 y (+.f64 x t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (+.f64 t y) a (Rewrite<= fma-def_binary64 (+.f64 (*.f64 x z) (+.f64 (*.f64 y z) (neg.f64 (*.f64 y b)))))) (+.f64 y (+.f64 x t))): 13 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (+.f64 t y) a (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (*.f64 x z) (*.f64 y z)) (neg.f64 (*.f64 y b))))) (+.f64 y (+.f64 x t))): 13 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (+.f64 t y) a (+.f64 (Rewrite<= distribute-rgt-in_binary64 (*.f64 z (+.f64 x y))) (neg.f64 (*.f64 y b)))) (+.f64 y (+.f64 x t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 (+.f64 t y) a (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 x y) z)) (neg.f64 (*.f64 y b)))) (+.f64 y (+.f64 x t))): 0 points increase in error, 13 points decrease in error
      (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 t y) a) (+.f64 (*.f64 (+.f64 x y) z) (neg.f64 (*.f64 y b))))) (+.f64 y (+.f64 x t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (*.f64 (+.f64 t y) a) (*.f64 (+.f64 x y) z)) (neg.f64 (*.f64 y b)))) (+.f64 y (+.f64 x t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a))) (neg.f64 (*.f64 y b))) (+.f64 y (+.f64 x t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b))) (+.f64 y (+.f64 x t))): 13 points increase in error, 0 points decrease in error
      (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 x t) y))): 0 points increase in error, 13 points decrease in error

   3. Taylor expanded in z around inf 63.8

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

   4. Simplified 0.2

      \[\leadsto \color{blue}{\left(\frac{a}{x + \left(t + y\right)} \cdot \left(t + y\right) + \frac{z}{\frac{x + \left(t + y\right)}{x + y}}\right) - \frac{y}{\frac{x + \left(t + y\right)}{b}}} \]
      Proof
      (-.f64 (+.f64 (*.f64 (/.f64 a (+.f64 x (+.f64 t y))) (+.f64 t y)) (/.f64 z (/.f64 (+.f64 x (+.f64 t y)) (+.f64 x y)))) (/.f64 y (/.f64 (+.f64 x (+.f64 t y)) b))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (*.f64 (/.f64 a (+.f64 x (Rewrite<= +-commutative_binary64 (+.f64 y t)))) (+.f64 t y)) (/.f64 z (/.f64 (+.f64 x (+.f64 t y)) (+.f64 x y)))) (/.f64 y (/.f64 (+.f64 x (+.f64 t y)) b))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (*.f64 (/.f64 a (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 y t) x))) (+.f64 t y)) (/.f64 z (/.f64 (+.f64 x (+.f64 t y)) (+.f64 x y)))) (/.f64 y (/.f64 (+.f64 x (+.f64 t y)) b))): 6 points increase in error, 15 points decrease in error
      (-.f64 (+.f64 (*.f64 (/.f64 a (Rewrite<= associate-+r+_binary64 (+.f64 y (+.f64 t x)))) (+.f64 t y)) (/.f64 z (/.f64 (+.f64 x (+.f64 t y)) (+.f64 x y)))) (/.f64 y (/.f64 (+.f64 x (+.f64 t y)) b))): 17 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (*.f64 (/.f64 a (+.f64 y (+.f64 t x))) (Rewrite<= +-commutative_binary64 (+.f64 y t))) (/.f64 z (/.f64 (+.f64 x (+.f64 t y)) (+.f64 x y)))) (/.f64 y (/.f64 (+.f64 x (+.f64 t y)) b))): 4 points increase in error, 17 points decrease in error
      (-.f64 (+.f64 (Rewrite<= associate-/r/_binary64 (/.f64 a (/.f64 (+.f64 y (+.f64 t x)) (+.f64 y t)))) (/.f64 z (/.f64 (+.f64 x (+.f64 t y)) (+.f64 x y)))) (/.f64 y (/.f64 (+.f64 x (+.f64 t y)) b))): 4 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x)))) (/.f64 z (/.f64 (+.f64 x (+.f64 t y)) (+.f64 x y)))) (/.f64 y (/.f64 (+.f64 x (+.f64 t y)) b))): 11 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x))) (/.f64 z (/.f64 (+.f64 x (Rewrite<= +-commutative_binary64 (+.f64 y t))) (+.f64 x y)))) (/.f64 y (/.f64 (+.f64 x (+.f64 t y)) b))): 0 points increase in error, 15 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x))) (/.f64 z (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 y t) x)) (+.f64 x y)))) (/.f64 y (/.f64 (+.f64 x (+.f64 t y)) b))): 11 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x))) (/.f64 z (/.f64 (Rewrite<= associate-+r+_binary64 (+.f64 y (+.f64 t x))) (+.f64 x y)))) (/.f64 y (/.f64 (+.f64 x (+.f64 t y)) b))): 0 points increase in error, 11 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x))) (/.f64 z (/.f64 (+.f64 y (+.f64 t x)) (Rewrite<= +-commutative_binary64 (+.f64 y x))))) (/.f64 y (/.f64 (+.f64 x (+.f64 t y)) b))): 5 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x))) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 z (+.f64 y x)) (+.f64 y (+.f64 t x))))) (/.f64 y (/.f64 (+.f64 x (+.f64 t y)) b))): 10 points increase in error, 5 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x))) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 y x) z)) (+.f64 y (+.f64 t x)))) (/.f64 y (/.f64 (+.f64 x (+.f64 t y)) b))): 0 points increase in error, 10 points decrease in error
      (-.f64 (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 (+.f64 y x) z) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x))))) (/.f64 y (/.f64 (+.f64 x (+.f64 t y)) b))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (+.f64 y x) z) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x)))) (/.f64 y (/.f64 (+.f64 x (Rewrite<= +-commutative_binary64 (+.f64 y t))) b))): 0 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (+.f64 y x) z) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x)))) (/.f64 y (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 y t) x)) b))): 21 points increase in error, 0 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (+.f64 y x) z) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x)))) (/.f64 y (/.f64 (Rewrite<= associate-+r+_binary64 (+.f64 y (+.f64 t x))) b))): 11 points increase in error, 6 points decrease in error
      (-.f64 (+.f64 (/.f64 (*.f64 (+.f64 y x) z) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x)))) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y b) (+.f64 y (+.f64 t x))))): 0 points increase in error, 15 points decrease in error
      (Rewrite<= unsub-neg_binary64 (+.f64 (+.f64 (/.f64 (*.f64 (+.f64 y x) z) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x)))) (neg.f64 (/.f64 (*.f64 y b) (+.f64 y (+.f64 t x)))))): 15 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (/.f64 (*.f64 (+.f64 y x) z) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x)))) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (*.f64 y b) (+.f64 y (+.f64 t x)))))): 0 points increase in error, 11 points decrease in error
      (Rewrite<= associate-+r+_binary64 (+.f64 (/.f64 (*.f64 (+.f64 y x) z) (+.f64 y (+.f64 t x))) (+.f64 (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x))) (*.f64 -1 (/.f64 (*.f64 y b) (+.f64 y (+.f64 t x))))))): 17 points increase in error, 4 points decrease in error

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.9999999999999999e304

   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. Taylor expanded in z around 0 0.5

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

   3. Simplified 0.5

      \[\leadsto \color{blue}{z \cdot \left(\frac{x}{y + \left(t + x\right)} + \frac{y}{y + \left(t + x\right)}\right) + \frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(t + x\right)}} \]
      Proof
      (+.f64 (*.f64 z (+.f64 (/.f64 x (+.f64 y (+.f64 t x))) (/.f64 y (+.f64 y (+.f64 t x))))) (/.f64 (-.f64 (*.f64 a (+.f64 y t)) (*.f64 y b)) (+.f64 y (+.f64 t x)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 (/.f64 x (+.f64 y (+.f64 t x))) (/.f64 y (+.f64 y (+.f64 t x)))) z)) (/.f64 (-.f64 (*.f64 a (+.f64 y t)) (*.f64 y b)) (+.f64 y (+.f64 t x)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (+.f64 (/.f64 x (+.f64 y (+.f64 t x))) (/.f64 y (+.f64 y (+.f64 t x)))) z) (/.f64 (-.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 y t) a)) (*.f64 y b)) (+.f64 y (+.f64 t x)))): 0 points increase in error, 12 points decrease in error
      (+.f64 (*.f64 (+.f64 (/.f64 x (+.f64 y (+.f64 t x))) (/.f64 y (+.f64 y (+.f64 t x)))) z) (/.f64 (-.f64 (*.f64 (+.f64 y t) a) (*.f64 y b)) (Rewrite=> associate-+r+_binary64 (+.f64 (+.f64 y t) x)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (+.f64 (/.f64 x (+.f64 y (+.f64 t x))) (/.f64 y (+.f64 y (+.f64 t x)))) z) (/.f64 (-.f64 (*.f64 (+.f64 y t) a) (*.f64 y b)) (Rewrite<= +-commutative_binary64 (+.f64 x (+.f64 y t))))): 12 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (+.f64 (/.f64 x (+.f64 y (+.f64 t x))) (/.f64 y (+.f64 y (+.f64 t x)))) z) (Rewrite=> div-sub_binary64 (-.f64 (/.f64 (*.f64 (+.f64 y t) a) (+.f64 x (+.f64 y t))) (/.f64 (*.f64 y b) (+.f64 x (+.f64 y t)))))): 12 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (+.f64 (/.f64 x (+.f64 y (+.f64 t x))) (/.f64 y (+.f64 y (+.f64 t x)))) z) (-.f64 (/.f64 (Rewrite=> *-commutative_binary64 (*.f64 a (+.f64 y t))) (+.f64 x (+.f64 y t))) (/.f64 (*.f64 y b) (+.f64 x (+.f64 y t))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (+.f64 (/.f64 x (+.f64 y (+.f64 t x))) (/.f64 y (+.f64 y (+.f64 t x)))) z) (-.f64 (/.f64 (*.f64 a (+.f64 y t)) (Rewrite=> +-commutative_binary64 (+.f64 (+.f64 y t) x))) (/.f64 (*.f64 y b) (+.f64 x (+.f64 y t))))): 0 points increase in error, 12 points decrease in error
      (+.f64 (*.f64 (+.f64 (/.f64 x (+.f64 y (+.f64 t x))) (/.f64 y (+.f64 y (+.f64 t x)))) z) (-.f64 (/.f64 (*.f64 a (+.f64 y t)) (Rewrite<= associate-+r+_binary64 (+.f64 y (+.f64 t x)))) (/.f64 (*.f64 y b) (+.f64 x (+.f64 y t))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (+.f64 (/.f64 x (+.f64 y (+.f64 t x))) (/.f64 y (+.f64 y (+.f64 t x)))) z) (-.f64 (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 y b) (Rewrite=> +-commutative_binary64 (+.f64 (+.f64 y t) x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (+.f64 (/.f64 x (+.f64 y (+.f64 t x))) (/.f64 y (+.f64 y (+.f64 t x)))) z) (-.f64 (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x))) (/.f64 (*.f64 y b) (Rewrite<= associate-+r+_binary64 (+.f64 y (+.f64 t x)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (*.f64 (+.f64 (/.f64 x (+.f64 y (+.f64 t x))) (/.f64 y (+.f64 y (+.f64 t x)))) z) (/.f64 (*.f64 a (+.f64 y t)) (+.f64 y (+.f64 t x)))) (/.f64 (*.f64 y b) (+.f64 y (+.f64 t x))))): 0 points increase in error, 0 points decrease in error
3. Recombined 2 regimes into one program.

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 2 \cdot 10^{+304}\right):\\ \;\;\;\;\left(\left(y + t\right) \cdot \frac{a}{x + \left(y + t\right)} + \frac{z}{\frac{x + \left(y + t\right)}{x + y}}\right) - \frac{y}{\frac{x + \left(y + t\right)}{b}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{y + \left(x + t\right)} + \frac{y}{y + \left(x + t\right)}\right) + \frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.4
Cost	4937

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \left(y + t\right) \cdot a\\ t_4 := \frac{\left(t_3 + z \cdot \left(x + y\right)\right) - y \cdot b}{t_2}\\ \mathbf{if}\;t_4 \leq -\infty \lor \neg \left(t_4 \leq 2 \cdot 10^{+304}\right):\\ \;\;\;\;y \cdot \frac{z - b}{t_1} + \left(\left(y + t\right) \cdot \frac{a}{t_1} + x \cdot \frac{z}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{x}{t_2} + \frac{y}{t_2}\right) + \frac{t_3 - y \cdot b}{t_2}\\ \end{array} \]

Alternative 2
Error	3.1
Cost	4936

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(y + t\right) \cdot a\\ t_3 := \frac{\left(t_2 + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ t_4 := x + \left(y + t\right)\\ t_5 := \frac{y}{\frac{t_4}{b}}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\left(a + \frac{z}{\frac{t_4}{x + y}}\right) - t_5\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;z \cdot \left(\frac{x}{t_1} + \frac{y}{t_1}\right) + \frac{t_2 - y \cdot b}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) \cdot \frac{a}{t_4} + \frac{z}{1 + \frac{t}{x}}\right) - t_5\\ \end{array} \]

Alternative 3
Error	0.4
Cost	4936

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(y + t\right) \cdot a\\ t_3 := \frac{\left(t_2 + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ t_4 := x + \left(y + t\right)\\ t_5 := \left(y + t\right) \cdot \frac{a}{t_4}\\ t_6 := \frac{z}{t_4}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;y \cdot \frac{z - b}{t_4} + \left(t_5 + x \cdot t_6\right)\\ \mathbf{elif}\;t_3 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;z \cdot \left(\frac{x}{t_1} + \frac{y}{t_1}\right) + \frac{t_2 - y \cdot b}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\left(t_5 + t_6 \cdot \left(x + y\right)\right) - \frac{y}{\frac{t_4}{b}}\\ \end{array} \]

Alternative 4
Error	3.0
Cost	4680

\[\begin{array}{l} t_1 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := x + \left(y + t\right)\\ t_3 := \frac{y}{\frac{t_2}{b}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(a + \frac{z}{\frac{t_2}{x + y}}\right) - t_3\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) \cdot \frac{a}{t_2} + \frac{z}{1 + \frac{t}{x}}\right) - t_3\\ \end{array} \]

Alternative 5
Error	2.6
Cost	4297

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 2 \cdot 10^{+304}\right):\\ \;\;\;\;\left(a + \frac{z}{\frac{t_1}{x + y}}\right) - \frac{y}{\frac{t_1}{b}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	2.6
Cost	4296

\[\begin{array}{l} t_1 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := x + \left(y + t\right)\\ t_3 := \frac{y}{\frac{t_2}{b}}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;\left(a + \frac{z}{\frac{t_2}{x + y}}\right) - t_3\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z + \left(y + t\right) \cdot \frac{a}{t_2}\right) - t_3\\ \end{array} \]

Alternative 7
Error	5.9
Cost	4169

\[\begin{array}{l} t_1 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+283}\right):\\ \;\;\;\;\left(a + \frac{z}{\frac{x + \left(y + t\right)}{x + y}}\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	26.4
Cost	2288

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := z \cdot \frac{x + y}{t_2}\\ t_4 := z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{+230}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{+105}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{+92}:\\ \;\;\;\;\frac{-b}{\frac{t_2}{y}}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9 \cdot 10^{-121}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-171}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-105}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 35000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+106}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 9
Error	26.4
Cost	2288

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := z \cdot \frac{x + y}{t_2}\\ t_4 := z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+231}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{+104}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -8.4 \cdot 10^{+92}:\\ \;\;\;\;\frac{-b}{\frac{t_2}{y}}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-120}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-174}:\\ \;\;\;\;\frac{a}{\frac{t_2}{y + t}}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-106}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1300:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+106}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+185}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 10
Error	26.3
Cost	2288

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ t_3 := z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{+230}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1 \cdot 10^{+105}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \mathbf{elif}\;x \leq -8.4 \cdot 10^{+92}:\\ \;\;\;\;\frac{-b}{\frac{t_1}{y}}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-118}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-253}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-174}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-105}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 14200:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+106}:\\ \;\;\;\;z \cdot \frac{x + y}{t_1}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+185}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 11
Error	22.0
Cost	1876

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \frac{x \cdot z + t \cdot a}{x + t}\\ t_3 := \left(a + \frac{z}{\frac{t_1}{x + y}}\right) - b\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{-58}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-191}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-158}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+61}:\\ \;\;\;\;\left(a + \frac{x + y}{\frac{t}{z}}\right) - \frac{y}{\frac{t_1}{b}}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Error	28.0
Cost	1769

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z \cdot \frac{x}{x + t}\\ \mathbf{if}\;x \leq -5 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-118}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-174}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-106}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 37000 \lor \neg \left(x \leq 2 \cdot 10^{+105}\right) \land x \leq 1.45 \cdot 10^{+187}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	27.1
Cost	1760

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{a}{\frac{x + t}{t}}\\ t_3 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ t_4 := z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{if}\;y \leq -9.6 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-79}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.22 \cdot 10^{-175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-214}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-66}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{+41}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	28.6
Cost	1628

\[\begin{array}{l} t_1 := \frac{a}{\frac{x + t}{t}}\\ t_2 := \left(z + a\right) - b\\ t_3 := z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{if}\;y \leq -3.05 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.06 \cdot 10^{-215}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-157}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-67}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 10^{+38}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	21.3
Cost	1488

\[\begin{array}{l} t_1 := \frac{x \cdot z + t \cdot a}{x + t}\\ t_2 := \left(a + \frac{z}{\frac{x + \left(y + t\right)}{x + y}}\right) - b\\ \mathbf{if}\;y \leq -5.7 \cdot 10^{-61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.6 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-191}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-123}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	20.8
Cost	1488

\[\begin{array}{l} t_1 := \left(a + \frac{z}{\frac{x + \left(y + t\right)}{x + y}}\right) - b\\ t_2 := z + y \cdot \left(\frac{a}{x} - \frac{b}{x}\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+222}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 0.004:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+108}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+184}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Error	27.6
Cost	1376

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+163}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-118}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-172}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.4 \cdot 10^{-106}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+185}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 18
Error	35.6
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+58}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 8600000000:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 19
Error	43.5
Cost	64

\[a \]

Reproduce

herbie shell --seed 2022340 
(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)))