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

Average Error: 26.7 → 6.4

Time: 17.9s

Precision: binary64

Cost: 5320

Math

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

↓

\[\begin{array}{l} t_1 := \frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_2 := y + \left(t + x\right)\\ t_3 := a \cdot \left(\frac{y}{t_2} + \frac{t}{t_2}\right)\\ t_4 := \left(z + t_3\right) - b\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+239}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+215}:\\ \;\;\;\;\left(\frac{\left(y + x\right) \cdot z}{t_2} + t_3\right) - \frac{y \cdot b}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

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) z) (* (+ t y) a)) (* y b)) (+ (+ x t) y)))
        (t_2 (+ y (+ t x)))
        (t_3 (* a (+ (/ y t_2) (/ t t_2))))
        (t_4 (- (+ z t_3) b)))
   (if (<= t_1 -5e+239)
     t_4
     (if (<= t_1 2e+215)
       (- (+ (/ (* (+ y x) z) t_2) t_3) (/ (* y b) t_2))
       t_4))))

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) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = y + (t + x);
	double t_3 = a * ((y / t_2) + (t / t_2));
	double t_4 = (z + t_3) - b;
	double tmp;
	if (t_1 <= -5e+239) {
		tmp = t_4;
	} else if (t_1 <= 2e+215) {
		tmp = ((((y + x) * z) / t_2) + t_3) - ((y * b) / t_2);
	} else {
		tmp = t_4;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
    t_2 = y + (t + x)
    t_3 = a * ((y / t_2) + (t / t_2))
    t_4 = (z + t_3) - b
    if (t_1 <= (-5d+239)) then
        tmp = t_4
    else if (t_1 <= 2d+215) then
        tmp = ((((y + x) * z) / t_2) + t_3) - ((y * b) / t_2)
    else
        tmp = t_4
    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 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	double t_2 = y + (t + x);
	double t_3 = a * ((y / t_2) + (t / t_2));
	double t_4 = (z + t_3) - b;
	double tmp;
	if (t_1 <= -5e+239) {
		tmp = t_4;
	} else if (t_1 <= 2e+215) {
		tmp = ((((y + x) * z) / t_2) + t_3) - ((y * b) / t_2);
	} else {
		tmp = t_4;
	}
	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 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y)
	t_2 = y + (t + x)
	t_3 = a * ((y / t_2) + (t / t_2))
	t_4 = (z + t_3) - b
	tmp = 0
	if t_1 <= -5e+239:
		tmp = t_4
	elif t_1 <= 2e+215:
		tmp = ((((y + x) * z) / t_2) + t_3) - ((y * b) / t_2)
	else:
		tmp = t_4
	return tmp

Julia

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

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(Float64(Float64(x + y) * z) + Float64(Float64(t + y) * a)) - Float64(y * b)) / Float64(Float64(x + t) + y))
	t_2 = Float64(y + Float64(t + x))
	t_3 = Float64(a * Float64(Float64(y / t_2) + Float64(t / t_2)))
	t_4 = Float64(Float64(z + t_3) - b)
	tmp = 0.0
	if (t_1 <= -5e+239)
		tmp = t_4;
	elseif (t_1 <= 2e+215)
		tmp = Float64(Float64(Float64(Float64(Float64(y + x) * z) / t_2) + t_3) - Float64(Float64(y * b) / t_2));
	else
		tmp = t_4;
	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 = ((((x + y) * z) + ((t + y) * a)) - (y * b)) / ((x + t) + y);
	t_2 = y + (t + x);
	t_3 = a * ((y / t_2) + (t / t_2));
	t_4 = (z + t_3) - b;
	tmp = 0.0;
	if (t_1 <= -5e+239)
		tmp = t_4;
	elseif (t_1 <= 2e+215)
		tmp = ((((y + x) * z) / t_2) + t_3) - ((y * b) / t_2);
	else
		tmp = t_4;
	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[(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]}, Block[{t$95$2 = N[(y + N[(t + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(y / t$95$2), $MachinePrecision] + N[(t / t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(z + t$95$3), $MachinePrecision] - b), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+239], t$95$4, If[LessEqual[t$95$1, 2e+215], N[(N[(N[(N[(N[(y + x), $MachinePrecision] * z), $MachinePrecision] / t$95$2), $MachinePrecision] + t$95$3), $MachinePrecision] - N[(N[(y * b), $MachinePrecision] / t$95$2), $MachinePrecision]), $MachinePrecision], t$95$4]]]]]]

Target

Original	26.7
Target	11.6
Herbie	6.4

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

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)) < -5.00000000000000007e239 or 1.99999999999999981e215 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 57.8

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

   2. Taylor expanded in a around 0 39.5

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

   3. Taylor expanded in y around inf 22.0

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

   4. Taylor expanded in y around inf 13.4

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

   if -5.00000000000000007e239 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 1.99999999999999981e215

   1. Initial program 0.3

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

   2. Taylor expanded in a around 0 0.4

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

4. Final simplification 6.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq -5 \cdot 10^{+239}:\\ \;\;\;\;\left(z + a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right)\right) - b\\ \mathbf{elif}\;\frac{\left(\left(x + y\right) \cdot z + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y} \leq 2 \cdot 10^{+215}:\\ \;\;\;\;\left(\frac{\left(y + x\right) \cdot z}{y + \left(t + x\right)} + a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right)\right) - \frac{y \cdot b}{y + \left(t + x\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(z + a \cdot \left(\frac{y}{y + \left(t + x\right)} + \frac{t}{y + \left(t + x\right)}\right)\right) - b\\ \end{array} \]

Alternatives

Alternative 1
Error	6.3
Cost	4168

\[\begin{array}{l} t_1 := \left(x + y\right) \cdot z\\ t_2 := \frac{\left(t_1 + \left(t + y\right) \cdot a\right) - y \cdot b}{\left(x + t\right) + y}\\ t_3 := y + \left(t + x\right)\\ t_4 := \left(z + a \cdot \left(\frac{y}{t_3} + \frac{t}{t_3}\right)\right) - b\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+239}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+215}:\\ \;\;\;\;\frac{t_1 + \left(t \cdot a + y \cdot \left(a - b\right)\right)}{x + \left(y + t\right)}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 2
Error	31.5
Cost	1768

\[\begin{array}{l} t_1 := \frac{z \cdot x}{t + x}\\ t_2 := \left(a + z\right) - b\\ t_3 := \frac{t \cdot a}{t + x}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-218}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-306}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-216}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-99}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq 4600000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	31.9
Cost	1768

\[\begin{array}{l} t_1 := \frac{z \cdot x}{t + x}\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-217}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-305}:\\ \;\;\;\;\frac{a \cdot t}{x + \left(y + t\right)}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.25 \cdot 10^{-217}:\\ \;\;\;\;\frac{t \cdot a}{t + x}\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-99}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq 4600000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.22 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	32.1
Cost	1768

\[\begin{array}{l} t_1 := \frac{z \cdot x}{t + x}\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.56 \cdot 10^{-34}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-303}:\\ \;\;\;\;\frac{t \cdot a - y \cdot b}{x}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-216}:\\ \;\;\;\;\frac{t \cdot a}{t + x}\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-134}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-99}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq 4600000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.22 \cdot 10^{+55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	32.5
Cost	1768

\[\begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;z \leq -1.26 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-35}:\\ \;\;\;\;a + \left(\frac{z}{t} - \frac{a}{t}\right) \cdot x\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-303}:\\ \;\;\;\;\frac{t \cdot a - y \cdot b}{x}\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-217}:\\ \;\;\;\;\frac{t \cdot a}{t + x}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.7 \cdot 10^{-99}:\\ \;\;\;\;a\\ \mathbf{elif}\;z \leq 4600000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+54}:\\ \;\;\;\;\frac{z \cdot x}{t + x}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	17.1
Cost	1744

\[\begin{array}{l} t_1 := \left(\frac{x}{t + x} \cdot z + a\right) - \frac{y \cdot b}{y + \left(t + x\right)}\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -8.5 \cdot 10^{-251}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-301}:\\ \;\;\;\;\frac{z \cdot x + a \cdot t}{t + x}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	18.8
Cost	1744

\[\begin{array}{l} t_1 := y + \left(t + x\right)\\ t_2 := \frac{y \cdot b}{t_1}\\ t_3 := \left(\frac{x}{t + x} \cdot z + a\right) - t_2\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{-7}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-49}:\\ \;\;\;\;\left(\frac{y}{y + t} \cdot z + a\right) - t_2\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{+20}:\\ \;\;\;\;\left(z + a \cdot \left(\frac{y}{t_1} + \frac{t}{t_1}\right)\right) - b\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+166}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{x} - \frac{z}{x}\right) \cdot t + z\\ \end{array} \]

Alternative 8
Error	18.7
Cost	1612

\[\begin{array}{l} t_1 := \frac{y \cdot b}{y + \left(t + x\right)}\\ t_2 := \left(\frac{x}{t + x} \cdot z + a\right) - t_1\\ \mathbf{if}\;x \leq -2.8 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 0.000125:\\ \;\;\;\;\left(\frac{y}{y + t} \cdot z + a\right) - t_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+166}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{x} - \frac{z}{x}\right) \cdot t + z\\ \end{array} \]

Alternative 9
Error	27.8
Cost	1496

\[\begin{array}{l} t_1 := \left(\frac{a}{x} - \frac{z}{x}\right) \cdot t + z\\ t_2 := \left(a + z\right) - b\\ t_3 := a + \left(\frac{z}{t} - \frac{a}{t}\right) \cdot x\\ \mathbf{if}\;y \leq -1.3 \cdot 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.26 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-250}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-175}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	27.8
Cost	1496

\[\begin{array}{l} t_1 := \left(\frac{a}{x} - \frac{z}{x}\right) \cdot t + z\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -7.7 \cdot 10^{-56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-251}:\\ \;\;\;\;a - \frac{y \cdot b}{y + \left(t + x\right)}\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-178}:\\ \;\;\;\;a + \left(\frac{z}{t} - \frac{a}{t}\right) \cdot x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Error	26.5
Cost	1232

\[\begin{array}{l} t_1 := \left(\frac{x}{t + x} \cdot z + a\right) - b\\ \mathbf{if}\;x \leq -5 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-271}:\\ \;\;\;\;\left(a + z\right) - b\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-52}:\\ \;\;\;\;a - \frac{y \cdot b}{y + \left(t + x\right)}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+166}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{a}{x} - \frac{z}{x}\right) \cdot t + z\\ \end{array} \]

Alternative 12
Error	24.0
Cost	1232

\[\begin{array}{l} t_1 := \frac{z \cdot x + a \cdot t}{t + x}\\ t_2 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-53}:\\ \;\;\;\;\left(\frac{x}{t + x} \cdot z + a\right) - b\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-49}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	28.8
Cost	716

\[\begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -2.95 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-179}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-50}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Error	29.4
Cost	716

\[\begin{array}{l} t_1 := \left(a + z\right) - b\\ \mathbf{if}\;y \leq -8 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-175}:\\ \;\;\;\;\frac{t \cdot a}{t + x}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-52}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	37.0
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+78}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-179}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-256}:\\ \;\;\;\;-b\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-51}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 16
Error	35.5
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+69}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-16}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 17
Error	42.8
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023090 
(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)))