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

Average Accuracy: 58.8% → 87.7%

Time: 39.2s

Precision: binary64

Cost: 2244

Math

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

↓

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{+145}:\\ \;\;\;\;z + \left(\left(\frac{y}{x} \cdot \left(a - \left(b - z\right)\right) + \frac{a}{x} \cdot t\right) - \frac{z}{x} \cdot \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z - b}{\frac{t_1}{y}} + \left(\frac{x \cdot z}{t_1} + \frac{a}{\frac{t_1}{y + t}}\right)\\ \end{array} \]

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 (+ y (+ x t))))
   (if (<= x -1.15e+145)
     (+ z (- (+ (* (/ y x) (- a (- b z))) (* (/ a x) t)) (* (/ z x) (+ y t))))
     (+ (/ (- z b) (/ t_1 y)) (+ (/ (* x z) t_1) (/ a (/ t_1 (+ 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 = y + (x + t);
	double tmp;
	if (x <= -1.15e+145) {
		tmp = z + ((((y / x) * (a - (b - z))) + ((a / x) * t)) - ((z / x) * (y + t)));
	} else {
		tmp = ((z - b) / (t_1 / y)) + (((x * z) / t_1) + (a / (t_1 / (y + t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
end function

↓

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (x + t)
    if (x <= (-1.15d+145)) then
        tmp = z + ((((y / x) * (a - (b - z))) + ((a / x) * t)) - ((z / x) * (y + t)))
    else
        tmp = ((z - b) / (t_1 / y)) + (((x * z) / t_1) + (a / (t_1 / (y + t))))
    end if
    code = tmp
end function

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 tmp;
	if (x <= -1.15e+145) {
		tmp = z + ((((y / x) * (a - (b - z))) + ((a / x) * t)) - ((z / x) * (y + t)));
	} else {
		tmp = ((z - b) / (t_1 / y)) + (((x * z) / t_1) + (a / (t_1 / (y + t))));
	}
	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)
	tmp = 0
	if x <= -1.15e+145:
		tmp = z + ((((y / x) * (a - (b - z))) + ((a / x) * t)) - ((z / x) * (y + t)))
	else:
		tmp = ((z - b) / (t_1 / y)) + (((x * z) / t_1) + (a / (t_1 / (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(y + Float64(x + t))
	tmp = 0.0
	if (x <= -1.15e+145)
		tmp = Float64(z + Float64(Float64(Float64(Float64(y / x) * Float64(a - Float64(b - z))) + Float64(Float64(a / x) * t)) - Float64(Float64(z / x) * Float64(y + t))));
	else
		tmp = Float64(Float64(Float64(z - b) / Float64(t_1 / y)) + Float64(Float64(Float64(x * z) / t_1) + Float64(a / Float64(t_1 / Float64(y + t)))));
	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);
	tmp = 0.0;
	if (x <= -1.15e+145)
		tmp = z + ((((y / x) * (a - (b - z))) + ((a / x) * t)) - ((z / x) * (y + t)));
	else
		tmp = ((z - b) / (t_1 / y)) + (((x * z) / t_1) + (a / (t_1 / (y + t))));
	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]}, If[LessEqual[x, -1.15e+145], N[(z + N[(N[(N[(N[(y / x), $MachinePrecision] * N[(a - N[(b - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(a / x), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision] - N[(N[(z / x), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - b), $MachinePrecision] / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x * z), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	58.8%
Target	82.4%
Herbie	87.7%

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

Derivation

1. Split input into 2 regimes

2. if x < -1.15e145

   1. Initial program 41.7%

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

   2. Simplified 41.7%

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

      [Start] 41.7	\[ \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Taylor expanded in x around inf 53.6%

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

   4. Simplified 74.7%

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

      [Start] 53.6	\[ \left(z + \left(\frac{y \cdot \left(\left(a + z\right) - b\right)}{x} + \frac{a \cdot t}{x}\right)\right) - \frac{z \cdot \left(y + t\right)}{x} \]
      associate--l+ [=>] 54.2	\[ \color{blue}{z + \left(\left(\frac{y \cdot \left(\left(a + z\right) - b\right)}{x} + \frac{a \cdot t}{x}\right) - \frac{z \cdot \left(y + t\right)}{x}\right)} \]
      associate-/l* [=>] 58.7	\[ z + \left(\left(\color{blue}{\frac{y}{\frac{x}{\left(a + z\right) - b}}} + \frac{a \cdot t}{x}\right) - \frac{z \cdot \left(y + t\right)}{x}\right) \]
      associate-/r/ [=>] 57.8	\[ z + \left(\left(\color{blue}{\frac{y}{x} \cdot \left(\left(a + z\right) - b\right)} + \frac{a \cdot t}{x}\right) - \frac{z \cdot \left(y + t\right)}{x}\right) \]
      associate--l+ [=>] 57.8	\[ z + \left(\left(\frac{y}{x} \cdot \color{blue}{\left(a + \left(z - b\right)\right)} + \frac{a \cdot t}{x}\right) - \frac{z \cdot \left(y + t\right)}{x}\right) \]
      associate-/l* [=>] 61.8	\[ z + \left(\left(\frac{y}{x} \cdot \left(a + \left(z - b\right)\right) + \color{blue}{\frac{a}{\frac{x}{t}}}\right) - \frac{z \cdot \left(y + t\right)}{x}\right) \]
      associate-/r/ [=>] 61.7	\[ z + \left(\left(\frac{y}{x} \cdot \left(a + \left(z - b\right)\right) + \color{blue}{\frac{a}{x} \cdot t}\right) - \frac{z \cdot \left(y + t\right)}{x}\right) \]
      associate-/l* [=>] 74.6	\[ z + \left(\left(\frac{y}{x} \cdot \left(a + \left(z - b\right)\right) + \frac{a}{x} \cdot t\right) - \color{blue}{\frac{z}{\frac{x}{y + t}}}\right) \]
      associate-/r/ [=>] 74.7	\[ z + \left(\left(\frac{y}{x} \cdot \left(a + \left(z - b\right)\right) + \frac{a}{x} \cdot t\right) - \color{blue}{\frac{z}{x} \cdot \left(y + t\right)}\right) \]
      +-commutative [=>] 74.7	\[ z + \left(\left(\frac{y}{x} \cdot \left(a + \left(z - b\right)\right) + \frac{a}{x} \cdot t\right) - \frac{z}{x} \cdot \color{blue}{\left(t + y\right)}\right) \]

   if -1.15e145 < x

   1. Initial program 61.5%

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

   2. Simplified 61.5%

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

      [Start] 61.5	\[ \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]

   3. Taylor expanded in a around inf 61.5%

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

   4. Simplified 89.7%

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

      [Start] 61.5	\[ \frac{\left(z - b\right) \cdot y}{y + \left(t + x\right)} + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      associate-/l* [=>] 71.6	\[ \color{blue}{\frac{z - b}{\frac{y + \left(t + x\right)}{y}}} + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      associate-/l* [=>] 89.7	\[ \frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \color{blue}{\frac{a}{\frac{y + \left(t + x\right)}{y + t}}}\right) \]
      +-commutative [=>] 89.7	\[ \frac{z - b}{\frac{y + \left(t + x\right)}{y}} + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a}{\frac{y + \left(t + x\right)}{\color{blue}{t + y}}}\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{+145}:\\ \;\;\;\;z + \left(\left(\frac{y}{x} \cdot \left(a - \left(b - z\right)\right) + \frac{a}{x} \cdot t\right) - \frac{z}{x} \cdot \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z - b}{\frac{y + \left(x + t\right)}{y}} + \left(\frac{x \cdot z}{y + \left(x + t\right)} + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	88.1%
Cost	4169

\[\begin{array}{l} t_1 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(x + y\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+234}\right):\\ \;\;\;\;z - \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	55.9%
Cost	2681

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := z - \left(b - a\right)\\ t_3 := y \cdot \frac{a - \left(b - z\right)}{t_1}\\ t_4 := a + \left(x \cdot \frac{z}{t} - \frac{a}{\frac{t}{x}}\right)\\ t_5 := z \cdot \left(x + y\right)\\ t_6 := x + \left(y + t\right)\\ t_7 := \frac{1}{t_6} \cdot \left(a \cdot \left(y + t\right) + t_5\right)\\ t_8 := \frac{x \cdot z - y \cdot \left(b - \left(z + a\right)\right)}{x + y}\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{+183}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-38}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq -8 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-107}:\\ \;\;\;\;\frac{a}{\frac{t_6}{y + t}}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-155}:\\ \;\;\;\;\frac{t_5 - y \cdot b}{t_1}\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-306}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-137}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-44}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 76000000000:\\ \;\;\;\;t_7\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+171}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{+248} \lor \neg \left(t \leq 1.35 \cdot 10^{+270}\right):\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\frac{z - b}{\frac{y + t}{y}}\\ \end{array} \]

Alternative 3
Accuracy	56.7%
Cost	2284

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ t_3 := y \cdot \frac{a - \left(b - z\right)}{t_1}\\ t_4 := z - \left(b - a\right)\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{-7}:\\ \;\;\;\;\frac{z}{\frac{t_1}{x + y}}\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-65}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-236}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-280}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-251}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{t_1}\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-146}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-25}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 41000:\\ \;\;\;\;\frac{y}{\frac{y + t}{t_4}}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+59}:\\ \;\;\;\;\frac{x \cdot z + a \cdot t}{x + t}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{+105}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \end{array} \]

Alternative 4
Accuracy	56.0%
Cost	2156

\[\begin{array}{l} t_1 := z - \left(b - a\right)\\ t_2 := t + \left(x + y\right)\\ t_3 := \frac{x \cdot z + a \cdot t}{x + t}\\ t_4 := y + \left(x + t\right)\\ t_5 := y \cdot \frac{-b}{t_4}\\ \mathbf{if}\;z \leq -0.00033:\\ \;\;\;\;\frac{z}{\frac{t_4}{x + y}}\\ \mathbf{elif}\;z \leq -2.85 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-241}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-284}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-307}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-243}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-169}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_2}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{+74}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.25 \cdot 10^{+117}:\\ \;\;\;\;\frac{y}{\frac{y + t}{t_1}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{t_2}\\ \end{array} \]

Alternative 5
Accuracy	56.1%
Cost	2156

\[\begin{array}{l} t_1 := z - \left(b - a\right)\\ t_2 := \frac{x \cdot z + a \cdot t}{x + t}\\ t_3 := t + \left(x + y\right)\\ t_4 := y + \left(x + t\right)\\ \mathbf{if}\;z \leq -0.0165:\\ \;\;\;\;\frac{z}{\frac{t_4}{x + y}}\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-241}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-282}:\\ \;\;\;\;y \cdot \frac{-b}{t_4}\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-244}:\\ \;\;\;\;\frac{z - b}{\frac{t_4}{y}}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-169}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_3}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+116}:\\ \;\;\;\;\frac{y}{\frac{y + t}{t_1}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{t_3}\\ \end{array} \]

Alternative 6
Accuracy	56.7%
Cost	2016

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := y \cdot \frac{a - \left(b - z\right)}{t_1}\\ t_3 := \frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{if}\;z \leq -7.2 \cdot 10^{-7}:\\ \;\;\;\;\frac{z}{\frac{t_1}{x + y}}\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-236}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-278}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-294}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-253}:\\ \;\;\;\;\frac{y \cdot \left(\left(z + a\right) - b\right)}{t_1}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-138}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-64}:\\ \;\;\;\;\frac{a \cdot t - y \cdot \left(b - \left(z + a\right)\right)}{y + t}\\ \mathbf{elif}\;z \leq 1.01 \cdot 10^{+40}:\\ \;\;\;\;\frac{x \cdot z + a \cdot t}{x + t}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \end{array} \]

Alternative 7
Accuracy	56.7%
Cost	1888

\[\begin{array}{l} t_1 := z - \left(b - a\right)\\ t_2 := y + \left(x + t\right)\\ t_3 := y \cdot \frac{a - \left(b - z\right)}{t_2}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{-6}:\\ \;\;\;\;\frac{z}{\frac{t_2}{x + y}}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-70}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-236}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;z \leq 10^{-145}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3550000:\\ \;\;\;\;\frac{y}{\frac{y + t}{t_1}}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+52}:\\ \;\;\;\;\frac{x \cdot z + a \cdot t}{x + t}\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+111}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \end{array} \]

Alternative 8
Accuracy	58.2%
Cost	1756

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := y \cdot \frac{a - \left(b - z\right)}{t_1}\\ \mathbf{if}\;z \leq -0.00019:\\ \;\;\;\;\frac{z}{\frac{t_1}{x + y}}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-127}:\\ \;\;\;\;z - \left(b - a\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-298}:\\ \;\;\;\;\frac{y \cdot \left(a - b\right) + a \cdot t}{t_1}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-139}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-27}:\\ \;\;\;\;\frac{x \cdot z - y \cdot \left(b - \left(z + a\right)\right)}{x + y}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{+53}:\\ \;\;\;\;\frac{x \cdot z + a \cdot t}{x + t}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{t + \left(x + y\right)}\\ \end{array} \]

Alternative 9
Accuracy	56.7%
Cost	1500

\[\begin{array}{l} t_1 := z - \left(b - a\right)\\ t_2 := y \cdot \frac{z - b}{y + t}\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+117}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-239}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-91}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-61}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{\left(-x\right) - t}{x}}\\ \end{array} \]

Alternative 10
Accuracy	57.2%
Cost	1500

\[\begin{array}{l} t_1 := z - \left(b - a\right)\\ t_2 := \frac{z - b}{\frac{y + t}{y}}\\ \mathbf{if}\;x \leq -1.42 \cdot 10^{+122}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-61}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{\left(-x\right) - t}{x}}\\ \end{array} \]

Alternative 11
Accuracy	57.3%
Cost	1500

\[\begin{array}{l} t_1 := z - \left(b - a\right)\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-240}:\\ \;\;\;\;\frac{z - b}{\frac{y + t}{y}}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-80}:\\ \;\;\;\;y \cdot \frac{-b}{y + \left(x + t\right)}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-61}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{\left(-x\right) - t}{x}}\\ \end{array} \]

Alternative 12
Accuracy	57.3%
Cost	1500

\[\begin{array}{l} t_1 := z - \left(b - a\right)\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{+115}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-240}:\\ \;\;\;\;\frac{z - b}{\frac{y + t}{y}}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-80}:\\ \;\;\;\;\frac{-y}{\frac{t + \left(x + y\right)}{b}}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-61}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{\left(-x\right) - t}{x}}\\ \end{array} \]

Alternative 13
Accuracy	57.1%
Cost	1500

\[\begin{array}{l} t_1 := z - \left(b - a\right)\\ t_2 := t + \left(x + y\right)\\ \mathbf{if}\;x \leq -5.2 \cdot 10^{+118}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-263}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-235}:\\ \;\;\;\;\frac{z - b}{\frac{y + t}{y}}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-80}:\\ \;\;\;\;\frac{-y}{\frac{t_2}{b}}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{-61}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_2}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{\left(-x\right) - t}{x}}\\ \end{array} \]

Alternative 14
Accuracy	56.2%
Cost	1496

\[\begin{array}{l} t_1 := z - \left(b - a\right)\\ t_2 := t + \left(x + y\right)\\ t_3 := z \cdot \frac{x + y}{t_2}\\ \mathbf{if}\;z \leq -0.0115:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-293}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-246}:\\ \;\;\;\;\frac{-y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-169}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_2}\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 15
Accuracy	56.2%
Cost	1496

\[\begin{array}{l} t_1 := z - \left(b - a\right)\\ t_2 := t + \left(x + y\right)\\ t_3 := y + \left(x + t\right)\\ \mathbf{if}\;z \leq -0.0165:\\ \;\;\;\;\frac{z}{\frac{t_3}{x + y}}\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-133}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-293}:\\ \;\;\;\;\frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-246}:\\ \;\;\;\;\frac{-y \cdot b}{t_3}\\ \mathbf{elif}\;z \leq 10^{-168}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_2}\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{t_2}\\ \end{array} \]

Alternative 16
Accuracy	62.7%
Cost	1492

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := y \cdot \frac{a - \left(b - z\right)}{t_1}\\ \mathbf{if}\;y \leq -8.8 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-236}:\\ \;\;\;\;\frac{x \cdot z + a \cdot t}{x + t}\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-92}:\\ \;\;\;\;\frac{y \cdot \left(a - b\right) + a \cdot t}{t_1}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-10}:\\ \;\;\;\;z \cdot \left(\left(x + y\right) \cdot \frac{1}{t_1}\right)\\ \mathbf{elif}\;y \leq 1400:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z - \left(b - a\right)\\ \end{array} \]

Alternative 17
Accuracy	32.6%
Cost	1384

\[\begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+223}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+73}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{+21}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-40}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-144}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-282}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+49}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+145}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{+222}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+263}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 18
Accuracy	56.1%
Cost	1368

\[\begin{array}{l} t_1 := z - \left(b - a\right)\\ \mathbf{if}\;y \leq -9.4 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-268}:\\ \;\;\;\;\frac{-z}{\frac{\left(-x\right) - t}{x}}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-149}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-47}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-32}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 0.00082:\\ \;\;\;\;z \cdot \left(\frac{y}{t} + \frac{x}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 19
Accuracy	56.5%
Cost	1240

\[\begin{array}{l} t_1 := z \cdot \frac{x}{x + t}\\ t_2 := z - \left(b - a\right)\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-150}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-32}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 0.00102:\\ \;\;\;\;z \cdot \frac{y}{y + t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 20
Accuracy	56.1%
Cost	1240

\[\begin{array}{l} t_1 := z \cdot \frac{x}{x + t}\\ t_2 := z - \left(b - a\right)\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{-52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-270}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-150}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-32}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 0.00082:\\ \;\;\;\;\frac{z \cdot \left(x + y\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 21
Accuracy	56.1%
Cost	1240

\[\begin{array}{l} t_1 := z \cdot \frac{x}{x + t}\\ t_2 := z - \left(b - a\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-276}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-150}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-32}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 0.00082:\\ \;\;\;\;\frac{x + y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 22
Accuracy	56.1%
Cost	1240

\[\begin{array}{l} t_1 := z - \left(b - a\right)\\ \mathbf{if}\;y \leq -4.7 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-268}:\\ \;\;\;\;\frac{-z}{\frac{\left(-x\right) - t}{x}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-149}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-48}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-32}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 0.00082:\\ \;\;\;\;\frac{x + y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 23
Accuracy	57.1%
Cost	1236

\[\begin{array}{l} t_1 := z - \left(b - a\right)\\ t_2 := t + \left(x + y\right)\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+60}:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_2}\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-204}:\\ \;\;\;\;\frac{z - b}{\frac{y + t}{y}}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-210}:\\ \;\;\;\;z \cdot \frac{x + y}{t_2}\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{z - b}{y + t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 24
Accuracy	55.5%
Cost	1113

\[\begin{array}{l} t_1 := z \cdot \frac{x}{x + t}\\ t_2 := z - \left(b - a\right)\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{-54}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{-150}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 0.00092:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6800000 \lor \neg \left(y \leq 5.3 \cdot 10^{+65}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z - b\\ \end{array} \]

Alternative 25
Accuracy	46.3%
Cost	984

\[\begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+63}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-117}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-80}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-47}:\\ \;\;\;\;z - b\\ \mathbf{elif}\;t \leq 54000000000:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{+48}:\\ \;\;\;\;z - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 26
Accuracy	55.7%
Cost	849

\[\begin{array}{l} t_1 := z - \left(b - a\right)\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-279}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-247} \lor \neg \left(y \leq 3.5 \cdot 10^{-108}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 27
Accuracy	32.2%
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023133 
(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)))