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

Average Accuracy: 58.0% → 99.6%

Time: 19.8s

Precision: binary64

Cost: 16713

Math

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

↓

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;\left(\frac{a}{t_1} \cdot \left(y + t\right) - \frac{b}{\frac{t_1}{y}}\right) + \frac{z}{\frac{t_1}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, z - b, \mathsf{fma}\left(y + t, a, x \cdot z\right)\right)}{t_1}\\ \end{array} \]

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 (- INFINITY)) (not (<= t_2 5e+305)))
     (+ (- (* (/ a t_1) (+ y t)) (/ b (/ t_1 y))) (/ z (/ t_1 (+ x y))))
     (/ (fma y (- z b) (fma (+ y t) a (* x z))) 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 <= -((double) INFINITY)) || !(t_2 <= 5e+305)) {
		tmp = (((a / t_1) * (y + t)) - (b / (t_1 / y))) + (z / (t_1 / (x + y)));
	} else {
		tmp = fma(y, (z - b), fma((y + t), a, (x * z))) / 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 <= Float64(-Inf)) || !(t_2 <= 5e+305))
		tmp = Float64(Float64(Float64(Float64(a / t_1) * Float64(y + t)) - Float64(b / Float64(t_1 / y))) + Float64(z / Float64(t_1 / Float64(x + y))));
	else
		tmp = Float64(fma(y, Float64(z - b), fma(Float64(y + t), a, Float64(x * z))) / 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, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+305]], $MachinePrecision]], N[(N[(N[(N[(a / t$95$1), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision] - N[(b / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z / N[(t$95$1 / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z - b), $MachinePrecision] + N[(N[(y + t), $MachinePrecision] * a + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]]]]

Target

Original	58.0%
Target	82.1%
Herbie	99.6%

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

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 5.00000000000000009e305 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 0.2%

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

   2. Simplified 0.2%

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

      [Start] 0.2	\[ \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
      sub-neg [=>] 0.2	\[ \frac{\color{blue}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) + \left(-y \cdot b\right)}}{\left(x + t\right) + y} \]
      +-commutative [=>] 0.2	\[ \frac{\color{blue}{\left(-y \cdot b\right) + \left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right)}}{\left(x + t\right) + y} \]
      *-commutative [=>] 0.2	\[ \frac{\left(-y \cdot b\right) + \left(\color{blue}{z \cdot \left(x + y\right)} + \left(t + y\right) \cdot a\right)}{\left(x + t\right) + y} \]
      +-commutative [=>] 0.2	\[ \frac{\left(-y \cdot b\right) + \left(z \cdot \color{blue}{\left(y + x\right)} + \left(t + y\right) \cdot a\right)}{\left(x + t\right) + y} \]
      distribute-rgt-in [=>] 0.2	\[ \frac{\left(-y \cdot b\right) + \left(\color{blue}{\left(y \cdot z + x \cdot z\right)} + \left(t + y\right) \cdot a\right)}{\left(x + t\right) + y} \]
      associate-+l+ [=>] 0.2	\[ \frac{\left(-y \cdot b\right) + \color{blue}{\left(y \cdot z + \left(x \cdot z + \left(t + y\right) \cdot a\right)\right)}}{\left(x + t\right) + y} \]
      associate-+r+ [=>] 0.2	\[ \frac{\color{blue}{\left(\left(-y \cdot b\right) + y \cdot z\right) + \left(x \cdot z + \left(t + y\right) \cdot a\right)}}{\left(x + t\right) + y} \]
      +-commutative [<=] 0.2	\[ \frac{\color{blue}{\left(y \cdot z + \left(-y \cdot b\right)\right)} + \left(x \cdot z + \left(t + y\right) \cdot a\right)}{\left(x + t\right) + y} \]
      sub-neg [<=] 0.2	\[ \frac{\color{blue}{\left(y \cdot z - y \cdot b\right)} + \left(x \cdot z + \left(t + y\right) \cdot a\right)}{\left(x + t\right) + y} \]
      distribute-lft-out-- [=>] 0.2	\[ \frac{\color{blue}{y \cdot \left(z - b\right)} + \left(x \cdot z + \left(t + y\right) \cdot a\right)}{\left(x + t\right) + y} \]
      fma-def [=>] 0.2	\[ \frac{\color{blue}{\mathsf{fma}\left(y, z - b, x \cdot z + \left(t + y\right) \cdot a\right)}}{\left(x + t\right) + y} \]
      +-commutative [=>] 0.2	\[ \frac{\mathsf{fma}\left(y, z - b, \color{blue}{\left(t + y\right) \cdot a + x \cdot z}\right)}{\left(x + t\right) + y} \]
      fma-def [=>] 0.2	\[ \frac{\mathsf{fma}\left(y, z - b, \color{blue}{\mathsf{fma}\left(t + y, a, x \cdot z\right)}\right)}{\left(x + t\right) + y} \]
      +-commutative [=>] 0.2	\[ \frac{\mathsf{fma}\left(y, z - b, \mathsf{fma}\left(\color{blue}{y + t}, a, x \cdot z\right)\right)}{\left(x + t\right) + y} \]
      associate-+l+ [=>] 0.2	\[ \frac{\mathsf{fma}\left(y, z - b, \mathsf{fma}\left(y + t, a, x \cdot z\right)\right)}{\color{blue}{x + \left(t + y\right)}} \]
      +-commutative [=>] 0.2	\[ \frac{\mathsf{fma}\left(y, z - b, \mathsf{fma}\left(y + t, a, x \cdot z\right)\right)}{x + \color{blue}{\left(y + t\right)}} \]

   3. Taylor expanded in z around inf 0.2%

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

   4. Simplified 99.7%

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

      [Start] 0.2	\[ \frac{\left(y + x\right) \cdot z}{y + \left(t + x\right)} + \left(\frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)} + -1 \cdot \frac{y \cdot b}{y + \left(t + x\right)}\right) \]
      +-commutative [=>] 0.2	\[ \color{blue}{\left(\frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)} + -1 \cdot \frac{y \cdot b}{y + \left(t + x\right)}\right) + \frac{\left(y + x\right) \cdot z}{y + \left(t + x\right)}} \]

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.00000000000000009e305

   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%

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

      [Start] 99.6	\[ \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
      sub-neg [=>] 99.6	\[ \frac{\color{blue}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) + \left(-y \cdot b\right)}}{\left(x + t\right) + y} \]
      +-commutative [=>] 99.6	\[ \frac{\color{blue}{\left(-y \cdot b\right) + \left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right)}}{\left(x + t\right) + y} \]
      *-commutative [=>] 99.6	\[ \frac{\left(-y \cdot b\right) + \left(\color{blue}{z \cdot \left(x + y\right)} + \left(t + y\right) \cdot a\right)}{\left(x + t\right) + y} \]
      +-commutative [=>] 99.6	\[ \frac{\left(-y \cdot b\right) + \left(z \cdot \color{blue}{\left(y + x\right)} + \left(t + y\right) \cdot a\right)}{\left(x + t\right) + y} \]
      distribute-rgt-in [=>] 99.6	\[ \frac{\left(-y \cdot b\right) + \left(\color{blue}{\left(y \cdot z + x \cdot z\right)} + \left(t + y\right) \cdot a\right)}{\left(x + t\right) + y} \]
      associate-+l+ [=>] 99.6	\[ \frac{\left(-y \cdot b\right) + \color{blue}{\left(y \cdot z + \left(x \cdot z + \left(t + y\right) \cdot a\right)\right)}}{\left(x + t\right) + y} \]
      associate-+r+ [=>] 99.6	\[ \frac{\color{blue}{\left(\left(-y \cdot b\right) + y \cdot z\right) + \left(x \cdot z + \left(t + y\right) \cdot a\right)}}{\left(x + t\right) + y} \]
      +-commutative [<=] 99.6	\[ \frac{\color{blue}{\left(y \cdot z + \left(-y \cdot b\right)\right)} + \left(x \cdot z + \left(t + y\right) \cdot a\right)}{\left(x + t\right) + y} \]
      sub-neg [<=] 99.6	\[ \frac{\color{blue}{\left(y \cdot z - y \cdot b\right)} + \left(x \cdot z + \left(t + y\right) \cdot a\right)}{\left(x + t\right) + y} \]
      distribute-lft-out-- [=>] 99.6	\[ \frac{\color{blue}{y \cdot \left(z - b\right)} + \left(x \cdot z + \left(t + y\right) \cdot a\right)}{\left(x + t\right) + y} \]
      fma-def [=>] 99.6	\[ \frac{\color{blue}{\mathsf{fma}\left(y, z - b, x \cdot z + \left(t + y\right) \cdot a\right)}}{\left(x + t\right) + y} \]
      +-commutative [=>] 99.6	\[ \frac{\mathsf{fma}\left(y, z - b, \color{blue}{\left(t + y\right) \cdot a + x \cdot z}\right)}{\left(x + t\right) + y} \]
      fma-def [=>] 99.6	\[ \frac{\mathsf{fma}\left(y, z - b, \color{blue}{\mathsf{fma}\left(t + y, a, x \cdot z\right)}\right)}{\left(x + t\right) + y} \]
      +-commutative [=>] 99.6	\[ \frac{\mathsf{fma}\left(y, z - b, \mathsf{fma}\left(\color{blue}{y + t}, a, x \cdot z\right)\right)}{\left(x + t\right) + y} \]
      associate-+l+ [=>] 99.6	\[ \frac{\mathsf{fma}\left(y, z - b, \mathsf{fma}\left(y + t, a, x \cdot z\right)\right)}{\color{blue}{x + \left(t + y\right)}} \]
      +-commutative [=>] 99.6	\[ \frac{\mathsf{fma}\left(y, z - b, \mathsf{fma}\left(y + t, a, x \cdot z\right)\right)}{x + \color{blue}{\left(y + t\right)}} \]

3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;\left(\frac{a}{x + \left(y + t\right)} \cdot \left(y + t\right) - \frac{b}{\frac{x + \left(y + t\right)}{y}}\right) + \frac{z}{\frac{x + \left(y + t\right)}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, z - b, \mathsf{fma}\left(y + t, a, x \cdot z\right)\right)}{x + \left(y + t\right)}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	99.6%
Cost	4937

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;\left(\frac{a}{t_1} \cdot \left(y + t\right) - \frac{b}{\frac{t_1}{y}}\right) + \frac{z}{\frac{t_1}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Accuracy	95.4%
Cost	4297

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 2 \cdot 10^{+103}\right):\\ \;\;\;\;\frac{z}{\frac{t_1}{x + y}} + \left(a - \frac{b}{\frac{t_1}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	95.9%
Cost	4297

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;z + \left(\frac{a}{t_1} \cdot \left(y + t\right) - \frac{b}{\frac{t_1}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	91.7%
Cost	4168

\[\begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ t_2 := x + \left(y + t\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;z + \left(a - \frac{b}{\frac{t_2}{y}}\right)\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+103}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t_2}{x + y}} + \left(a - \frac{b}{1 + \frac{x}{y}}\right)\\ \end{array} \]

Alternative 5
Accuracy	59.1%
Cost	1628

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z \cdot \frac{x + y}{t + \left(x + y\right)}\\ t_3 := y + \left(x + t\right)\\ t_4 := a \cdot \frac{y + t}{t_3}\\ \mathbf{if}\;a \leq -7.8 \cdot 10^{+183}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-170}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \frac{-y}{t_3}\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 0.0003:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 6
Accuracy	59.0%
Cost	1628

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \mathbf{if}\;a \leq -1.02 \cdot 10^{+185}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8 \cdot 10^{-170}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \frac{-y}{t_2}\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{-119}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 0.0004:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{+34}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{t_2}\\ \end{array} \]

Alternative 7
Accuracy	59.1%
Cost	1628

\[\begin{array}{l} t_1 := z \cdot \frac{x + y}{t + \left(x + y\right)}\\ t_2 := x + \left(y + t\right)\\ t_3 := \left(z + a\right) - b\\ t_4 := y + \left(x + t\right)\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+184}:\\ \;\;\;\;\frac{a}{\frac{t_2}{y + t}}\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-96}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-170}:\\ \;\;\;\;\frac{z}{\frac{t_2}{x + y}}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-216}:\\ \;\;\;\;b \cdot \frac{-y}{t_4}\\ \mathbf{elif}\;a \leq 5.1 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 0.00028:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+34}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{t_4}\\ \end{array} \]

Alternative 8
Accuracy	71.4%
Cost	1620

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := z + \left(a - \frac{b}{\frac{t_1}{y}}\right)\\ \mathbf{if}\;a \leq -3.3 \cdot 10^{+184}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;a \leq -9.2 \cdot 10^{-104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-168}:\\ \;\;\;\;\frac{z}{\frac{t_1}{x + y}}\\ \mathbf{elif}\;a \leq 0.00047:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+182}:\\ \;\;\;\;z + \left(\frac{a}{t_1} \cdot \left(y + t\right) - b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 9
Accuracy	76.3%
Cost	1608

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+182}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;a \leq 1.66 \cdot 10^{+156}:\\ \;\;\;\;\frac{z}{\frac{t_1}{x + y}} + \left(a - \frac{b}{1 + \frac{x}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 10
Accuracy	56.8%
Cost	1496

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := a \cdot \frac{y + t}{t_2}\\ \mathbf{if}\;a \leq -2.5 \cdot 10^{+182}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \frac{-y}{t_2}\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-274}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.86 \cdot 10^{-293}:\\ \;\;\;\;\frac{y}{\frac{t + \left(x + y\right)}{-b}}\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+101}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 11
Accuracy	54.4%
Cost	1372

\[\begin{array}{l} t_1 := t \cdot \frac{a}{x + t}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{-98}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-131}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-149}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-285}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-245}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Accuracy	71.8%
Cost	1360

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := z + \left(a - \frac{b}{\frac{t_1}{y}}\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{+184}:\\ \;\;\;\;\frac{a}{\frac{t_1}{y + t}}\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-167}:\\ \;\;\;\;\frac{z}{\frac{t_1}{x + y}}\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+165}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{y + t}{y + \left(x + t\right)}\\ \end{array} \]

Alternative 13
Accuracy	56.2%
Cost	1240

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-130}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-298}:\\ \;\;\;\;\frac{a}{x + \left(y + t\right)} \cdot \left(y + t\right)\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-259}:\\ \;\;\;\;\frac{x}{\frac{x + t}{z}}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-146}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Accuracy	57.5%
Cost	977

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-130}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-147} \lor \neg \left(y \leq 2 \cdot 10^{-143}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{1 + \frac{x}{t}}\\ \end{array} \]

Alternative 15
Accuracy	54.3%
Cost	717

\[\begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+265}:\\ \;\;\;\;t \cdot \frac{a}{x}\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{+208} \lor \neg \left(x \leq -1.8 \cdot 10^{+102}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 16
Accuracy	44.3%
Cost	592

\[\begin{array}{l} \mathbf{if}\;a \leq -0.86:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-173}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-213}:\\ \;\;\;\;-b\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-25}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 17
Accuracy	45.2%
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+86}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1100000000:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 18
Accuracy	32.7%
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023143 
(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)))