Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B

Average Error: 16.5 → 7.4

Time: 36.9s

Precision: binary64

Cost: 3400

Math

\[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

↓

\[\begin{array}{l} t_1 := \frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;z \cdot \frac{y}{t + t \cdot \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+304}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))

↓

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (* y z) t)) (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_1 (- INFINITY))
     (* z (/ y (+ t (* t (+ a (/ y (/ t b)))))))
     (if (<= t_1 2e+304) t_1 (/ z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

↓

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = z * (y / (t + (t * (a + (y / (t / b))))));
	} else if (t_1 <= 2e+304) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
}

↓

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (y / (t + (t * (a + (y / (t / b))))));
	} else if (t_1 <= 2e+304) {
		tmp = t_1;
	} else {
		tmp = z / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	return (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t))

↓

def code(x, y, z, t, a, b):
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = z * (y / (t + (t * (a + (y / (t / b))))))
	elif t_1 <= 2e+304:
		tmp = t_1
	else:
		tmp = z / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(a + 1.0) + Float64(Float64(y * b) / t)))
end

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(Float64(y * z) / t)) / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(z * Float64(y / Float64(t + Float64(t * Float64(a + Float64(y / Float64(t / b)))))));
	elseif (t_1 <= 2e+304)
		tmp = t_1;
	else
		tmp = Float64(z / b);
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x + ((y * z) / t)) / ((a + 1.0) + ((y * b) / t));
end

↓

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + ((y * z) / t)) / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = z * (y / (t + (t * (a + (y / (t / b))))));
	elseif (t_1 <= 2e+304)
		tmp = t_1;
	else
		tmp = z / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(a + 1.0), $MachinePrecision] + N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(z * N[(y / N[(t + N[(t * N[(a + N[(y / N[(t / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+304], t$95$1, N[(z / b), $MachinePrecision]]]]

Target

Original	16.5
Target	13.0
Herbie	7.4

\[\begin{array}{l} \mathbf{if}\;t < -1.3659085366310088 \cdot 10^{-271}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \mathbf{elif}\;t < 3.036967103737246 \cdot 10^{-130}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;1 \cdot \left(\left(x + \frac{y}{t} \cdot z\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y}{t} \cdot b}\right)\\ \end{array} \]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -inf.0

   1. Initial program 64.0

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in x around 0 36.7

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

   3. Simplified 10.1

      \[\leadsto \color{blue}{\frac{y}{t + t \cdot \left(\frac{y}{\frac{t}{b}} + a\right)} \cdot z} \]
      Proof
      (*.f64 (/.f64 y (+.f64 t (*.f64 t (+.f64 (/.f64 y (/.f64 t b)) a)))) z): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 y (+.f64 (Rewrite<= *-rgt-identity_binary64 (*.f64 t 1)) (*.f64 t (+.f64 (/.f64 y (/.f64 t b)) a)))) z): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 y (+.f64 (*.f64 t 1) (*.f64 t (+.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y b) t)) a)))) z): 4 points increase in error, 11 points decrease in error
      (*.f64 (/.f64 y (Rewrite<= distribute-lft-in_binary64 (*.f64 t (+.f64 1 (+.f64 (/.f64 (*.f64 y b) t) a))))) z): 0 points increase in error, 2 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 y (/.f64 (*.f64 t (+.f64 1 (+.f64 (/.f64 (*.f64 y b) t) a))) z))): 38 points increase in error, 37 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y z) (*.f64 t (+.f64 1 (+.f64 (/.f64 (*.f64 y b) t) a))))): 50 points increase in error, 33 points decrease in error

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 1.9999999999999999e304

   1. Initial program 6.1

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   if 1.9999999999999999e304 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 63.3

      \[\frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   2. Taylor expanded in y around inf 13.9

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 7.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \frac{y}{t + t \cdot \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+304}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternatives

Alternative 1
Error	25.0
Cost	2016

\[\begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ t_2 := 1 + \left(a + b \cdot \frac{y}{t}\right)\\ t_3 := \frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{if}\;t \leq -3.4839573225035066 \cdot 10^{+40}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -6.601803281891866 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.1629846613260496 \cdot 10^{-225}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 8.266072221618103 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.252615744420136 \cdot 10^{-136}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 2.2676946752879208 \cdot 10^{-45}:\\ \;\;\;\;z \cdot \frac{y}{t + t \cdot \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t \leq 3.436421677954066 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{t_2}\\ \mathbf{elif}\;t \leq 3.6412690829238184 \cdot 10^{+115}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t_2}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	24.2
Cost	1892

\[\begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ t_2 := \frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{if}\;t \leq -3.4839573225035066 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.601803281891866 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.200309420219119 \cdot 10^{-171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9.599943326637684 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.572262051878389 \cdot 10^{-253}:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 8.266072221618103 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.911390428045428 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.2676946752879208 \cdot 10^{-45}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 4.940911257088082 \cdot 10^{-11}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	29.1
Cost	1760

\[\begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{x + \frac{z}{\frac{t}{y}}}{a}\\ \mathbf{if}\;a \leq -1.6732540477867598 \cdot 10^{+55}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.1470736129717932 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.9304934126020845 \cdot 10^{-25}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;a \leq -8.408506461319172 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.588976137481753 \cdot 10^{-228}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.0695147119881423 \cdot 10^{-239}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 4.4701207075682485 \cdot 10^{-86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.4768478888177527 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	23.9
Cost	1752

\[\begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ t_2 := \frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{if}\;t \leq -3.4839573225035066 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.601803281891866 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.1629846613260496 \cdot 10^{-225}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 8.266072221618103 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.252615744420136 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.424130974233972 \cdot 10^{-99}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;t \leq 2.053323109205267 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	38.6
Cost	1636

\[\begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := y \cdot \frac{z}{t + y \cdot b}\\ t_3 := \frac{x}{a + 1}\\ \mathbf{if}\;z \leq -1.0096451378587061 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.0367605423389776 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.939648315288972 \cdot 10^{-78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.8058469942709434 \cdot 10^{-290}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.7418729438618934 \cdot 10^{-241}:\\ \;\;\;\;x \cdot \frac{t}{y \cdot b}\\ \mathbf{elif}\;z \leq 2.6359345634334725 \cdot 10^{+109}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 10^{+252}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 10^{+270}:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+292}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	23.7
Cost	1628

\[\begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ t_2 := \frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{if}\;t \leq -3.4839573225035066 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.601803281891866 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.1629846613260496 \cdot 10^{-225}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 8.266072221618103 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.911390428045428 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.2676946752879208 \cdot 10^{-45}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.053323109205267 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	23.9
Cost	1628

\[\begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ t_2 := \frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{if}\;t \leq -3.4839573225035066 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.601803281891866 \cdot 10^{-143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.1629846613260496 \cdot 10^{-225}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{elif}\;t \leq 8.266072221618103 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.911390428045428 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.2676946752879208 \cdot 10^{-45}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 2.053323109205267 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	29.2
Cost	1368

\[\begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{a}\\ t_2 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -46051144.22601811:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.749573157820109 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \frac{z}{t + y \cdot b}\\ \mathbf{elif}\;a \leq -6.588976137481753 \cdot 10^{-228}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.0695147119881423 \cdot 10^{-239}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.4307979707997733 \cdot 10^{-11}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.064098146882649 \cdot 10^{+30}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Error	27.3
Cost	1364

\[\begin{array}{l} t_1 := \frac{x + \frac{z}{\frac{t}{y}}}{a}\\ t_2 := \frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{if}\;a \leq -1.7684394772383506 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.299316809580509 \cdot 10^{-190}:\\ \;\;\;\;\frac{x}{1 + \left(a + b \cdot \frac{y}{t}\right)}\\ \mathbf{elif}\;a \leq -1.0695147119881423 \cdot 10^{-239}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.4701207075682485 \cdot 10^{-86}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 1.4768478888177527 \cdot 10^{+23}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	28.3
Cost	1236

\[\begin{array}{l} t_1 := \frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{if}\;a \leq -46051144.22601811:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.299316809580509 \cdot 10^{-190}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;a \leq -1.0695147119881423 \cdot 10^{-239}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.4307979707997733 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 3.064098146882649 \cdot 10^{+30}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	28.3
Cost	1236

\[\begin{array}{l} t_1 := \frac{x + \frac{z}{\frac{t}{y}}}{a}\\ \mathbf{if}\;a \leq -46051144.22601811:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.299316809580509 \cdot 10^{-190}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;a \leq -1.0695147119881423 \cdot 10^{-239}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.4307979707997733 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 3.064098146882649 \cdot 10^{+30}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	28.3
Cost	1236

\[\begin{array}{l} t_1 := \frac{x + \frac{z}{\frac{t}{y}}}{a}\\ \mathbf{if}\;a \leq -46051144.22601811:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7.299316809580509 \cdot 10^{-190}:\\ \;\;\;\;x \cdot \frac{1}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;a \leq -1.0695147119881423 \cdot 10^{-239}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.4307979707997733 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 3.064098146882649 \cdot 10^{+30}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	31.6
Cost	848

\[\begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;y \leq -1.9324229593642623 \cdot 10^{+220}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2.3299655028674916 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.029962680260646 \cdot 10^{-54}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 0.0080796858189481:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 14
Error	39.6
Cost	720

\[\begin{array}{l} \mathbf{if}\;y \leq -1.9324229593642623 \cdot 10^{+220}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.09394268161179 \cdot 10^{+134}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;y \leq -8.884738256319005 \cdot 10^{-98}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 0.0080796858189481:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 15
Error	39.6
Cost	720

\[\begin{array}{l} \mathbf{if}\;a \leq -1.6732540477867598 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.0695147119881423 \cdot 10^{-239}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.792016448369227 \cdot 10^{-148}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{elif}\;a \leq 3.064098146882649 \cdot 10^{+30}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 16
Error	39.6
Cost	720

\[\begin{array}{l} \mathbf{if}\;a \leq -1.6732540477867598 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.0695147119881423 \cdot 10^{-239}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.792016448369227 \cdot 10^{-148}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 3.064098146882649 \cdot 10^{+30}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 17
Error	47.8
Cost	192

\[\frac{x}{a} \]

Reproduce

herbie shell --seed 2022317 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Tridiagonal:solveCyclicTriDiagonal from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (if (< t -1.3659085366310088e-271) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b))))) (if (< t 3.036967103737246e-130) (/ z b) (* 1.0 (* (+ x (* (/ y t) z)) (/ 1.0 (+ (+ a 1.0) (* (/ y t) b)))))))

  (/ (+ x (/ (* y z) t)) (+ (+ a 1.0) (/ (* y b) t))))