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

Average Error: 16.6 → 7.9

Time: 21.1s

Precision: binary64

Cost: 3400

Math

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

↓

\[\begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t_1}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;z \cdot \frac{y}{t + t \cdot \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+256}:\\ \;\;\;\;\frac{t_1}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

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))) (t_2 (/ t_1 (+ (/ (* y b) t) (+ a 1.0)))))
   (if (<= t_2 (- INFINITY))
     (* z (/ y (+ t (* t (+ a (/ y (/ t b)))))))
     (if (<= t_2 2e+256) (/ t_1 (+ (* b (/ y t)) (+ a 1.0))) (/ 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);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = z * (y / (t + (t * (a + (y / (t / b))))));
	} else if (t_2 <= 2e+256) {
		tmp = t_1 / ((b * (y / t)) + (a + 1.0));
	} 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);
	double t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = z * (y / (t + (t * (a + (y / (t / b))))));
	} else if (t_2 <= 2e+256) {
		tmp = t_1 / ((b * (y / t)) + (a + 1.0));
	} 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)
	t_2 = t_1 / (((y * b) / t) + (a + 1.0))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = z * (y / (t + (t * (a + (y / (t / b))))))
	elif t_2 <= 2e+256:
		tmp = t_1 / ((b * (y / t)) + (a + 1.0))
	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(x + Float64(Float64(y * z) / t))
	t_2 = Float64(t_1 / Float64(Float64(Float64(y * b) / t) + Float64(a + 1.0)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(z * Float64(y / Float64(t + Float64(t * Float64(a + Float64(y / Float64(t / b)))))));
	elseif (t_2 <= 2e+256)
		tmp = Float64(t_1 / Float64(Float64(b * Float64(y / t)) + Float64(a + 1.0)));
	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);
	t_2 = t_1 / (((y * b) / t) + (a + 1.0));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = z * (y / (t + (t * (a + (y / (t / b))))));
	elseif (t_2 <= 2e+256)
		tmp = t_1 / ((b * (y / t)) + (a + 1.0));
	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[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 / N[(N[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-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$2, 2e+256], N[(t$95$1 / N[(N[(b * N[(y / t), $MachinePrecision]), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]

Target

Original	16.6
Target	13.6
Herbie	7.9

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

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 39.5

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

   3. Simplified 14.2

      \[\leadsto \color{blue}{\frac{y}{t + t \cdot \left(\frac{y}{\frac{t}{b}} + a\right)} \cdot z} \]
      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): 3 points increase in error, 12 points decrease in error
      (*.f64 (/.f64 y (Rewrite<= distribute-lft-in_binary64 (*.f64 t (+.f64 1 (+.f64 (/.f64 (*.f64 y b) t) a))))) z): 3 points increase in error, 1 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 y (/.f64 (*.f64 t (+.f64 1 (+.f64 (/.f64 (*.f64 y b) t) a))) z))): 30 points increase in error, 25 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 y z) (*.f64 t (+.f64 1 (+.f64 (/.f64 (*.f64 y b) t) a))))): 49 points increase in error, 26 points decrease in error

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 2.0000000000000001e256

   1. Initial program 6.3

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

   2. Applied egg-rr 5.9

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

   if 2.0000000000000001e256 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 58.6

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

   2. Taylor expanded in y around inf 17.0

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

4. Final simplification 7.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;z \cdot \frac{y}{t + t \cdot \left(a + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 2 \cdot 10^{+256}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternatives

Alternative 1
Error	25.6
Cost	1628

\[\begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{if}\;y \leq -4.3359755879646585 \cdot 10^{+157}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.7636530055529275 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.7682891450836 \cdot 10^{+19}:\\ \;\;\;\;\frac{y \cdot z + x \cdot t}{y \cdot b}\\ \mathbf{elif}\;y \leq -2.2701494801102777 \cdot 10^{-13}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;y \leq 1.3456239265303775 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.8595628899043368 \cdot 10^{+120}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 7.657818024590273 \cdot 10^{+208}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 2
Error	25.4
Cost	1628

\[\begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{if}\;y \leq -4.3359755879646585 \cdot 10^{+157}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -1.7636530055529275 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.7682891450836 \cdot 10^{+19}:\\ \;\;\;\;\frac{y \cdot z + x \cdot t}{y \cdot b}\\ \mathbf{elif}\;y \leq -2.2701494801102777 \cdot 10^{-13}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{x}{b}\\ \mathbf{elif}\;y \leq 1.3456239265303775 \cdot 10^{+37}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;y \leq 1.8595628899043368 \cdot 10^{+120}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 7.657818024590273 \cdot 10^{+208}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 3
Error	24.0
Cost	1620

\[\begin{array}{l} \mathbf{if}\;y \leq -1.7471671690572272 \cdot 10^{+208}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2.3660645553334912 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;y \leq -2.2701494801102777 \cdot 10^{-13}:\\ \;\;\;\;\frac{y \cdot z + x \cdot t}{y \cdot b}\\ \mathbf{elif}\;y \leq 6.687284355470966 \cdot 10^{-12}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 7.657818024590273 \cdot 10^{+208}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 4
Error	25.2
Cost	1496

\[\begin{array}{l} t_1 := \frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{if}\;y \leq -4.3359755879646585 \cdot 10^{+157}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -6.746568039395299 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.2701494801102777 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{z}{t + y \cdot b}\\ \mathbf{elif}\;y \leq 1.3456239265303775 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.8595628899043368 \cdot 10^{+120}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 7.657818024590273 \cdot 10^{+208}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 5
Error	25.3
Cost	1496

\[\begin{array}{l} \mathbf{if}\;y \leq -1.7471671690572272 \cdot 10^{+208}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2.3660645553334912 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;y \leq -2.2701494801102777 \cdot 10^{-13}:\\ \;\;\;\;\frac{y \cdot z + x \cdot t}{y \cdot b}\\ \mathbf{elif}\;y \leq 1.3456239265303775 \cdot 10^{+37}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{elif}\;y \leq 1.8595628899043368 \cdot 10^{+120}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 7.657818024590273 \cdot 10^{+208}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 6
Error	24.2
Cost	1496

\[\begin{array}{l} \mathbf{if}\;y \leq -1.7471671690572272 \cdot 10^{+208}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2.3660645553334912 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;y \leq -2.2701494801102777 \cdot 10^{-13}:\\ \;\;\;\;\frac{y \cdot z + x \cdot t}{y \cdot b}\\ \mathbf{elif}\;y \leq 1.3456239265303775 \cdot 10^{+37}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{elif}\;y \leq 1.8595628899043368 \cdot 10^{+120}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 7.657818024590273 \cdot 10^{+208}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 7
Error	24.0
Cost	1496

\[\begin{array}{l} \mathbf{if}\;y \leq -1.7471671690572272 \cdot 10^{+208}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq -2.3660645553334912 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{1 + \left(a + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;y \leq -2.2701494801102777 \cdot 10^{-13}:\\ \;\;\;\;\frac{y \cdot z + x \cdot t}{y \cdot b}\\ \mathbf{elif}\;y \leq 1.3456239265303775 \cdot 10^{+37}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a + 1}\\ \mathbf{elif}\;y \leq 1.8595628899043368 \cdot 10^{+120}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 7.657818024590273 \cdot 10^{+208}:\\ \;\;\;\;\frac{x + y \cdot \frac{z}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 8
Error	29.0
Cost	1368

\[\begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -4.961791646070864 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a}\\ \mathbf{elif}\;a \leq -1.5780482099453485 \cdot 10^{-88}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -2.739236100982556 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.904305530997936 \cdot 10^{-164}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.6721137907544977 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;a \leq 4.27818985246302 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{z}{t + y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \]

Alternative 9
Error	29.2
Cost	1236

\[\begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t_1}{a}\\ \mathbf{if}\;a \leq -4.961791646070864 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.5780482099453485 \cdot 10^{-88}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -2.601819683875348 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.6721137907544977 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;a \leq 4.27818985246302 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{z}{t + y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	29.2
Cost	1236

\[\begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -4.961791646070864 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{elif}\;a \leq -1.5780482099453485 \cdot 10^{-88}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -2.601819683875348 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.6721137907544977 \cdot 10^{-62}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;a \leq 4.27818985246302 \cdot 10^{+29}:\\ \;\;\;\;y \cdot \frac{z}{t + y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \]

Alternative 11
Error	29.7
Cost	1104

\[\begin{array}{l} \mathbf{if}\;y \leq -6.7682891450836 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 31277.82007463906:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;y \leq 1.8595628899043368 \cdot 10^{+120}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 7.657818024590273 \cdot 10^{+208}:\\ \;\;\;\;\frac{z}{t} \cdot \frac{y}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 12
Error	29.6
Cost	848

\[\begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;y \leq -6.7682891450836 \cdot 10^{+19}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 31277.82007463906:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.8595628899043368 \cdot 10^{+120}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;y \leq 7.657818024590273 \cdot 10^{+208}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 13
Error	36.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -4.961791646070864 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 4.27818985246302 \cdot 10^{+29}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 14
Error	47.3
Cost	192

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

Reproduce

herbie shell --seed 2022300 
(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))))