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

Average Error: 41.68% → 9.12%

Time: 23.0s

Precision: binary64

Cost: 16713

Math

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

↓

\[\begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{t_2}\\ \mathbf{if}\;t_3 \leq -\infty \lor \neg \left(t_3 \leq 10^{+275}\right):\\ \;\;\;\;y \cdot \frac{z - b}{t_1} + \left(z + \left(y + t\right) \cdot \frac{a}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, \mathsf{fma}\left(y, z + \left(a - b\right), t \cdot a\right)\right)}{t_2}\\ \end{array} \]

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 (+ t (+ x y)))
        (t_2 (+ y (+ x t)))
        (t_3 (/ (- (+ (* z (+ x y)) (* (+ y t) a)) (* y b)) t_2)))
   (if (or (<= t_3 (- INFINITY)) (not (<= t_3 1e+275)))
     (+ (* y (/ (- z b) t_1)) (+ z (* (+ y t) (/ a t_1))))
     (/ (fma x z (fma y (+ z (- a b)) (* t a))) 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 = t + (x + y);
	double t_2 = y + (x + t);
	double t_3 = (((z * (x + y)) + ((y + t) * a)) - (y * b)) / t_2;
	double tmp;
	if ((t_3 <= -((double) INFINITY)) || !(t_3 <= 1e+275)) {
		tmp = (y * ((z - b) / t_1)) + (z + ((y + t) * (a / t_1)));
	} else {
		tmp = fma(x, z, fma(y, (z + (a - b)), (t * a))) / 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(t + Float64(x + y))
	t_2 = Float64(y + Float64(x + t))
	t_3 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(Float64(y + t) * a)) - Float64(y * b)) / t_2)
	tmp = 0.0
	if ((t_3 <= Float64(-Inf)) || !(t_3 <= 1e+275))
		tmp = Float64(Float64(y * Float64(Float64(z - b) / t_1)) + Float64(z + Float64(Float64(y + t) * Float64(a / t_1))));
	else
		tmp = Float64(fma(x, z, fma(y, Float64(z + Float64(a - b)), Float64(t * a))) / t_2);
	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[(t + N[(x + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[Or[LessEqual[t$95$3, (-Infinity)], N[Not[LessEqual[t$95$3, 1e+275]], $MachinePrecision]], N[(N[(y * N[(N[(z - b), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] + N[(z + N[(N[(y + t), $MachinePrecision] * N[(a / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * z + N[(y * N[(z + N[(a - b), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]]]]]

Target

Original	41.68%
Target	18.08%
Herbie	9.12%

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

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 9.9999999999999996e274 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 98.49

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

   2. Simplified 98.49

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

      [Start] 98.49	\[ \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Taylor expanded in a around inf 98.49

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

   4. Simplified 30.74

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

      [Start] 98.49	\[ \frac{\left(z - b\right) \cdot y}{y + \left(t + x\right)} + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      associate-/l* [=>] 73.59	\[ \color{blue}{\frac{z - b}{\frac{y + \left(t + x\right)}{y}}} + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      associate-/r/ [=>] 74.39	\[ \color{blue}{\frac{z - b}{y + \left(t + x\right)} \cdot y} + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      +-commutative [=>] 74.39	\[ \frac{z - b}{\color{blue}{\left(t + x\right) + y}} \cdot y + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      associate-+l+ [=>] 74.39	\[ \frac{z - b}{\color{blue}{t + \left(x + y\right)}} \cdot y + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      +-commutative [<=] 74.39	\[ \frac{z - b}{t + \color{blue}{\left(y + x\right)}} \cdot y + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      +-commutative [=>] 74.39	\[ \frac{z - b}{t + \left(y + x\right)} \cdot y + \left(\frac{z \cdot x}{\color{blue}{\left(t + x\right) + y}} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      associate-+l+ [=>] 74.39	\[ \frac{z - b}{t + \left(y + x\right)} \cdot y + \left(\frac{z \cdot x}{\color{blue}{t + \left(x + y\right)}} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      +-commutative [<=] 74.39	\[ \frac{z - b}{t + \left(y + x\right)} \cdot y + \left(\frac{z \cdot x}{t + \color{blue}{\left(y + x\right)}} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      associate-/l* [=>] 30.36	\[ \frac{z - b}{t + \left(y + x\right)} \cdot y + \left(\frac{z \cdot x}{t + \left(y + x\right)} + \color{blue}{\frac{a}{\frac{y + \left(t + x\right)}{y + t}}}\right) \]
      associate-/r/ [=>] 30.74	\[ \frac{z - b}{t + \left(y + x\right)} \cdot y + \left(\frac{z \cdot x}{t + \left(y + x\right)} + \color{blue}{\frac{a}{y + \left(t + x\right)} \cdot \left(y + t\right)}\right) \]
      +-commutative [=>] 30.74	\[ \frac{z - b}{t + \left(y + x\right)} \cdot y + \left(\frac{z \cdot x}{t + \left(y + x\right)} + \frac{a}{\color{blue}{\left(t + x\right) + y}} \cdot \left(y + t\right)\right) \]
      associate-+l+ [=>] 30.74	\[ \frac{z - b}{t + \left(y + x\right)} \cdot y + \left(\frac{z \cdot x}{t + \left(y + x\right)} + \frac{a}{\color{blue}{t + \left(x + y\right)}} \cdot \left(y + t\right)\right) \]
      +-commutative [<=] 30.74	\[ \frac{z - b}{t + \left(y + x\right)} \cdot y + \left(\frac{z \cdot x}{t + \left(y + x\right)} + \frac{a}{t + \color{blue}{\left(y + x\right)}} \cdot \left(y + t\right)\right) \]
      +-commutative [=>] 30.74	\[ \frac{z - b}{t + \left(y + x\right)} \cdot y + \left(\frac{z \cdot x}{t + \left(y + x\right)} + \frac{a}{t + \left(y + x\right)} \cdot \color{blue}{\left(t + y\right)}\right) \]

   5. Taylor expanded in x around inf 21.01

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

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.9999999999999996e274

   1. Initial program 0.52

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

   2. Simplified 0.51

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

      [Start] 0.52	\[ \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

3. Recombined 2 regimes into one program.

4. Final simplification 9.12

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+275}\right):\\ \;\;\;\;y \cdot \frac{z - b}{t + \left(x + y\right)} + \left(z + \left(y + t\right) \cdot \frac{a}{t + \left(x + y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, \mathsf{fma}\left(y, z + \left(a - b\right), t \cdot a\right)\right)}{y + \left(x + t\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error	9.13%
Cost	4425

\[\begin{array}{l} t_1 := t + \left(x + y\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 10^{+275}\right):\\ \;\;\;\;y \cdot \frac{z - b}{t_1} + \left(z + \left(y + t\right) \cdot \frac{a}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	13.36%
Cost	4168

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + \left(y + t\right) \cdot a\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+239}:\\ \;\;\;\;a + \left(z - b\right) \cdot \frac{y}{t_1}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+215}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(z + a\right) - b\\ \end{array} \]

Alternative 3
Error	24.48%
Cost	2137

\[\begin{array}{l} t_1 := z + a \cdot \left(\frac{y}{x} + \frac{t}{x}\right)\\ t_2 := y + \left(x + t\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{+137}:\\ \;\;\;\;\left(z - b\right) \cdot \frac{y}{t_2} + \left(a + \frac{z}{\frac{t}{x}}\right)\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{+76}:\\ \;\;\;\;z \cdot \frac{x + y}{t_2}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-45} \lor \neg \left(x \leq 1.25 \cdot 10^{-8}\right) \land x \leq 6 \cdot 10^{+152}:\\ \;\;\;\;\frac{z - b}{\frac{y + t}{y}} + \left(a + \frac{x \cdot z}{t + \left(x + y\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	26.93%
Cost	1888

\[\begin{array}{l} t_1 := z + a \cdot \left(\frac{y}{x} + \frac{t}{x}\right)\\ t_2 := \frac{x \cdot z + t \cdot a}{x + t}\\ t_3 := \left(z - b\right) \cdot \frac{y}{y + \left(x + t\right)}\\ t_4 := a + t_3\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{+196}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.1 \cdot 10^{+136}:\\ \;\;\;\;t_3 + \left(a + \frac{z}{\frac{t}{x}}\right)\\ \mathbf{elif}\;x \leq -6 \cdot 10^{+87}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-48}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+21}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{+163}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	45.09%
Cost	1760

\[\begin{array}{l} t_1 := \frac{x \cdot z + t \cdot a}{x + t}\\ t_2 := \left(z + a\right) - b\\ t_3 := y + \left(x + t\right)\\ t_4 := \frac{a}{\frac{t_3}{y + t}}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{+116}:\\ \;\;\;\;z \cdot \frac{x + y}{t_3}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-176}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-244}:\\ \;\;\;\;y \cdot \frac{-b}{t_3}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-216}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-16}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \end{array} \]

Alternative 6
Error	25.73%
Cost	1624

\[\begin{array}{l} t_1 := \frac{x \cdot z + t \cdot a}{x + t}\\ t_2 := a + \left(z - b\right) \cdot \frac{y}{y + \left(x + t\right)}\\ t_3 := z + a \cdot \left(\frac{y}{x} + \frac{t}{x}\right)\\ \mathbf{if}\;x \leq -8.5 \cdot 10^{+191}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+164}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	42.72%
Cost	1496

\[\begin{array}{l} t_1 := z \cdot \frac{x + y}{y + \left(x + t\right)}\\ t_2 := \left(z + a\right) - b\\ t_3 := \frac{a}{\frac{x + t}{t}}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-280}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-199}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	42.74%
Cost	1496

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z \cdot \frac{x + y}{t_1}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-198}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-281}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-297}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-199}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Error	45%
Cost	1240

\[\begin{array}{l} t_1 := x \cdot \frac{z}{x + t}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-252}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-291}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-200}:\\ \;\;\;\;t \cdot \frac{a}{x + t}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	43.51%
Cost	1240

\[\begin{array}{l} t_1 := z + a \cdot \frac{t}{x}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-251}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-200}:\\ \;\;\;\;t \cdot \frac{a}{x + t}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	42.58%
Cost	1240

\[\begin{array}{l} t_1 := z + a \cdot \frac{t}{x}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-252}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-298}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-177}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	44.94%
Cost	716

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{-176}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-52}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	44.95%
Cost	716

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-200}:\\ \;\;\;\;t \cdot \frac{a}{x + t}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-52}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	57.85%
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+78}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-179}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-256}:\\ \;\;\;\;-b\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-50}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 15
Error	55.49%
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+74}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-16}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 16
Error	66.95%
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023090 
(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)))