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

Average Accuracy: 58.7% → 88.0%

Time: 27.7s

Precision: binary64

Cost: 16713

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+303} \lor \neg \left(t_2 \leq 10^{+273}\right):\\ \;\;\;\;a + z \cdot \left(\frac{x}{t_1} + \frac{y}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, \mathsf{fma}\left(y, a + \left(z - b\right), t \cdot a\right)\right)}{t_1}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (- (+ (* (+ x y) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))

↓

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ y t)))
        (t_2 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_2 -5e+303) (not (<= t_2 1e+273)))
     (+ a (* z (+ (/ x t_1) (/ y t_1))))
     (/ (fma x z (fma y (+ a (- z b)) (* t a))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
}

↓

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (y + t);
	double t_2 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_2 <= -5e+303) || !(t_2 <= 1e+273)) {
		tmp = a + (z * ((x / t_1) + (y / t_1)));
	} else {
		tmp = fma(x, z, fma(y, (a + (z - b)), (t * a))) / t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
end

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(y + t))
	t_2 = Float64(Float64(Float64(Float64(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_2 <= -5e+303) || !(t_2 <= 1e+273))
		tmp = Float64(a + Float64(z * Float64(Float64(x / t_1) + Float64(y / t_1))));
	else
		tmp = Float64(fma(x, z, fma(y, Float64(a + Float64(z - b)), Float64(t * a))) / t_1);
	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[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -5e+303], N[Not[LessEqual[t$95$2, 1e+273]], $MachinePrecision]], N[(a + N[(z * N[(N[(x / t$95$1), $MachinePrecision] + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * z + N[(y * N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Target

Original	58.7%
Target	82.9%
Herbie	88.0%

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

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < -4.9999999999999997e303 or 9.99999999999999945e272 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 1.9%

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

   2. Taylor expanded in z around 0 31.1%

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

   3. Simplified 31.1%

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

      [Start] 31.1	\[ \left(\left(\frac{x}{y + \left(t + x\right)} + \frac{y}{y + \left(t + x\right)}\right) \cdot z + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) - \frac{y \cdot b}{y + \left(t + x\right)} \]
      associate--l+ [=>] 31.1	\[ \color{blue}{\left(\frac{x}{y + \left(t + x\right)} + \frac{y}{y + \left(t + x\right)}\right) \cdot z + \left(\frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)} - \frac{y \cdot b}{y + \left(t + x\right)}\right)} \]
      *-commutative [=>] 31.1	\[ \color{blue}{z \cdot \left(\frac{x}{y + \left(t + x\right)} + \frac{y}{y + \left(t + x\right)}\right)} + \left(\frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)} - \frac{y \cdot b}{y + \left(t + x\right)}\right) \]
      associate-+r+ [=>] 31.1	\[ z \cdot \left(\frac{x}{\color{blue}{\left(y + t\right) + x}} + \frac{y}{y + \left(t + x\right)}\right) + \left(\frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)} - \frac{y \cdot b}{y + \left(t + x\right)}\right) \]
      associate-+r+ [=>] 31.1	\[ z \cdot \left(\frac{x}{\left(y + t\right) + x} + \frac{y}{\color{blue}{\left(y + t\right) + x}}\right) + \left(\frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)} - \frac{y \cdot b}{y + \left(t + x\right)}\right) \]
      div-sub [<=] 31.1	\[ z \cdot \left(\frac{x}{\left(y + t\right) + x} + \frac{y}{\left(y + t\right) + x}\right) + \color{blue}{\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(t + x\right)}} \]
      associate-+r+ [=>] 31.1	\[ z \cdot \left(\frac{x}{\left(y + t\right) + x} + \frac{y}{\left(y + t\right) + x}\right) + \frac{a \cdot \left(y + t\right) - y \cdot b}{\color{blue}{\left(y + t\right) + x}} \]

   4. Taylor expanded in t around inf 72.0%

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

   if -4.9999999999999997e303 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.99999999999999945e272

   1. Initial program 99.6%

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

   2. Simplified 99.6%

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

      [Start] 99.6	\[ \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

3. Recombined 2 regimes into one program.

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -5 \cdot 10^{+303} \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+273}\right):\\ \;\;\;\;a + z \cdot \left(\frac{x}{x + \left(y + t\right)} + \frac{y}{x + \left(y + t\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, \mathsf{fma}\left(y, a + \left(z - b\right), t \cdot a\right)\right)}{x + \left(y + t\right)}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	88.0%
Cost	10441

\[\begin{array}{l} t_1 := a \cdot \left(y + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + t_1\right) - y \cdot b}{y + \left(x + t\right)}\\ t_3 := x + \left(y + t\right)\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+303} \lor \neg \left(t_2 \leq 10^{+273}\right):\\ \;\;\;\;a + z \cdot \left(\frac{x}{t_3} + \frac{y}{t_3}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, t_1\right) - y \cdot b}{t_3}\\ \end{array} \]

Alternative 2
Accuracy	88.0%
Cost	4169

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+303} \lor \neg \left(t_2 \leq 10^{+273}\right):\\ \;\;\;\;a + z \cdot \left(\frac{x}{t_1} + \frac{y}{t_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	54.6%
Cost	2424

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \left(z + a\right) - b\\ t_3 := y + \left(x + t\right)\\ t_4 := \frac{z}{\frac{t_3}{x + y}}\\ t_5 := a + z \cdot \frac{y}{y + t}\\ t_6 := t + \left(x + y\right)\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+98}:\\ \;\;\;\;\frac{y + t}{\frac{t_6}{a}}\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-13}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-59}:\\ \;\;\;\;\frac{t \cdot a - y \cdot b}{t_1}\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-119}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-167}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-200}:\\ \;\;\;\;z - \frac{y \cdot b}{t_1}\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-262}:\\ \;\;\;\;\frac{t \cdot a + y \cdot t_2}{y + t}\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-302}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-216}:\\ \;\;\;\;\frac{x \cdot z + y \cdot \left(z - b\right)}{t_3}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-134}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{-123}:\\ \;\;\;\;b \cdot \frac{-y}{t_6}\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-59}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-35}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{+80}:\\ \;\;\;\;a + x \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 4
Accuracy	63.4%
Cost	2276

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := z - \frac{y \cdot b - a \cdot \left(y + t\right)}{t_1}\\ t_3 := \frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ t_4 := a + z \cdot \frac{y}{y + t}\\ t_5 := \left(z + a\right) - b\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+179}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+126}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.76 \cdot 10^{+16}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -192000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-151}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-109}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 1650:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+84}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+99}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Accuracy	71.6%
Cost	2008

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := z - \frac{y \cdot b - a \cdot \left(y + t\right)}{t_1}\\ t_3 := a + z \cdot \left(\frac{x}{t_1} + \frac{y}{t_1}\right)\\ \mathbf{if}\;z \leq -30000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-153}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-108}:\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-36}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Accuracy	62.7%
Cost	1892

\[\begin{array}{l} t_1 := \frac{t \cdot a + x \cdot z}{x + t}\\ t_2 := x + \left(y + t\right)\\ t_3 := \left(z + a\right) - b\\ t_4 := z - \frac{y \cdot b}{t_2}\\ t_5 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{if}\;y \leq -6.2 \cdot 10^{-19}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-130}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-142}:\\ \;\;\;\;\frac{a}{\frac{t_2}{y + t}}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-243}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-83}:\\ \;\;\;\;a + z \cdot \frac{y}{y + t}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+51}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+87}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Accuracy	60.0%
Cost	1884

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+126}:\\ \;\;\;\;a + z \cdot \frac{y}{y + t}\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-155}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{x + \left(y + t\right)}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-37}:\\ \;\;\;\;\frac{t \cdot a + y \cdot t_1}{y + t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Accuracy	61.4%
Cost	1760

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-77}:\\ \;\;\;\;a + x \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-188}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-250}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-263}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-206}:\\ \;\;\;\;z - \frac{t \cdot \left(z - a\right)}{x}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-133}:\\ \;\;\;\;a + \frac{x + y}{\frac{t}{z}}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+87}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	61.5%
Cost	1760

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-77}:\\ \;\;\;\;a + x \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-183}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-250}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{x + y}}\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-263}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-213}:\\ \;\;\;\;z - \frac{t \cdot \left(z - a\right)}{x}\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-130}:\\ \;\;\;\;a + \frac{x + y}{\frac{t}{z}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+95}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Accuracy	55.7%
Cost	1500

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-85}:\\ \;\;\;\;a + x \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-210}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{-130}:\\ \;\;\;\;a + \frac{x + y}{\frac{t}{z}}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{+51}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+78}:\\ \;\;\;\;\frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{else}:\\ \;\;\;\;a + z \cdot \frac{y}{y + t}\\ \end{array} \]

Alternative 11
Accuracy	62.0%
Cost	1496

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-77}:\\ \;\;\;\;a + x \cdot \frac{z}{t}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-180}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-204}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{-132}:\\ \;\;\;\;a + \frac{x + y}{\frac{t}{z}}\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+92}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Accuracy	65.2%
Cost	1364

\[\begin{array}{l} t_1 := \frac{t \cdot a + x \cdot z}{x + t}\\ t_2 := \left(z + a\right) - b\\ t_3 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{-18}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-242}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+95}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Accuracy	53.3%
Cost	1237

\[\begin{array}{l} t_1 := b \cdot \frac{-y}{t + \left(x + y\right)}\\ \mathbf{if}\;b \leq -6.7 \cdot 10^{+180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{+120}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;b \leq -8.6 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-11} \lor \neg \left(b \leq 1.6 \cdot 10^{-89}\right):\\ \;\;\;\;a + z \cdot \frac{y}{y + t}\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 14
Accuracy	60.5%
Cost	976

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := a + x \cdot \frac{z}{t}\\ \mathbf{if}\;t \leq -1.65 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+131}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+206}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Accuracy	57.4%
Cost	848

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-30}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+130}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+206}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 16
Accuracy	59.9%
Cost	841

\[\begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{+98} \lor \neg \left(x \leq 1.85 \cdot 10^{+82}\right):\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{else}:\\ \;\;\;\;a + z \cdot \frac{y}{y + t}\\ \end{array} \]

Alternative 17
Accuracy	51.3%
Cost	721

\[\begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{-68}:\\ \;\;\;\;z + a\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-124} \lor \neg \left(x \leq -8 \cdot 10^{-169}\right) \land x \leq 1.95 \cdot 10^{-301}:\\ \;\;\;\;a - b\\ \mathbf{else}:\\ \;\;\;\;z + a\\ \end{array} \]

Alternative 18
Accuracy	42.7%
Cost	592

\[\begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+146}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+124}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{+16}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-117}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 19
Accuracy	52.7%
Cost	324

\[\begin{array}{l} \mathbf{if}\;t \leq 1.65 \cdot 10^{+207}:\\ \;\;\;\;z + a\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 20
Accuracy	32.7%
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023151 
(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)))