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

Average Accuracy: 58.1% → 89.9%

Time: 22.9s

Precision: binary64

Cost: 2377

Math

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

↓

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+126} \lor \neg \left(y \leq 2 \cdot 10^{+138}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - b\right)}{t_1} + \left(\frac{z}{\frac{t_1}{x}} + \frac{a}{\frac{t_1}{y + t}}\right)\\ \end{array} \]

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 (or (<= y -5.8e+126) (not (<= y 2e+138)))
     (- (+ z a) b)
     (+ (/ (* y (- z b)) t_1) (+ (/ z (/ t_1 x)) (/ 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 ((y <= -5.8e+126) || !(y <= 2e+138)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((y * (z - b)) / t_1) + ((z / (t_1 / x)) + (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 ((y <= (-5.8d+126)) .or. (.not. (y <= 2d+138))) then
        tmp = (z + a) - b
    else
        tmp = ((y * (z - b)) / t_1) + ((z / (t_1 / x)) + (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 ((y <= -5.8e+126) || !(y <= 2e+138)) {
		tmp = (z + a) - b;
	} else {
		tmp = ((y * (z - b)) / t_1) + ((z / (t_1 / x)) + (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 (y <= -5.8e+126) or not (y <= 2e+138):
		tmp = (z + a) - b
	else:
		tmp = ((y * (z - b)) / t_1) + ((z / (t_1 / x)) + (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 ((y <= -5.8e+126) || !(y <= 2e+138))
		tmp = Float64(Float64(z + a) - b);
	else
		tmp = Float64(Float64(Float64(y * Float64(z - b)) / t_1) + Float64(Float64(z / Float64(t_1 / x)) + 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 ((y <= -5.8e+126) || ~((y <= 2e+138)))
		tmp = (z + a) - b;
	else
		tmp = ((y * (z - b)) / t_1) + ((z / (t_1 / x)) + (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[Or[LessEqual[y, -5.8e+126], N[Not[LessEqual[y, 2e+138]], $MachinePrecision]], N[(N[(z + a), $MachinePrecision] - b), $MachinePrecision], N[(N[(N[(y * N[(z - b), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision] + N[(N[(z / N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision] + N[(a / N[(t$95$1 / N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Target

Original	58.1%
Target	82.4%
Herbie	89.9%

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

Derivation

1. Split input into 2 regimes

2. if y < -5.79999999999999971e126 or 2.0000000000000001e138 < y

   1. Initial program 25.2%

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

   2. Simplified 25.2%

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

      [Start] 25.2	\[ \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
      sub-neg [=>] 25.2	\[ \frac{\color{blue}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) + \left(-y \cdot b\right)}}{\left(x + t\right) + y} \]
      +-commutative [=>] 25.2	\[ \frac{\color{blue}{\left(\left(t + y\right) \cdot a + \left(x + y\right) \cdot z\right)} + \left(-y \cdot b\right)}{\left(x + t\right) + y} \]
      associate-+l+ [=>] 25.2	\[ \frac{\color{blue}{\left(t + y\right) \cdot a + \left(\left(x + y\right) \cdot z + \left(-y \cdot b\right)\right)}}{\left(x + t\right) + y} \]
      fma-def [=>] 25.2	\[ \frac{\color{blue}{\mathsf{fma}\left(t + y, a, \left(x + y\right) \cdot z + \left(-y \cdot b\right)\right)}}{\left(x + t\right) + y} \]
      +-commutative [=>] 25.2	\[ \frac{\mathsf{fma}\left(\color{blue}{y + t}, a, \left(x + y\right) \cdot z + \left(-y \cdot b\right)\right)}{\left(x + t\right) + y} \]
      *-commutative [=>] 25.2	\[ \frac{\mathsf{fma}\left(y + t, a, \color{blue}{z \cdot \left(x + y\right)} + \left(-y \cdot b\right)\right)}{\left(x + t\right) + y} \]
      distribute-rgt-in [=>] 25.2	\[ \frac{\mathsf{fma}\left(y + t, a, \color{blue}{\left(x \cdot z + y \cdot z\right)} + \left(-y \cdot b\right)\right)}{\left(x + t\right) + y} \]
      associate-+l+ [=>] 25.2	\[ \frac{\mathsf{fma}\left(y + t, a, \color{blue}{x \cdot z + \left(y \cdot z + \left(-y \cdot b\right)\right)}\right)}{\left(x + t\right) + y} \]
      fma-def [=>] 25.2	\[ \frac{\mathsf{fma}\left(y + t, a, \color{blue}{\mathsf{fma}\left(x, z, y \cdot z + \left(-y \cdot b\right)\right)}\right)}{\left(x + t\right) + y} \]
      sub-neg [<=] 25.2	\[ \frac{\mathsf{fma}\left(y + t, a, \mathsf{fma}\left(x, z, \color{blue}{y \cdot z - y \cdot b}\right)\right)}{\left(x + t\right) + y} \]
      distribute-lft-out-- [=>] 25.2	\[ \frac{\mathsf{fma}\left(y + t, a, \mathsf{fma}\left(x, z, \color{blue}{y \cdot \left(z - b\right)}\right)\right)}{\left(x + t\right) + y} \]
      +-commutative [=>] 25.2	\[ \frac{\mathsf{fma}\left(y + t, a, \mathsf{fma}\left(x, z, y \cdot \left(z - b\right)\right)\right)}{\color{blue}{y + \left(x + t\right)}} \]

   3. Taylor expanded in y around inf 81.7%

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

   4. Simplified 81.7%

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

      [Start] 81.7	\[ \left(a + z\right) - b \]
      +-commutative [=>] 81.7	\[ \color{blue}{\left(z + a\right)} - b \]

   if -5.79999999999999971e126 < y < 2.0000000000000001e138

   1. Initial program 70.9%

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

   2. Simplified 70.9%

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

      [Start] 70.9	\[ \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \]
      sub-neg [=>] 70.9	\[ \frac{\color{blue}{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) + \left(-y \cdot b\right)}}{\left(x + t\right) + y} \]
      +-commutative [=>] 70.9	\[ \frac{\color{blue}{\left(\left(t + y\right) \cdot a + \left(x + y\right) \cdot z\right)} + \left(-y \cdot b\right)}{\left(x + t\right) + y} \]
      associate-+l+ [=>] 70.9	\[ \frac{\color{blue}{\left(t + y\right) \cdot a + \left(\left(x + y\right) \cdot z + \left(-y \cdot b\right)\right)}}{\left(x + t\right) + y} \]
      fma-def [=>] 70.9	\[ \frac{\color{blue}{\mathsf{fma}\left(t + y, a, \left(x + y\right) \cdot z + \left(-y \cdot b\right)\right)}}{\left(x + t\right) + y} \]
      +-commutative [=>] 70.9	\[ \frac{\mathsf{fma}\left(\color{blue}{y + t}, a, \left(x + y\right) \cdot z + \left(-y \cdot b\right)\right)}{\left(x + t\right) + y} \]
      *-commutative [=>] 70.9	\[ \frac{\mathsf{fma}\left(y + t, a, \color{blue}{z \cdot \left(x + y\right)} + \left(-y \cdot b\right)\right)}{\left(x + t\right) + y} \]
      distribute-rgt-in [=>] 70.9	\[ \frac{\mathsf{fma}\left(y + t, a, \color{blue}{\left(x \cdot z + y \cdot z\right)} + \left(-y \cdot b\right)\right)}{\left(x + t\right) + y} \]
      associate-+l+ [=>] 70.9	\[ \frac{\mathsf{fma}\left(y + t, a, \color{blue}{x \cdot z + \left(y \cdot z + \left(-y \cdot b\right)\right)}\right)}{\left(x + t\right) + y} \]
      fma-def [=>] 70.9	\[ \frac{\mathsf{fma}\left(y + t, a, \color{blue}{\mathsf{fma}\left(x, z, y \cdot z + \left(-y \cdot b\right)\right)}\right)}{\left(x + t\right) + y} \]
      sub-neg [<=] 70.9	\[ \frac{\mathsf{fma}\left(y + t, a, \mathsf{fma}\left(x, z, \color{blue}{y \cdot z - y \cdot b}\right)\right)}{\left(x + t\right) + y} \]
      distribute-lft-out-- [=>] 70.9	\[ \frac{\mathsf{fma}\left(y + t, a, \mathsf{fma}\left(x, z, \color{blue}{y \cdot \left(z - b\right)}\right)\right)}{\left(x + t\right) + y} \]
      +-commutative [=>] 70.9	\[ \frac{\mathsf{fma}\left(y + t, a, \mathsf{fma}\left(x, z, y \cdot \left(z - b\right)\right)\right)}{\color{blue}{y + \left(x + t\right)}} \]

   3. Taylor expanded in a around inf 70.9%

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

   4. Simplified 93.1%

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

      [Start] 70.9	\[ \frac{\left(z - b\right) \cdot y}{y + \left(t + x\right)} + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      *-commutative [<=] 70.9	\[ \frac{\color{blue}{y \cdot \left(z - b\right)}}{y + \left(t + x\right)} + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      +-commutative [=>] 70.9	\[ \frac{y \cdot \left(z - b\right)}{\color{blue}{\left(t + x\right) + y}} + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      +-commutative [=>] 70.9	\[ \frac{y \cdot \left(z - b\right)}{\color{blue}{\left(x + t\right)} + y} + \left(\frac{z \cdot x}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      associate-/l* [=>] 80.1	\[ \frac{y \cdot \left(z - b\right)}{\left(x + t\right) + y} + \left(\color{blue}{\frac{z}{\frac{y + \left(t + x\right)}{x}}} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      +-commutative [=>] 80.1	\[ \frac{y \cdot \left(z - b\right)}{\left(x + t\right) + y} + \left(\frac{z}{\frac{\color{blue}{\left(t + x\right) + y}}{x}} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      +-commutative [=>] 80.1	\[ \frac{y \cdot \left(z - b\right)}{\left(x + t\right) + y} + \left(\frac{z}{\frac{\color{blue}{\left(x + t\right)} + y}{x}} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) \]
      associate-/l* [=>] 93.1	\[ \frac{y \cdot \left(z - b\right)}{\left(x + t\right) + y} + \left(\frac{z}{\frac{\left(x + t\right) + y}{x}} + \color{blue}{\frac{a}{\frac{y + \left(t + x\right)}{y + t}}}\right) \]
      +-commutative [=>] 93.1	\[ \frac{y \cdot \left(z - b\right)}{\left(x + t\right) + y} + \left(\frac{z}{\frac{\left(x + t\right) + y}{x}} + \frac{a}{\frac{\color{blue}{\left(t + x\right) + y}}{y + t}}\right) \]
      +-commutative [=>] 93.1	\[ \frac{y \cdot \left(z - b\right)}{\left(x + t\right) + y} + \left(\frac{z}{\frac{\left(x + t\right) + y}{x}} + \frac{a}{\frac{\color{blue}{\left(x + t\right)} + y}{y + t}}\right) \]
      +-commutative [=>] 93.1	\[ \frac{y \cdot \left(z - b\right)}{\left(x + t\right) + y} + \left(\frac{z}{\frac{\left(x + t\right) + y}{x}} + \frac{a}{\frac{\left(x + t\right) + y}{\color{blue}{t + y}}}\right) \]

3. Recombined 2 regimes into one program.

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+126} \lor \neg \left(y \leq 2 \cdot 10^{+138}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - b\right)}{y + \left(x + t\right)} + \left(\frac{z}{\frac{y + \left(x + t\right)}{x}} + \frac{a}{\frac{y + \left(x + t\right)}{y + t}}\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	88.2%
Cost	4169

\[\begin{array}{l} t_1 := \frac{\left(a \cdot \left(y + t\right) + z \cdot \left(y + x\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+261}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 2
Accuracy	58.5%
Cost	2144

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ t_3 := y + \left(x + t\right)\\ t_4 := \frac{a \cdot \left(y + t\right) + z \cdot \left(y + x\right)}{t_3}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+67}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.52 \cdot 10^{-61}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 2.15 \cdot 10^{-174}:\\ \;\;\;\;\frac{z}{\frac{t_3}{y + x}}\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-89}:\\ \;\;\;\;\frac{z \cdot x - y \cdot b}{t_3}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+161}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	58.4%
Cost	2144

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ t_3 := y + \left(x + t\right)\\ \mathbf{if}\;a \leq -4.3 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{+63}:\\ \;\;\;\;\frac{y \cdot \left(z - b\right)}{t_3} + \left(z + \frac{y}{\frac{y + x}{a}}\right)\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-162}:\\ \;\;\;\;\frac{y \cdot t_1}{t_3}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-176}:\\ \;\;\;\;\frac{z}{\frac{t_3}{y + x}}\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-89}:\\ \;\;\;\;\frac{z \cdot x - y \cdot b}{t_3}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+161}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) + z \cdot \left(y + x\right)}{t_3}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	55.2%
Cost	1892

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := z \cdot \frac{y + x}{t + \left(y + x\right)}\\ t_3 := \left(y + t\right) \cdot \frac{a}{x + \left(y + t\right)}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+205}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{+59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-98}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-100}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-225}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 520:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Accuracy	57.9%
Cost	1496

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ t_3 := x + \left(y + t\right)\\ t_4 := \frac{a}{\frac{t_3}{y + t}}\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+104}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -47000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2800000:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_3}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-173}:\\ \;\;\;\;\frac{z}{\frac{t_1}{y + x}}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-89}:\\ \;\;\;\;\frac{y \cdot t_2}{t_1}\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 6
Accuracy	58.2%
Cost	1496

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \left(z + a\right) - b\\ t_3 := x + \left(y + t\right)\\ t_4 := \frac{a}{\frac{t_3}{y + t}}\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+104}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -65000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4400000:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_3}\\ \mathbf{elif}\;a \leq 4.3 \cdot 10^{-175}:\\ \;\;\;\;\frac{z}{\frac{t_1}{y + x}}\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-85}:\\ \;\;\;\;\frac{z \cdot x - y \cdot b}{t_1}\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 7
Accuracy	51.9%
Cost	1364

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := \left(y + t\right) \cdot \frac{a}{x + \left(y + t\right)}\\ \mathbf{if}\;a \leq -9.8 \cdot 10^{+104}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-174}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{-89}:\\ \;\;\;\;b \cdot \frac{-y}{y + \left(x + t\right)}\\ \mathbf{elif}\;a \leq 2.65 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Accuracy	59.0%
Cost	1364

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := x + \left(y + t\right)\\ t_3 := \frac{a}{\frac{t_2}{y + t}}\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+104}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -66000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3700000:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_2}\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{-57}:\\ \;\;\;\;z \cdot \frac{y + x}{t + \left(y + x\right)}\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Accuracy	59.1%
Cost	1364

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ t_2 := x + \left(y + t\right)\\ t_3 := \frac{a}{\frac{t_2}{y + t}}\\ \mathbf{if}\;a \leq -5.4 \cdot 10^{+104}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -52000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -57000:\\ \;\;\;\;\left(y + t\right) \cdot \frac{a}{t_2}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-58}:\\ \;\;\;\;\frac{z}{\frac{y + \left(x + t\right)}{y + x}}\\ \mathbf{elif}\;a \leq 1.62 \cdot 10^{+35}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Accuracy	52.4%
Cost	976

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+38}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-297}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 8 \cdot 10^{+251}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{y + t}\\ \end{array} \]

Alternative 11
Accuracy	53.8%
Cost	976

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+38}:\\ \;\;\;\;a + x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-297}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+254}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{y + t}\\ \end{array} \]

Alternative 12
Accuracy	52.5%
Cost	848

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+38}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -1.02 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{-297}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 2.65 \cdot 10^{+259}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{t}\\ \end{array} \]

Alternative 13
Accuracy	52.4%
Cost	848

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;t \leq -3.3 \cdot 10^{+38}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.45 \cdot 10^{-297}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 1.32 \cdot 10^{+258}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{y}}\\ \end{array} \]

Alternative 14
Accuracy	42.8%
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{-75}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-18}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+72}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+144}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 15
Accuracy	32.5%
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023129 
(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)))