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

Average Error: 40.38% → 0.78%

Time: 18.2s

Precision: binary64

Cost: 5449

Math

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

↓

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 10^{+259}\right):\\ \;\;\;\;\left(\frac{0}{t_1} + \frac{a}{t_1} \cdot \left(y + t\right)\right) + \left(z \cdot \frac{x + y}{t_1} - \frac{b}{\frac{t_1}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

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 (/ (- (+ (* z (+ x y)) (* a (+ y t))) (* y b)) t_1)))
   (if (or (<= t_2 (- INFINITY)) (not (<= t_2 1e+259)))
     (+
      (+ (/ 0.0 t_1) (* (/ a t_1) (+ y t)))
      (- (* z (/ (+ x y) t_1)) (/ b (/ t_1 y))))
     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 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -((double) INFINITY)) || !(t_2 <= 1e+259)) {
		tmp = ((0.0 / t_1) + ((a / t_1) * (y + t))) + ((z * ((x + y) / t_1)) - (b / (t_1 / y)));
	} 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 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	double tmp;
	if ((t_2 <= -Double.POSITIVE_INFINITY) || !(t_2 <= 1e+259)) {
		tmp = ((0.0 / t_1) + ((a / t_1) * (y + t))) + ((z * ((x + y) / t_1)) - (b / (t_1 / y)));
	} 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 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1
	tmp = 0
	if (t_2 <= -math.inf) or not (t_2 <= 1e+259):
		tmp = ((0.0 / t_1) + ((a / t_1) * (y + t))) + ((z * ((x + y) / t_1)) - (b / (t_1 / y)))
	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(z * Float64(x + y)) + Float64(a * Float64(y + t))) - Float64(y * b)) / t_1)
	tmp = 0.0
	if ((t_2 <= Float64(-Inf)) || !(t_2 <= 1e+259))
		tmp = Float64(Float64(Float64(0.0 / t_1) + Float64(Float64(a / t_1) * Float64(y + t))) + Float64(Float64(z * Float64(Float64(x + y) / t_1)) - Float64(b / Float64(t_1 / y))));
	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 = (((z * (x + y)) + (a * (y + t))) - (y * b)) / t_1;
	tmp = 0.0;
	if ((t_2 <= -Inf) || ~((t_2 <= 1e+259)))
		tmp = ((0.0 / t_1) + ((a / t_1) * (y + t))) + ((z * ((x + y) / t_1)) - (b / (t_1 / y)));
	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[(z * N[(x + y), $MachinePrecision]), $MachinePrecision] + N[(a * N[(y + t), $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, 1e+259]], $MachinePrecision]], N[(N[(N[(0.0 / t$95$1), $MachinePrecision] + N[(N[(a / t$95$1), $MachinePrecision] * N[(y + t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(N[(x + y), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] - N[(b / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]

Target

Original	40.38%
Target	17.44%
Herbie	0.78%

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

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 9.999999999999999e258 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y))

   1. Initial program 97.02

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

   2. Applied egg-rr 97.02

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

   3. Simplified 97.02

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(z, y + x, a \cdot \left(y + t\right) - y \cdot b\right) + 2 \cdot \mathsf{fma}\left(-b, y, y \cdot b\right)}}{\left(x + t\right) + y} \]
      Proof

      [Start] 97.02	\[ \frac{\left(\mathsf{fma}\left(x + y, z, \left(y + t\right) \cdot a\right) - y \cdot b\right) + \left(\mathsf{fma}\left(-b, y, y \cdot b\right) + \mathsf{fma}\left(-b, y, y \cdot b\right)\right)}{\left(x + t\right) + y} \]
      +-commutative [<=] 97.02	\[ \frac{\left(\mathsf{fma}\left(\color{blue}{y + x}, z, \left(y + t\right) \cdot a\right) - y \cdot b\right) + \left(\mathsf{fma}\left(-b, y, y \cdot b\right) + \mathsf{fma}\left(-b, y, y \cdot b\right)\right)}{\left(x + t\right) + y} \]
      fma-udef [=>] 97.02	\[ \frac{\left(\color{blue}{\left(\left(y + x\right) \cdot z + \left(y + t\right) \cdot a\right)} - y \cdot b\right) + \left(\mathsf{fma}\left(-b, y, y \cdot b\right) + \mathsf{fma}\left(-b, y, y \cdot b\right)\right)}{\left(x + t\right) + y} \]
      +-commutative [=>] 97.02	\[ \frac{\left(\left(\color{blue}{\left(x + y\right)} \cdot z + \left(y + t\right) \cdot a\right) - y \cdot b\right) + \left(\mathsf{fma}\left(-b, y, y \cdot b\right) + \mathsf{fma}\left(-b, y, y \cdot b\right)\right)}{\left(x + t\right) + y} \]
      associate-+r- [<=] 97.02	\[ \frac{\color{blue}{\left(\left(x + y\right) \cdot z + \left(\left(y + t\right) \cdot a - y \cdot b\right)\right)} + \left(\mathsf{fma}\left(-b, y, y \cdot b\right) + \mathsf{fma}\left(-b, y, y \cdot b\right)\right)}{\left(x + t\right) + y} \]
      +-commutative [<=] 97.02	\[ \frac{\left(\color{blue}{\left(y + x\right)} \cdot z + \left(\left(y + t\right) \cdot a - y \cdot b\right)\right) + \left(\mathsf{fma}\left(-b, y, y \cdot b\right) + \mathsf{fma}\left(-b, y, y \cdot b\right)\right)}{\left(x + t\right) + y} \]
      *-commutative [=>] 97.02	\[ \frac{\left(\color{blue}{z \cdot \left(y + x\right)} + \left(\left(y + t\right) \cdot a - y \cdot b\right)\right) + \left(\mathsf{fma}\left(-b, y, y \cdot b\right) + \mathsf{fma}\left(-b, y, y \cdot b\right)\right)}{\left(x + t\right) + y} \]
      fma-udef [<=] 97.02	\[ \frac{\color{blue}{\mathsf{fma}\left(z, y + x, \left(y + t\right) \cdot a - y \cdot b\right)} + \left(\mathsf{fma}\left(-b, y, y \cdot b\right) + \mathsf{fma}\left(-b, y, y \cdot b\right)\right)}{\left(x + t\right) + y} \]
      *-commutative [=>] 97.02	\[ \frac{\mathsf{fma}\left(z, y + x, \color{blue}{a \cdot \left(y + t\right)} - y \cdot b\right) + \left(\mathsf{fma}\left(-b, y, y \cdot b\right) + \mathsf{fma}\left(-b, y, y \cdot b\right)\right)}{\left(x + t\right) + y} \]
      count-2 [=>] 97.02	\[ \frac{\mathsf{fma}\left(z, y + x, a \cdot \left(y + t\right) - y \cdot b\right) + \color{blue}{2 \cdot \mathsf{fma}\left(-b, y, y \cdot b\right)}}{\left(x + t\right) + y} \]

   4. Taylor expanded in z around inf 97.02

      \[\leadsto \color{blue}{\left(\frac{\left(y + x\right) \cdot z}{y + \left(t + x\right)} + \left(\frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)} + 2 \cdot \frac{y \cdot b + -1 \cdot \left(y \cdot b\right)}{y + \left(t + x\right)}\right)\right) - \frac{y \cdot b}{y + \left(t + x\right)}} \]

   5. Simplified 1.23

      \[\leadsto \color{blue}{\left(\frac{0}{y + \left(t + x\right)} + \frac{a}{y + \left(t + x\right)} \cdot \left(y + t\right)\right) + \left(\frac{y + x}{y + \left(t + x\right)} \cdot z - \frac{b}{\frac{y + \left(t + x\right)}{y}}\right)} \]
      Proof

      [Start] 97.02	\[ \left(\frac{\left(y + x\right) \cdot z}{y + \left(t + x\right)} + \left(\frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)} + 2 \cdot \frac{y \cdot b + -1 \cdot \left(y \cdot b\right)}{y + \left(t + x\right)}\right)\right) - \frac{y \cdot b}{y + \left(t + x\right)} \]
      +-commutative [=>] 97.02	\[ \left(\frac{\left(y + x\right) \cdot z}{y + \left(t + x\right)} + \color{blue}{\left(2 \cdot \frac{y \cdot b + -1 \cdot \left(y \cdot b\right)}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right)}\right) - \frac{y \cdot b}{y + \left(t + x\right)} \]
      +-commutative [=>] 97.02	\[ \color{blue}{\left(\left(2 \cdot \frac{y \cdot b + -1 \cdot \left(y \cdot b\right)}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) + \frac{\left(y + x\right) \cdot z}{y + \left(t + x\right)}\right)} - \frac{y \cdot b}{y + \left(t + x\right)} \]
      associate--l+ [=>] 97.02	\[ \color{blue}{\left(2 \cdot \frac{y \cdot b + -1 \cdot \left(y \cdot b\right)}{y + \left(t + x\right)} + \frac{a \cdot \left(y + t\right)}{y + \left(t + x\right)}\right) + \left(\frac{\left(y + x\right) \cdot z}{y + \left(t + x\right)} - \frac{y \cdot b}{y + \left(t + x\right)}\right)} \]

   if -inf.0 < (/.f64 (-.f64 (+.f64 (*.f64 (+.f64 x y) z) (*.f64 (+.f64 t y) a)) (*.f64 y b)) (+.f64 (+.f64 x t) y)) < 9.999999999999999e258

   1. Initial program 0.47

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

4. Final simplification 0.78

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq -\infty \lor \neg \left(\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)} \leq 10^{+259}\right):\\ \;\;\;\;\left(\frac{0}{y + \left(x + t\right)} + \frac{a}{y + \left(x + t\right)} \cdot \left(y + t\right)\right) + \left(z \cdot \frac{x + y}{y + \left(x + t\right)} - \frac{b}{\frac{y + \left(x + t\right)}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error	4.53%
Cost	4809

\[\begin{array}{l} t_1 := y + \left(x + t\right)\\ t_2 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty \lor \neg \left(t_2 \leq 10^{+259}\right):\\ \;\;\;\;\left(\frac{0}{t_1} + \frac{a}{t_1} \cdot \left(y + t\right)\right) + \left(z - \frac{b}{\frac{t_1}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	11.56%
Cost	4169

\[\begin{array}{l} t_1 := \frac{\left(z \cdot \left(x + y\right) + a \cdot \left(y + t\right)\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+277}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	43.34%
Cost	1892

\[\begin{array}{l} t_1 := \frac{a}{\frac{x + \left(y + t\right)}{y + t}}\\ t_2 := a + \frac{x \cdot \left(z - a\right)}{t}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{-193}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-295}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-308}:\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-249}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-238}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-58}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-5}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	43.31%
Cost	1628

\[\begin{array}{l} t_1 := x + \left(y + t\right)\\ t_2 := \frac{a}{\frac{t_1}{y + t}}\\ t_3 := t + \left(x + y\right)\\ t_4 := \left(z + a\right) - b\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{-32}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-198}:\\ \;\;\;\;\frac{y \cdot \left(-b\right)}{t_1}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-29}:\\ \;\;\;\;\frac{y}{\frac{t_3}{-b}}\\ \mathbf{elif}\;z \leq 2.42 \cdot 10^{+36}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+177}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{x + y}{t_3}\\ \end{array} \]

Alternative 5
Error	42.82%
Cost	1372

\[\begin{array}{l} t_1 := a + \frac{x \cdot \left(z - a\right)}{t}\\ t_2 := \frac{a}{\frac{x + t}{t}}\\ t_3 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-193}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-303}:\\ \;\;\;\;z + t \cdot \left(\frac{a}{x} - \frac{z}{x}\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-247}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-238}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-106}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	37.77%
Cost	1360

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -480:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-158}:\\ \;\;\;\;\frac{a \cdot \left(y + t\right) - y \cdot b}{y + \left(x + t\right)}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{-201}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-79}:\\ \;\;\;\;\left(a + \frac{y \cdot z}{t}\right) - \frac{y \cdot b}{t}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-65}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	43.25%
Cost	1240

\[\begin{array}{l} t_1 := z \cdot \frac{x}{x + t}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -5.2 \cdot 10^{-209}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-284}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-275}:\\ \;\;\;\;t \cdot \frac{a}{x + t}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-107}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	38.87%
Cost	1228

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{-183}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-201}:\\ \;\;\;\;\frac{x \cdot z + t \cdot a}{x + t}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-81}:\\ \;\;\;\;\left(a + \frac{y \cdot z}{t}\right) - \frac{y \cdot b}{t}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-66}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	42.83%
Cost	976

\[\begin{array}{l} t_1 := \frac{a}{\frac{x + t}{t}}\\ t_2 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-220}:\\ \;\;\;\;z \cdot \frac{x}{x + t}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-109}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	42.88%
Cost	976

\[\begin{array}{l} t_1 := \left(z + a\right) - b\\ \mathbf{if}\;y \leq -3.6 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-238}:\\ \;\;\;\;a + \frac{x \cdot \left(z - a\right)}{t}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-221}:\\ \;\;\;\;x \cdot \frac{z}{x + t}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-110}:\\ \;\;\;\;\frac{a}{\frac{x + t}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	44.33%
Cost	585

\[\begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-258} \lor \neg \left(y \leq 5.7 \cdot 10^{-112}\right):\\ \;\;\;\;\left(z + a\right) - b\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 12
Error	56.04%
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+56}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+130}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 13
Error	67.94%
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023104 
(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)))