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

Average Accuracy: 58.1% → 98.4%

Time: 19.8s

Precision: binary64

Cost: 5321

Math

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

↓

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 5 \cdot 10^{+94}\right):\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}} + \left(a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right) - \frac{y}{\frac{t_1}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

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 (+ y (+ x t)))
        (t_2 (/ (- (+ (* (+ y t) a) (* z (+ x y))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 5e+94)))
     (+
      (/ (+ x y) (/ t_1 z))
      (- (* a (+ (/ y t_1) (/ t t_1))) (/ y (/ t_1 b))))
     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 = y + (x + t);
	double t_2 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 5e+94)) {
		tmp = ((x + y) / (t_1 / z)) + ((a * ((y / t_1) + (t / t_1))) - (y / (t_1 / b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static 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);
}

↓

public static 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 tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 5e+94)) {
		tmp = ((x + y) / (t_1 / z)) + ((a * ((y / t_1) + (t / t_1))) - (y / (t_1 / b)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	return ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)

↓

def code(x, y, z, t, a, b):
	t_1 = y + (x + t)
	t_2 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 5e+94):
		tmp = ((x + y) / (t_1 / z)) + ((a * ((y / t_1) + (t / t_1))) - (y / (t_1 / b)))
	else:
		tmp = 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(y + Float64(x + t))
	t_2 = Float64(Float64(Float64(Float64(Float64(y + t) * a) + Float64(z * Float64(x + y))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 5e+94))
		tmp = Float64(Float64(Float64(x + y) / Float64(t_1 / z)) + Float64(Float64(a * Float64(Float64(y / t_1) + Float64(t / t_1))) - Float64(y / Float64(t_1 / b))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
end

↓

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (x + t);
	t_2 = ((((y + t) * a) + (z * (x + y))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 5e+94)))
		tmp = ((x + y) / (t_1 / z)) + ((a * ((y / t_1) + (t / t_1))) - (y / (t_1 / b)));
	else
		tmp = t_2;
	end
	tmp_2 = 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]}, If[Or[LessEqual[t$95$2, (-Infinity)], N[Not[LessEqual[t$95$2, 5e+94]], $MachinePrecision]], N[(N[(N[(x + y), $MachinePrecision] / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision] + N[(N[(a * N[(N[(y / t$95$1), $MachinePrecision] + N[(t / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y / N[(t$95$1 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]

Target

Original	58.1%
Target	82.6%
Herbie	98.4%

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

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 5.0000000000000001e94 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 17.9%

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

   2. Taylor expanded in a around 0 42.2%

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

   3. Simplified 97.4%

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

      [Start] 42.2	\[ \left(\frac{\left(y + x\right) \cdot z}{y + \left(t + x\right)} + a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right)\right) - \frac{y \cdot b}{y + \left(t + x\right)} \]
      associate--l+ [=>] 42.2	\[ \color{blue}{\frac{\left(y + x\right) \cdot z}{y + \left(t + x\right)} + \left(a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) - \frac{y \cdot b}{y + \left(t + x\right)}\right)} \]
      associate-+r+ [=>] 42.2	\[ \frac{\left(y + x\right) \cdot z}{\color{blue}{\left(y + t\right) + x}} + \left(a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) - \frac{y \cdot b}{y + \left(t + x\right)}\right) \]
      +-commutative [<=] 42.2	\[ \frac{\left(y + x\right) \cdot z}{\color{blue}{x + \left(y + t\right)}} + \left(a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) - \frac{y \cdot b}{y + \left(t + x\right)}\right) \]
      associate-/l* [=>] 73.0	\[ \color{blue}{\frac{y + x}{\frac{x + \left(y + t\right)}{z}}} + \left(a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) - \frac{y \cdot b}{y + \left(t + x\right)}\right) \]
      +-commutative [=>] 73.0	\[ \frac{y + x}{\frac{\color{blue}{\left(y + t\right) + x}}{z}} + \left(a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) - \frac{y \cdot b}{y + \left(t + x\right)}\right) \]
      associate-+r+ [<=] 73.0	\[ \frac{y + x}{\frac{\color{blue}{y + \left(t + x\right)}}{z}} + \left(a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) - \frac{y \cdot b}{y + \left(t + x\right)}\right) \]
      associate-+r+ [=>] 73.0	\[ \frac{y + x}{\frac{y + \left(t + x\right)}{z}} + \left(a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) - \frac{y \cdot b}{\color{blue}{\left(y + t\right) + x}}\right) \]
      +-commutative [<=] 73.0	\[ \frac{y + x}{\frac{y + \left(t + x\right)}{z}} + \left(a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) - \frac{y \cdot b}{\color{blue}{x + \left(y + t\right)}}\right) \]
      associate-/l* [=>] 97.4	\[ \frac{y + x}{\frac{y + \left(t + x\right)}{z}} + \left(a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) - \color{blue}{\frac{y}{\frac{x + \left(y + t\right)}{b}}}\right) \]
      +-commutative [=>] 97.4	\[ \frac{y + x}{\frac{y + \left(t + x\right)}{z}} + \left(a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) - \frac{y}{\frac{\color{blue}{\left(y + t\right) + x}}{b}}\right) \]
      associate-+r+ [<=] 97.4	\[ \frac{y + x}{\frac{y + \left(t + x\right)}{z}} + \left(a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right) - \frac{y}{\frac{\color{blue}{y + \left(t + x\right)}}{b}}\right) \]

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 5.0000000000000001e94

   1. Initial program 99.5%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 5 \cdot 10^{+94}\right):\\ \;\;\;\;\frac{x + y}{\frac{y + \left(x + t\right)}{z}} + \left(a \cdot \left(\frac{y}{y + \left(x + t\right)} + \frac{t}{y + \left(x + t\right)}\right) - \frac{y}{\frac{y + \left(x + t\right)}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	96.0%
Cost	4297

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 10^{+267}\right):\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}} + \left(a - \frac{y}{\frac{t_1}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Accuracy	92.0%
Cost	4168

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(\left(y + t\right) \cdot a + z \cdot \left(x + y\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;z + \left(a - \frac{y}{\frac{t_1}{b}}\right)\\ \mathbf{elif}\;t_2 \leq 10^{+267}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}} + \left(a - b\right)\\ \end{array} \]

Alternative 3
Accuracy	57.1%
Cost	1892

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ t_3 := \frac{y + t}{\frac{t_2}{a}}\\ t_4 := \frac{x + y}{\frac{t_2}{z}}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+47}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-298}:\\ \;\;\;\;\frac{a - b}{\frac{x + y}{y}}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{-300}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-232}:\\ \;\;\;\;\frac{b}{t_2} \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-219}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-167}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-150}:\\ \;\;\;\;\frac{y \cdot \left(a - b\right)}{x + y}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+241}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 4
Accuracy	71.9%
Cost	1876

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a - \frac{y}{\frac{t_1}{b}}\\ t_3 := t_2 + x \cdot \frac{z}{x + t}\\ t_4 := a + \frac{x + y}{\frac{t_1}{z}}\\ \mathbf{if}\;t \leq -1.1 \cdot 10^{+175}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-75}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-166}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a + z \cdot \left(x + y\right)}{t_1}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-72}:\\ \;\;\;\;z + t_2\\ \mathbf{elif}\;t \leq 6.6 \cdot 10^{+129}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+142}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\left(a + z \cdot \frac{x + y}{t}\right) - b \cdot \frac{y}{t}\\ \end{array} \]

Alternative 5
Accuracy	72.3%
Cost	1876

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := a - \frac{y}{\frac{t_1}{b}}\\ t_3 := t_2 + \frac{z}{1 + \frac{t}{x}}\\ t_4 := a + \frac{x + y}{\frac{t_1}{z}}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+177}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-75}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-166}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a + z \cdot \left(x + y\right)}{t_1}\\ \mathbf{elif}\;t \leq 4.35 \cdot 10^{-72}:\\ \;\;\;\;z + t_2\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+132}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+142}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\left(a + z \cdot \frac{x + y}{t}\right) - b \cdot \frac{y}{t}\\ \end{array} \]

Alternative 6
Accuracy	55.8%
Cost	1496

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-247}:\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-194}:\\ \;\;\;\;\frac{x \cdot z}{t_2}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-135}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-60}:\\ \;\;\;\;\frac{y + t}{\frac{t_2}{a}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	72.7%
Cost	1488

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{-18}:\\ \;\;\;\;a + \frac{x + y}{\frac{t_1}{z}}\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+70}:\\ \;\;\;\;z + \left(a - \frac{y}{\frac{t_1}{b}}\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+92}:\\ \;\;\;\;\frac{\left(y + t\right) \cdot a + z \cdot \left(x + y\right)}{t_1}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+96}:\\ \;\;\;\;\frac{a - b}{\frac{x + y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}} + \left(a - b\right)\\ \end{array} \]

Alternative 8
Accuracy	73.2%
Cost	1224

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{-16}:\\ \;\;\;\;a + \frac{x + y}{\frac{t_1}{z}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+96}:\\ \;\;\;\;z + \left(a - \frac{y}{\frac{t_1}{b}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{x + \left(y + t\right)}{x + y}} + \left(a - b\right)\\ \end{array} \]

Alternative 9
Accuracy	69.1%
Cost	1097

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+49} \lor \neg \left(z \leq 1.95 \cdot 10^{+241}\right):\\ \;\;\;\;\frac{x + y}{\frac{t_1}{z}}\\ \mathbf{else}:\\ \;\;\;\;z + \left(a - \frac{y}{\frac{t_1}{b}}\right)\\ \end{array} \]

Alternative 10
Accuracy	74.2%
Cost	1097

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;z \leq -5 \cdot 10^{-16} \lor \neg \left(z \leq 5.8 \cdot 10^{+69}\right):\\ \;\;\;\;a + \frac{x + y}{\frac{t_1}{z}}\\ \mathbf{else}:\\ \;\;\;\;z + \left(a - \frac{y}{\frac{t_1}{b}}\right)\\ \end{array} \]

Alternative 11
Accuracy	56.0%
Cost	981

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-247}:\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-194}:\\ \;\;\;\;\frac{x \cdot z}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-171} \lor \neg \left(y \leq 6 \cdot 10^{-136}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 12
Accuracy	43.0%
Cost	856

\[\begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+90}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+35}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{-67}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-297}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-258}:\\ \;\;\;\;-b\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-31}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 13
Accuracy	43.1%
Cost	720

\[\begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-77}:\\ \;\;\;\;a - b\\ \mathbf{elif}\;a \leq 2.95 \cdot 10^{-297}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-253}:\\ \;\;\;\;-b\\ \mathbf{elif}\;a \leq 2 \cdot 10^{-148}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a - b\\ \end{array} \]

Alternative 14
Accuracy	56.0%
Cost	713

\[\begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-109} \lor \neg \left(y \leq 1.1 \cdot 10^{-258}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a - b \cdot \frac{y}{t}\\ \end{array} \]

Alternative 15
Accuracy	43.9%
Cost	592

\[\begin{array}{l} \mathbf{if}\;a \leq -2.1 \cdot 10^{+90}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+31}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq -3.4 \cdot 10^{-67}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 8.4 \cdot 10^{-32}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 16
Accuracy	56.0%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-166} \lor \neg \left(y \leq 4 \cdot 10^{-260}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 17
Accuracy	32.2%
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023137 
(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)))