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

Average Error: 26.7 → 0.7

Time: 35.0s

Precision: binary64

Cost: 11592

Math

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

↓

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ t_3 := x + \left(y + t\right)\\ t_4 := y \cdot \frac{z - b}{t_3} + \mathsf{fma}\left(a, \frac{y}{t_3} + \frac{t}{t_3}, z \cdot \frac{x}{t_3}\right)\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+221}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_2 \leq 10^{+300}:\\ \;\;\;\;\frac{x \cdot z + \left(y \cdot \left(\left(z + a\right) - b\right) + t \cdot a\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

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 (/ (- (+ (* (+ y t) a) (* z (+ x y))) (* y b)) t_1))
        (t_3 (+ x (+ y t)))
        (t_4
         (+
          (* y (/ (- z b) t_3))
          (fma a (+ (/ y t_3) (/ t t_3)) (* z (/ x t_3))))))
   (if (<= t_2 -2e+221)
     t_4
     (if (<= t_2 1e+300)
       (/ (+ (* x z) (+ (* y (- (+ z a) b)) (* t a))) t_1)
       t_4))))

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 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_1;
	double t_3 = x + (y + t);
	double t_4 = (y * ((z - b) / t_3)) + fma(a, ((y / t_3) + (t / t_3)), (z * (x / t_3)));
	double tmp;
	if (t_2 <= -2e+221) {
		tmp = t_4;
	} else if (t_2 <= 1e+300) {
		tmp = ((x * z) + ((y * ((z + a) - b)) + (t * a))) / t_1;
	} else {
		tmp = t_4;
	}
	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(Float64(y + t) * a) + Float64(z * Float64(x + y))) - Float64(y * b)) / t_1)
	t_3 = Float64(x + Float64(y + t))
	t_4 = Float64(Float64(y * Float64(Float64(z - b) / t_3)) + fma(a, Float64(Float64(y / t_3) + Float64(t / t_3)), Float64(z * Float64(x / t_3))))
	tmp = 0.0
	if (t_2 <= -2e+221)
		tmp = t_4;
	elseif (t_2 <= 1e+300)
		tmp = Float64(Float64(Float64(x * z) + Float64(Float64(y * Float64(Float64(z + a) - b)) + Float64(t * a))) / t_1);
	else
		tmp = t_4;
	end
	return 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[(N[(y + t), $MachinePrecision] * a), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y * N[(N[(z - b), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(a * N[(N[(y / t$95$3), $MachinePrecision] + N[(t / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -2e+221], t$95$4, If[LessEqual[t$95$2, 1e+300], N[(N[(N[(x * z), $MachinePrecision] + N[(N[(y * N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$4]]]]]]

Target

Original	26.7
Target	11.6
Herbie	0.7

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

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)) < -2.0000000000000001e221 or 1.0000000000000001e300 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 60.5

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

   2. Simplified 60.5

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, z - b, \mathsf{fma}\left(y + t, a, x \cdot z\right)\right)}{x + \left(y + t\right)}} \]
      Proof
      (/.f64 (fma.f64 y (-.f64 z b) (fma.f64 (+.f64 y t) a (*.f64 x z))) (+.f64 x (+.f64 y t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 y (-.f64 z b) (fma.f64 (Rewrite<= +-commutative_binary64 (+.f64 t y)) a (*.f64 x z))) (+.f64 x (+.f64 y t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 y (-.f64 z b) (fma.f64 (+.f64 t y) a (Rewrite<= *-commutative_binary64 (*.f64 z x)))) (+.f64 x (+.f64 y t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 y (-.f64 z b) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (+.f64 t y) a) (*.f64 z x)))) (+.f64 x (+.f64 y t))): 1 points increase in error, 0 points decrease in error
      (/.f64 (fma.f64 y (-.f64 z b) (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 z x) (*.f64 (+.f64 t y) a)))) (+.f64 x (+.f64 y t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 y (-.f64 z b)) (+.f64 (*.f64 z x) (*.f64 (+.f64 t y) a)))) (+.f64 x (+.f64 y t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (Rewrite<= distribute-lft-out--_binary64 (-.f64 (*.f64 y z) (*.f64 y b))) (+.f64 (*.f64 z x) (*.f64 (+.f64 t y) a))) (+.f64 x (+.f64 y t))): 0 points increase in error, 1 points decrease in error
      (/.f64 (+.f64 (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 y z) (neg.f64 (*.f64 y b)))) (+.f64 (*.f64 z x) (*.f64 (+.f64 t y) a))) (+.f64 x (+.f64 y t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (Rewrite=> +-commutative_binary64 (+.f64 (neg.f64 (*.f64 y b)) (*.f64 y z))) (+.f64 (*.f64 z x) (*.f64 (+.f64 t y) a))) (+.f64 x (+.f64 y t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= associate-+r+_binary64 (+.f64 (neg.f64 (*.f64 y b)) (+.f64 (*.f64 y z) (+.f64 (*.f64 z x) (*.f64 (+.f64 t y) a))))) (+.f64 x (+.f64 y t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (neg.f64 (*.f64 y b)) (+.f64 (*.f64 y z) (+.f64 (Rewrite=> *-commutative_binary64 (*.f64 x z)) (*.f64 (+.f64 t y) a)))) (+.f64 x (+.f64 y t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (neg.f64 (*.f64 y b)) (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (*.f64 y z) (*.f64 x z)) (*.f64 (+.f64 t y) a)))) (+.f64 x (+.f64 y t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (neg.f64 (*.f64 y b)) (+.f64 (Rewrite<= distribute-rgt-in_binary64 (*.f64 z (+.f64 y x))) (*.f64 (+.f64 t y) a))) (+.f64 x (+.f64 y t))): 1 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (neg.f64 (*.f64 y b)) (+.f64 (*.f64 z (Rewrite<= +-commutative_binary64 (+.f64 x y))) (*.f64 (+.f64 t y) a))) (+.f64 x (+.f64 y t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (+.f64 (neg.f64 (*.f64 y b)) (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (+.f64 x y) z)) (*.f64 (+.f64 t y) a))) (+.f64 x (+.f64 y t))): 0 points increase in error, 0 points decrease in error
      (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (neg.f64 (*.f64 y b)))) (+.f64 x (+.f64 y 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 x (+.f64 y t))): 0 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)) (+.f64 x (Rewrite<= +-commutative_binary64 (+.f64 t y)))): 0 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<= associate-+l+_binary64 (+.f64 (+.f64 x t) y))): 0 points increase in error, 1 points decrease in error

   3. Taylor expanded in a around 0 41.6

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

   4. Simplified 1.2

      \[\leadsto \color{blue}{\frac{z - b}{x + \left(t + y\right)} \cdot y + \mathsf{fma}\left(a, \frac{y}{x + \left(t + y\right)} + \frac{t}{x + \left(t + y\right)}, \frac{x}{x + \left(t + y\right)} \cdot z\right)} \]
      Proof
      (+.f64 (*.f64 (/.f64 (-.f64 z b) (+.f64 x (+.f64 t y))) y) (fma.f64 a (+.f64 (/.f64 y (+.f64 x (+.f64 t y))) (/.f64 t (+.f64 x (+.f64 t y)))) (*.f64 (/.f64 x (+.f64 x (+.f64 t y))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (/.f64 (-.f64 z b) (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 x t) y))) y) (fma.f64 a (+.f64 (/.f64 y (+.f64 x (+.f64 t y))) (/.f64 t (+.f64 x (+.f64 t y)))) (*.f64 (/.f64 x (+.f64 x (+.f64 t y))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (/.f64 (-.f64 z b) (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 t x)) y)) y) (fma.f64 a (+.f64 (/.f64 y (+.f64 x (+.f64 t y))) (/.f64 t (+.f64 x (+.f64 t y)))) (*.f64 (/.f64 x (+.f64 x (+.f64 t y))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (/.f64 (-.f64 z b) (Rewrite<= +-commutative_binary64 (+.f64 y (+.f64 t x)))) y) (fma.f64 a (+.f64 (/.f64 y (+.f64 x (+.f64 t y))) (/.f64 t (+.f64 x (+.f64 t y)))) (*.f64 (/.f64 x (+.f64 x (+.f64 t y))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-/r/_binary64 (/.f64 (-.f64 z b) (/.f64 (+.f64 y (+.f64 t x)) y))) (fma.f64 a (+.f64 (/.f64 y (+.f64 x (+.f64 t y))) (/.f64 t (+.f64 x (+.f64 t y)))) (*.f64 (/.f64 x (+.f64 x (+.f64 t y))) z))): 11 points increase in error, 19 points decrease in error
      (+.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (-.f64 z b) y) (+.f64 y (+.f64 t x)))) (fma.f64 a (+.f64 (/.f64 y (+.f64 x (+.f64 t y))) (/.f64 t (+.f64 x (+.f64 t y)))) (*.f64 (/.f64 x (+.f64 x (+.f64 t y))) z))): 48 points increase in error, 13 points decrease in error
      (+.f64 (/.f64 (*.f64 (-.f64 z b) y) (+.f64 y (+.f64 t x))) (fma.f64 a (+.f64 (/.f64 y (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 x t) y))) (/.f64 t (+.f64 x (+.f64 t y)))) (*.f64 (/.f64 x (+.f64 x (+.f64 t y))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 (-.f64 z b) y) (+.f64 y (+.f64 t x))) (fma.f64 a (+.f64 (/.f64 y (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 t x)) y)) (/.f64 t (+.f64 x (+.f64 t y)))) (*.f64 (/.f64 x (+.f64 x (+.f64 t y))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 (-.f64 z b) y) (+.f64 y (+.f64 t x))) (fma.f64 a (+.f64 (/.f64 y (Rewrite<= +-commutative_binary64 (+.f64 y (+.f64 t x)))) (/.f64 t (+.f64 x (+.f64 t y)))) (*.f64 (/.f64 x (+.f64 x (+.f64 t y))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 (-.f64 z b) y) (+.f64 y (+.f64 t x))) (fma.f64 a (+.f64 (/.f64 y (+.f64 y (+.f64 t x))) (/.f64 t (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 x t) y)))) (*.f64 (/.f64 x (+.f64 x (+.f64 t y))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 (-.f64 z b) y) (+.f64 y (+.f64 t x))) (fma.f64 a (+.f64 (/.f64 y (+.f64 y (+.f64 t x))) (/.f64 t (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 t x)) y))) (*.f64 (/.f64 x (+.f64 x (+.f64 t y))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 (-.f64 z b) y) (+.f64 y (+.f64 t x))) (fma.f64 a (+.f64 (/.f64 y (+.f64 y (+.f64 t x))) (/.f64 t (Rewrite<= +-commutative_binary64 (+.f64 y (+.f64 t x))))) (*.f64 (/.f64 x (+.f64 x (+.f64 t y))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 (-.f64 z b) y) (+.f64 y (+.f64 t x))) (fma.f64 a (+.f64 (/.f64 y (+.f64 y (+.f64 t x))) (/.f64 t (+.f64 y (+.f64 t x)))) (*.f64 (/.f64 x (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 x t) y))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 (-.f64 z b) y) (+.f64 y (+.f64 t x))) (fma.f64 a (+.f64 (/.f64 y (+.f64 y (+.f64 t x))) (/.f64 t (+.f64 y (+.f64 t x)))) (*.f64 (/.f64 x (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 t x)) y)) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 (-.f64 z b) y) (+.f64 y (+.f64 t x))) (fma.f64 a (+.f64 (/.f64 y (+.f64 y (+.f64 t x))) (/.f64 t (+.f64 y (+.f64 t x)))) (*.f64 (/.f64 x (Rewrite<= +-commutative_binary64 (+.f64 y (+.f64 t x)))) z))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 (-.f64 z b) y) (+.f64 y (+.f64 t x))) (fma.f64 a (+.f64 (/.f64 y (+.f64 y (+.f64 t x))) (/.f64 t (+.f64 y (+.f64 t x)))) (Rewrite<= associate-/r/_binary64 (/.f64 x (/.f64 (+.f64 y (+.f64 t x)) z))))): 23 points increase in error, 4 points decrease in error
      (+.f64 (/.f64 (*.f64 (-.f64 z b) y) (+.f64 y (+.f64 t x))) (fma.f64 a (+.f64 (/.f64 y (+.f64 y (+.f64 t x))) (/.f64 t (+.f64 y (+.f64 t x)))) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 x z) (+.f64 y (+.f64 t x)))))): 26 points increase in error, 17 points decrease in error
      (+.f64 (/.f64 (*.f64 (-.f64 z b) y) (+.f64 y (+.f64 t x))) (fma.f64 a (+.f64 (/.f64 y (+.f64 y (+.f64 t x))) (/.f64 t (+.f64 y (+.f64 t x)))) (/.f64 (Rewrite<= *-commutative_binary64 (*.f64 z x)) (+.f64 y (+.f64 t x))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 (-.f64 z b) y) (+.f64 y (+.f64 t x))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 a (+.f64 (/.f64 y (+.f64 y (+.f64 t x))) (/.f64 t (+.f64 y (+.f64 t x))))) (/.f64 (*.f64 z x) (+.f64 y (+.f64 t x)))))): 1 points increase in error, 0 points decrease in error
      (+.f64 (/.f64 (*.f64 (-.f64 z b) y) (+.f64 y (+.f64 t x))) (Rewrite<= +-commutative_binary64 (+.f64 (/.f64 (*.f64 z x) (+.f64 y (+.f64 t x))) (*.f64 a (+.f64 (/.f64 y (+.f64 y (+.f64 t x))) (/.f64 t (+.f64 y (+.f64 t x)))))))): 0 points increase in error, 0 points decrease in error

   if -2.0000000000000001e221 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.0000000000000001e300

   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 y around 0 0.3

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

4. Final simplification 0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -2 \cdot 10^{+221}:\\ \;\;\;\;y \cdot \frac{z - b}{x + \left(y + t\right)} + \mathsf{fma}\left(a, \frac{y}{x + \left(y + t\right)} + \frac{t}{x + \left(y + t\right)}, z \cdot \frac{x}{x + \left(y + t\right)}\right)\\ \mathbf{elif}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+300}:\\ \;\;\;\;\frac{x \cdot z + \left(y \cdot \left(\left(z + a\right) - b\right) + t \cdot a\right)}{y + \left(x + t\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - b}{x + \left(y + t\right)} + \mathsf{fma}\left(a, \frac{y}{x + \left(y + t\right)} + \frac{t}{x + \left(y + t\right)}, z \cdot \frac{x}{x + \left(y + t\right)}\right)\\ \end{array} \]

Alternatives

Alternative 1
Error	0.8
Cost	5064

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ t_3 := x + \left(y + t\right)\\ t_4 := y \cdot \frac{z - b}{t_3} + \left(\frac{z}{\frac{t_3}{x}} + a \cdot \left(\left(y + t\right) \cdot \frac{1}{t_3}\right)\right)\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+221}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_2 \leq 10^{+300}:\\ \;\;\;\;\frac{x \cdot z + \left(y \cdot \left(\left(z + a\right) - b\right) + t \cdot a\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 2
Error	3.2
Cost	4296

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ t_3 := x + \left(y + t\right)\\ t_4 := y \cdot \frac{z - b}{t_3} + \left(a + \frac{z}{\frac{t_3}{x}}\right)\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+221}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_2 \leq 10^{+300}:\\ \;\;\;\;\frac{x \cdot z + \left(y \cdot \left(\left(z + a\right) - b\right) + t \cdot a\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 3
Error	5.0
Cost	4168

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ t_3 := \frac{a - b}{\frac{x + y}{y}} + z \cdot \frac{x + y}{t_1}\\ \mathbf{if}\;t_2 \leq -2 \cdot 10^{+221}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_2 \leq 10^{+300}:\\ \;\;\;\;\frac{x \cdot z + \left(y \cdot \left(\left(z + a\right) - b\right) + t \cdot a\right)}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	31.8
Cost	3212

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z - b \cdot \frac{y}{x + y}\\ t_3 := \frac{x \cdot z + t \cdot a}{x + t}\\ t_4 := \left(z + a\right) - b\\ t_5 := \frac{-b}{\frac{t_1}{y}}\\ t_6 := a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ t_7 := \frac{z}{1 + \frac{t}{x + y}}\\ \mathbf{if}\;b \leq -5.79768039421059 \cdot 10^{+226}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -6.54744531912433 \cdot 10^{+182}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.7342145714676013 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.2998431563162997 \cdot 10^{-17}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -1.5232693266706994 \cdot 10^{-72}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq -6.676695321090535 \cdot 10^{-131}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -1.1018760514830507 \cdot 10^{-209}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.574858372593765 \cdot 10^{-148}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 1.3016438032518286 \cdot 10^{-107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 4.324503829914301 \cdot 10^{-87}:\\ \;\;\;\;z \cdot \frac{x + y}{t_1}\\ \mathbf{elif}\;b \leq 180009000526735.16:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{x + \left(y + t\right)}\\ \mathbf{elif}\;b \leq 1.3808485796614224 \cdot 10^{+51}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;b \leq 3.2079559856756205 \cdot 10^{+74}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 2.0200952040690287 \cdot 10^{+83}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;b \leq 1.0919259669324131 \cdot 10^{+89}:\\ \;\;\;\;a\\ \mathbf{elif}\;b \leq 8.455845083362147 \cdot 10^{+164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4.445830101733168 \cdot 10^{+201}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq 1.077745133402337 \cdot 10^{+239}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 1.9181869922250517 \cdot 10^{+290}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{t}\\ \end{array} \]

Alternative 5
Error	32.2
Cost	2948

\[\begin{array}{l} t_1 := z - b \cdot \frac{y}{x + y}\\ t_2 := \frac{x \cdot z + t \cdot a}{x + t}\\ t_3 := \left(z + a\right) - b\\ t_4 := \frac{-b}{\frac{y + \left(x + t\right)}{y}}\\ t_5 := a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{if}\;b \leq -5.79768039421059 \cdot 10^{+226}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -6.54744531912433 \cdot 10^{+182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.7342145714676013 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.2998431563162997 \cdot 10^{-17}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.5232693266706994 \cdot 10^{-72}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -6.676695321090535 \cdot 10^{-131}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.1018760514830507 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.574858372593765 \cdot 10^{-148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.3016438032518286 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.0571211638655815 \cdot 10^{-32}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 8.737833383815729 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 180009000526735.16:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{x + \left(y + t\right)}\\ \mathbf{elif}\;b \leq 3.817011986734303 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.4368949560484975 \cdot 10^{+107}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 4.445830101733168 \cdot 10^{+201}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.077745133402337 \cdot 10^{+239}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 1.9181869922250517 \cdot 10^{+290}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{t}\\ \end{array} \]

Alternative 6
Error	29.4
Cost	2160

\[\begin{array}{l} t_1 := a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -1.3503332533136637 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.351973558662906 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -8.279686620006479 \cdot 10^{-43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.1920578355095308 \cdot 10^{-68}:\\ \;\;\;\;\frac{-y}{\frac{y + t}{b}}\\ \mathbf{elif}\;x \leq -5.714642107311008 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.7975752692986263 \cdot 10^{-162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.655962863078994 \cdot 10^{-178}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.161150318573349 \cdot 10^{-246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.4320097710680017 \cdot 10^{-295}:\\ \;\;\;\;a + \frac{y \cdot \left(z - b\right)}{t}\\ \mathbf{elif}\;x \leq 1.64763499392081 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.3746474462130088 \cdot 10^{+171}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x}}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+208}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z - b \cdot \frac{y}{x + y}\\ \end{array} \]

Alternative 7
Error	17.5
Cost	2008

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := y \cdot \frac{z - b}{t_1}\\ t_3 := t_2 + \left(a + \frac{x \cdot z}{t}\right)\\ t_4 := z + \frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t \leq -2.8248162899849157 \cdot 10^{+20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.8719340435796674 \cdot 10^{-243}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 8.164149345492814 \cdot 10^{-147}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 3.4508497714494788 \cdot 10^{-6}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 1.5347307192204898 \cdot 10^{+166}:\\ \;\;\;\;a + t_2\\ \mathbf{elif}\;t \leq 2.933572946653842 \cdot 10^{+271}:\\ \;\;\;\;\left(a + \frac{z}{\frac{t_1}{x}}\right) + \frac{y \cdot \left(z - b\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 8
Error	29.7
Cost	1764

\[\begin{array}{l} t_1 := a + \frac{y \cdot \left(z - b\right)}{t}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -1.3077160070993047 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.718896625220948 \cdot 10^{-49}:\\ \;\;\;\;a - \frac{x \cdot a}{y + t}\\ \mathbf{elif}\;x \leq -2.1920578355095308 \cdot 10^{-68}:\\ \;\;\;\;\frac{-y}{\frac{y + t}{b}}\\ \mathbf{elif}\;x \leq -5.714642107311008 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.161150318573349 \cdot 10^{-246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.4320097710680017 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.64763499392081 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.3746474462130088 \cdot 10^{+171}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x}}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+208}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z - b \cdot \frac{y}{x + y}\\ \end{array} \]

Alternative 9
Error	11.8
Cost	1744

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := y \cdot \frac{z - b}{t_1}\\ \mathbf{if}\;t \leq -2.8248162899849157 \cdot 10^{+20}:\\ \;\;\;\;t_3 + \left(a + \frac{x \cdot z}{t}\right)\\ \mathbf{elif}\;t \leq 1.505671395294463 \cdot 10^{-19}:\\ \;\;\;\;\frac{a - b}{\frac{x + y}{y}} + z \cdot \frac{x + y}{t_2}\\ \mathbf{elif}\;t \leq 8347287278546485000:\\ \;\;\;\;z + \frac{\left(y + t\right) \cdot a - y \cdot b}{t_2}\\ \mathbf{elif}\;t \leq 1.5347307192204898 \cdot 10^{+166}:\\ \;\;\;\;a + t_3\\ \mathbf{else}:\\ \;\;\;\;\left(a + \frac{z}{\frac{t_1}{x}}\right) + \frac{y \cdot \left(z - b\right)}{t}\\ \end{array} \]

Alternative 10
Error	17.3
Cost	1616

\[\begin{array}{l} t_1 := z + \frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ t_2 := a + y \cdot \frac{z - b}{x + \left(y + t\right)}\\ \mathbf{if}\;t \leq -2.8248162899849157 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.8719340435796674 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.164149345492814 \cdot 10^{-147}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;t \leq 3.4508497714494788 \cdot 10^{-6}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	18.7
Cost	1616

\[\begin{array}{l} t_1 := z + \frac{\left(y + t\right) \cdot a - y \cdot b}{y + \left(x + t\right)}\\ t_2 := y \cdot \frac{z - b}{x + \left(y + t\right)}\\ t_3 := a + t_2\\ \mathbf{if}\;y \leq -1.7209440997915852 \cdot 10^{-38}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.376173136530409 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.6661723911741783 \cdot 10^{-220}:\\ \;\;\;\;t_2 + \left(a + \frac{x \cdot z}{t}\right)\\ \mathbf{elif}\;y \leq -4.81406195343231 \cdot 10^{-245}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.858844070251093 \cdot 10^{-152}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Error	29.3
Cost	1372

\[\begin{array}{l} t_1 := a + \frac{y \cdot \left(z - b\right)}{t}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -1.3077160070993047 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.718896625220948 \cdot 10^{-49}:\\ \;\;\;\;a - \frac{x \cdot a}{y + t}\\ \mathbf{elif}\;x \leq -2.1920578355095308 \cdot 10^{-68}:\\ \;\;\;\;\frac{-y}{\frac{y + t}{b}}\\ \mathbf{elif}\;x \leq -5.714642107311008 \cdot 10^{-78}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.161150318573349 \cdot 10^{-246}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -3.4320097710680017 \cdot 10^{-295}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.64763499392081 \cdot 10^{+128}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x}}\\ \end{array} \]

Alternative 13
Error	25.1
Cost	1232

\[\begin{array}{l} t_1 := a + y \cdot \left(\frac{z}{t} - \frac{b}{t}\right)\\ \mathbf{if}\;t \leq -2.8248162899849157 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.2796829337702476 \cdot 10^{-105}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;t \leq 4.2539573590876484 \cdot 10^{-222}:\\ \;\;\;\;z - b \cdot \frac{y}{x + y}\\ \mathbf{elif}\;t \leq 1.6178249041377165 \cdot 10^{+78}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	28.9
Cost	1108

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -1.3077160070993047 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.718896625220948 \cdot 10^{-49}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -1.4516799984690396 \cdot 10^{-72}:\\ \;\;\;\;\frac{-y}{\frac{y + t}{b}}\\ \mathbf{elif}\;x \leq -5.714642107311008 \cdot 10^{-78}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.64763499392081 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x}}\\ \end{array} \]

Alternative 15
Error	29.0
Cost	1108

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -1.3077160070993047 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.718896625220948 \cdot 10^{-49}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -1.4516799984690396 \cdot 10^{-72}:\\ \;\;\;\;\frac{y \cdot \left(-b\right)}{y + t}\\ \mathbf{elif}\;x \leq -5.714642107311008 \cdot 10^{-78}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.64763499392081 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x}}\\ \end{array} \]

Alternative 16
Error	29.1
Cost	1108

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -1.3077160070993047 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.718896625220948 \cdot 10^{-49}:\\ \;\;\;\;a - \frac{x \cdot a}{y + t}\\ \mathbf{elif}\;x \leq -1.4516799984690396 \cdot 10^{-72}:\\ \;\;\;\;\frac{y \cdot \left(-b\right)}{y + t}\\ \mathbf{elif}\;x \leq -5.714642107311008 \cdot 10^{-78}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.64763499392081 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x}}\\ \end{array} \]

Alternative 17
Error	28.9
Cost	1108

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -1.3077160070993047 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -6.718896625220948 \cdot 10^{-49}:\\ \;\;\;\;a - \frac{x \cdot a}{y + t}\\ \mathbf{elif}\;x \leq -1.4516799984690396 \cdot 10^{-72}:\\ \;\;\;\;\frac{y \cdot \left(z - b\right)}{y + t}\\ \mathbf{elif}\;x \leq -5.714642107311008 \cdot 10^{-78}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.64763499392081 \cdot 10^{+128}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x}}\\ \end{array} \]

Alternative 18
Error	18.1
Cost	1104

\[\begin{array}{l} \mathbf{if}\;x \leq -2.3237586853623143 \cdot 10^{+167}:\\ \;\;\;\;\frac{z}{1 + \frac{t}{x + y}}\\ \mathbf{elif}\;x \leq 8.457823460731239 \cdot 10^{+133}:\\ \;\;\;\;a + y \cdot \frac{z - b}{x + \left(y + t\right)}\\ \mathbf{elif}\;x \leq 1.3746474462130088 \cdot 10^{+171}:\\ \;\;\;\;z \cdot \frac{x + y}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+208}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z - b \cdot \frac{y}{x + y}\\ \end{array} \]

Alternative 19
Error	27.7
Cost	976

\[\begin{array}{l} t_1 := \frac{z}{1 + \frac{t}{x}}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.5149852498413467 \cdot 10^{-40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.0781116927276733 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.547917531983199 \cdot 10^{-278}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 2.5985396227148092 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 20
Error	36.2
Cost	856

\[\begin{array}{l} \mathbf{if}\;z \leq -6.947776685669543 \cdot 10^{+78}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;z \leq -3.174089010002591 \cdot 10^{-34}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -4.285392796818727 \cdot 10^{-75}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;z \leq 2.261846502450983 \cdot 10^{-21}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq 3.534831525111706 \cdot 10^{+151}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;z \leq 2.962170466483353 \cdot 10^{+182}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 21
Error	29.1
Cost	716

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;x \leq -1.3077160070993047 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.714642107311008 \cdot 10^{-78}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{+208}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 22
Error	36.5
Cost	592

\[\begin{array}{l} \mathbf{if}\;z \leq -1.2053183229075939 \cdot 10^{+64}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 0.21325946579926813:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq 6.635878261167598 \cdot 10^{+87}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.962170466483353 \cdot 10^{+182}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 23
Error	43.4
Cost	64

\[z \]

Reproduce

herbie shell --seed 2022297 
(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)))