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

Average Accuracy: 58.4% → 88.1%

Time: 29.1s

Precision: binary64

Cost: 16713

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+288}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, \mathsf{fma}\left(y, a + \left(z - b\right), t \cdot a\right)\right)}{x + \left(y + t\right)}\\ \end{array} \]

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 (/ (- (+ (* a (+ y t)) (* z (+ x y))) (* y b)) (+ y (+ x t)))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+288)))
     (- (+ z a) b)
     (/ (fma x z (fma y (+ a (- z b)) (* t a))) (+ x (+ y t))))))

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 = (((a * (y + t)) + (z * (x + y))) - (y * b)) / (y + (x + t));
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+288)) {
		tmp = (z + a) - b;
	} else {
		tmp = fma(x, z, fma(y, (a + (z - b)), (t * a))) / (x + (y + t));
	}
	return tmp;
}

Julia

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

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(a * Float64(y + t)) + Float64(z * Float64(x + y))) - Float64(y * b)) / Float64(y + Float64(x + t)))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+288))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(fma(x, z, fma(y, Float64(a + Float64(z - b)), Float64(t * a))) / Float64(x + Float64(y + t)));
	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[(N[(N[(N[(a * N[(y + t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * b), $MachinePrecision]), $MachinePrecision] / N[(y + N[(x + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+288]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(x * z + N[(y * N[(a + N[(z - b), $MachinePrecision]), $MachinePrecision] + N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	58.4%
Target	82.0%
Herbie	88.1%

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

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 1e288 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 0.8%

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

   2. Simplified 0.8%

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

      [Start] 0.8	\[ \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
      fma-def [=>] 0.8	\[ \frac{\color{blue}{\mathsf{fma}\left(x + y, z, \left(t + y\right) \cdot a\right)} - y \cdot b}{\left(x + t\right) + y} \]
      +-commutative [=>] 0.8	\[ \frac{\mathsf{fma}\left(x + y, z, \color{blue}{\left(y + t\right)} \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
      +-commutative [=>] 0.8	\[ \frac{\mathsf{fma}\left(x + y, z, \left(y + t\right) \cdot a\right) - y \cdot b}{\color{blue}{y + \left(x + t\right)}} \]

   3. Taylor expanded in y around inf 71.9%

      \[\leadsto \color{blue}{\left(a + z\right) - b} \]

   4. Simplified 71.9%

      \[\leadsto \color{blue}{\left(z + a\right) - b} \]
      Proof

      [Start] 71.9	\[ \left(a + z\right) - b \]
      +-commutative [=>] 71.9	\[ \color{blue}{\left(z + a\right)} - b \]

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1e288

   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 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+288}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, z, \mathsf{fma}\left(y, a + \left(z - b\right), t \cdot a\right)\right)}{x + \left(y + t\right)}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	88.1%
Cost	10441

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a \cdot \left(y + t\right)\\ t_3 := \frac{\left(t_2 + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_3 \leq -\infty \lor \neg \left(t_3 \leq 10^{+288}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x + y, z, t_2\right) - y \cdot b}{t_1}\\ \end{array} \]

Alternative 2
Accuracy	88.1%
Cost	4169

\[\begin{array}{l} t_1 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+288}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Accuracy	49.5%
Cost	2294

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{x + y}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{+279}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{+239}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+202}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+193}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{+175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{+107}:\\ \;\;\;\;\frac{a}{\frac{x}{y + t}}\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-102}:\\ \;\;\;\;\frac{y}{\frac{x + y}{a - b}}\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-216} \lor \neg \left(t \leq 1.3 \cdot 10^{-211}\right) \land \left(t \leq 3.8 \cdot 10^{-61} \lor \neg \left(t \leq 4.3 \cdot 10^{+45}\right)\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x}\\ \end{array} \]

Alternative 4
Accuracy	57.4%
Cost	2156

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{x \cdot z + t \cdot a}{x + t}\\ t_3 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ t_4 := y \cdot t_1\\ t_5 := y + \left(x + t\right)\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;a \leq -2.65 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.02 \cdot 10^{-116}:\\ \;\;\;\;\frac{t \cdot a + t_4}{y + t}\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-202}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-272}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-296}:\\ \;\;\;\;\frac{t_4}{t_5}\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-184}:\\ \;\;\;\;\frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-63}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_5}\\ \end{array} \]

Alternative 5
Accuracy	58.0%
Cost	2024

\[\begin{array}{l} t_1 := y \cdot \left(a - b\right)\\ t_2 := z + \frac{t_1}{x + y}\\ t_3 := \left(z + a\right) - b\\ t_4 := y + \left(x + t\right)\\ t_5 := \left(y + t\right) \cdot \frac{a}{t_4}\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{+94}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-100}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -1.96 \cdot 10^{-112}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-207}:\\ \;\;\;\;z + \frac{t_1}{x}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-288}:\\ \;\;\;\;\frac{t \cdot a}{t_4}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+72}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{+116}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+179}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Accuracy	59.5%
Cost	2024

\[\begin{array}{l} t_1 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ t_2 := \left(z + a\right) - b\\ t_3 := \frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-114}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{-282}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+179}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Accuracy	60.4%
Cost	2024

\[\begin{array}{l} t_1 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ t_2 := \left(z + a\right) - b\\ t_3 := \frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-105}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-136}:\\ \;\;\;\;\frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-284}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+179}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Accuracy	54.2%
Cost	1893

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \left(y + t\right) \cdot \frac{a}{y + \left(x + t\right)}\\ \mathbf{if}\;a \leq -8.5 \cdot 10^{+133}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{+14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -24000000000000:\\ \;\;\;\;\frac{a}{\frac{x}{y + t}}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-20}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3 \cdot 10^{-295}:\\ \;\;\;\;\frac{-y}{\frac{t + \left(x + y\right)}{b}}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{-63} \lor \neg \left(a \leq 1.25 \cdot 10^{+150}\right) \land a \leq 1.48 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	57.4%
Cost	1892

\[\begin{array}{l} t_1 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ t_2 := \left(z + a\right) - b\\ t_3 := \frac{x \cdot z + t \cdot a}{x + t}\\ t_4 := y + \left(x + t\right)\\ \mathbf{if}\;a \leq -7.6 \cdot 10^{+133}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{+25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-203}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.85 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-294}:\\ \;\;\;\;\frac{y \cdot t_2}{t_4}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-184}:\\ \;\;\;\;\frac{z}{\frac{t + \left(x + y\right)}{x + y}}\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+63}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{+172}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_4}\\ \end{array} \]

Alternative 10
Accuracy	62.1%
Cost	1760

\[\begin{array}{l} t_1 := z + \frac{y \cdot \left(a - b\right)}{x + y}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3 \cdot 10^{+94}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 10^{-286}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+179}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Accuracy	59.9%
Cost	1760

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{x \cdot z + t \cdot a}{x + t}\\ t_3 := x + \left(y + t\right)\\ t_4 := y + \left(x + t\right)\\ \mathbf{if}\;a \leq -8.6 \cdot 10^{+132}:\\ \;\;\;\;\frac{a}{\frac{t_3}{y + t}}\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-217}:\\ \;\;\;\;\frac{x + y}{\frac{t_3}{z}}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-184}:\\ \;\;\;\;\frac{z \cdot \left(x + y\right) - y \cdot b}{t_4}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-64}:\\ \;\;\;\;z + \frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{+175}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_4}\\ \end{array} \]

Alternative 12
Accuracy	44.2%
Cost	1516

\[\begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{+202}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{+195}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq -1.52 \cdot 10^{+170}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-11}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-73}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-90}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-209}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-191}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-123}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{-39}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+52}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 13
Accuracy	55.6%
Cost	1240

\[\begin{array}{l} t_1 := z + \frac{y \cdot \left(a - b\right)}{x}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -0.2:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-184}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-282}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+41}:\\ \;\;\;\;\frac{z}{\frac{x + t}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Accuracy	54.9%
Cost	980

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.6 \cdot 10^{-183}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-243}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-261}:\\ \;\;\;\;t \cdot \frac{a}{x}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-241}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Accuracy	54.9%
Cost	980

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-182}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-243}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-260}:\\ \;\;\;\;\frac{a}{\frac{x}{t}}\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-241}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Accuracy	54.9%
Cost	980

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-184}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-243}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-260}:\\ \;\;\;\;\frac{a}{\frac{x}{y + t}}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-241}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Accuracy	55.6%
Cost	976

\[\begin{array}{l} t_1 := \frac{z}{\frac{x + t}{x}}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -8 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-283}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Accuracy	44.3%
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{+36}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 7.4 \cdot 10^{-60}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 19
Accuracy	32.0%
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023146 
(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)))