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

Average Accuracy: 73.8% → 87.1%

Time: 25.2s

Precision: binary64

Cost: 4556

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y \cdot b}{t} + \left(a + 1\right)\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t_1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{t_1}\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{-280}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+253}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

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 (+ (/ (* y b) t) (+ a 1.0))) (t_2 (/ (+ x (/ (* y z) t)) t_1)))
   (if (<= t_2 (- INFINITY))
     (* (/ y t) (/ z t_1))
     (if (<= t_2 -2e-280)
       t_2
       (if (<= t_2 5e+253)
         (/ (+ x (/ y (/ t z))) (+ a (+ 1.0 (/ b (/ t y)))))
         (/ 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 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = (y / t) * (z / t_1);
	} else if (t_2 <= -2e-280) {
		tmp = t_2;
	} else if (t_2 <= 5e+253) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b / (t / y))));
	} 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 = ((y * b) / t) + (a + 1.0);
	double t_2 = (x + ((y * z) / t)) / t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t) * (z / t_1);
	} else if (t_2 <= -2e-280) {
		tmp = t_2;
	} else if (t_2 <= 5e+253) {
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b / (t / y))));
	} 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 = ((y * b) / t) + (a + 1.0)
	t_2 = (x + ((y * z) / t)) / t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = (y / t) * (z / t_1)
	elif t_2 <= -2e-280:
		tmp = t_2
	elif t_2 <= 5e+253:
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b / (t / y))))
	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(Float64(y * b) / t) + Float64(a + 1.0))
	t_2 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = Float64(Float64(y / t) * Float64(z / t_1));
	elseif (t_2 <= -2e-280)
		tmp = t_2;
	elseif (t_2 <= 5e+253)
		tmp = Float64(Float64(x + Float64(y / Float64(t / z))) / Float64(a + Float64(1.0 + Float64(b / Float64(t / y)))));
	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 = ((y * b) / t) + (a + 1.0);
	t_2 = (x + ((y * z) / t)) / t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = (y / t) * (z / t_1);
	elseif (t_2 <= -2e-280)
		tmp = t_2;
	elseif (t_2 <= 5e+253)
		tmp = (x + (y / (t / z))) / (a + (1.0 + (b / (t / y))));
	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[(N[(y * b), $MachinePrecision] / t), $MachinePrecision] + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], N[(N[(y / t), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, -2e-280], t$95$2, If[LessEqual[t$95$2, 5e+253], N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(a + N[(1.0 + N[(b / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]

Target

Original	73.8%
Target	79.1%
Herbie	87.1%

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

Derivation

1. Split input into 4 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 0.0%

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

   2. Applied egg-rr 7.5%

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

      [Start] 0.0	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      div-inv [=>] 0.0	\[ \color{blue}{\left(x + \frac{y \cdot z}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}}} \]
      flip-+ [=>] 0.0	\[ \color{blue}{\frac{x \cdot x - \frac{y \cdot z}{t} \cdot \frac{y \cdot z}{t}}{x - \frac{y \cdot z}{t}}} \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-*l/ [=>] 0.0	\[ \color{blue}{\frac{\left(x \cdot x - \frac{y \cdot z}{t} \cdot \frac{y \cdot z}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}}}{x - \frac{y \cdot z}{t}}} \]
      flip-- [=>] 0.0	\[ \frac{\left(x \cdot x - \frac{y \cdot z}{t} \cdot \frac{y \cdot z}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}}}{\color{blue}{\frac{x \cdot x - \frac{y \cdot z}{t} \cdot \frac{y \cdot z}{t}}{x + \frac{y \cdot z}{t}}}} \]
      associate-/r/ [=>] 0.0	\[ \color{blue}{\frac{\left(x \cdot x - \frac{y \cdot z}{t} \cdot \frac{y \cdot z}{t}\right) \cdot \frac{1}{\left(a + 1\right) + \frac{y \cdot b}{t}}}{x \cdot x - \frac{y \cdot z}{t} \cdot \frac{y \cdot z}{t}} \cdot \left(x + \frac{y \cdot z}{t}\right)} \]

   3. Simplified 38.9%

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

      [Start] 7.5	\[ \frac{\left(x \cdot x - {\left(\frac{y}{\frac{t}{z}}\right)}^{2}\right) \cdot \frac{1}{a + \left(1 + \frac{b}{t} \cdot y\right)}}{x \cdot x - {\left(\frac{y}{\frac{t}{z}}\right)}^{2}} \cdot \left(x + \frac{y}{\frac{t}{z}}\right) \]
      *-commutative [=>] 7.5	\[ \color{blue}{\left(x + \frac{y}{\frac{t}{z}}\right) \cdot \frac{\left(x \cdot x - {\left(\frac{y}{\frac{t}{z}}\right)}^{2}\right) \cdot \frac{1}{a + \left(1 + \frac{b}{t} \cdot y\right)}}{x \cdot x - {\left(\frac{y}{\frac{t}{z}}\right)}^{2}}} \]
      associate-/l* [<=] 0.0	\[ \left(x + \color{blue}{\frac{y \cdot z}{t}}\right) \cdot \frac{\left(x \cdot x - {\left(\frac{y}{\frac{t}{z}}\right)}^{2}\right) \cdot \frac{1}{a + \left(1 + \frac{b}{t} \cdot y\right)}}{x \cdot x - {\left(\frac{y}{\frac{t}{z}}\right)}^{2}} \]
      associate-*l/ [<=] 7.5	\[ \left(x + \color{blue}{\frac{y}{t} \cdot z}\right) \cdot \frac{\left(x \cdot x - {\left(\frac{y}{\frac{t}{z}}\right)}^{2}\right) \cdot \frac{1}{a + \left(1 + \frac{b}{t} \cdot y\right)}}{x \cdot x - {\left(\frac{y}{\frac{t}{z}}\right)}^{2}} \]
      *-commutative [=>] 7.5	\[ \left(x + \color{blue}{z \cdot \frac{y}{t}}\right) \cdot \frac{\left(x \cdot x - {\left(\frac{y}{\frac{t}{z}}\right)}^{2}\right) \cdot \frac{1}{a + \left(1 + \frac{b}{t} \cdot y\right)}}{x \cdot x - {\left(\frac{y}{\frac{t}{z}}\right)}^{2}} \]
      associate-/l* [=>] 5.4	\[ \left(x + z \cdot \frac{y}{t}\right) \cdot \color{blue}{\frac{x \cdot x - {\left(\frac{y}{\frac{t}{z}}\right)}^{2}}{\frac{x \cdot x - {\left(\frac{y}{\frac{t}{z}}\right)}^{2}}{\frac{1}{a + \left(1 + \frac{b}{t} \cdot y\right)}}}} \]
      associate-/r/ [=>] 7.5	\[ \left(x + z \cdot \frac{y}{t}\right) \cdot \color{blue}{\left(\frac{x \cdot x - {\left(\frac{y}{\frac{t}{z}}\right)}^{2}}{x \cdot x - {\left(\frac{y}{\frac{t}{z}}\right)}^{2}} \cdot \frac{1}{a + \left(1 + \frac{b}{t} \cdot y\right)}\right)} \]
      *-inverses [=>] 38.9	\[ \left(x + z \cdot \frac{y}{t}\right) \cdot \left(\color{blue}{1} \cdot \frac{1}{a + \left(1 + \frac{b}{t} \cdot y\right)}\right) \]
      associate-*l/ [=>] 38.9	\[ \left(x + z \cdot \frac{y}{t}\right) \cdot \left(1 \cdot \frac{1}{a + \left(1 + \color{blue}{\frac{b \cdot y}{t}}\right)}\right) \]
      *-commutative [<=] 38.9	\[ \left(x + z \cdot \frac{y}{t}\right) \cdot \left(1 \cdot \frac{1}{a + \left(1 + \frac{\color{blue}{y \cdot b}}{t}\right)}\right) \]
      associate-*l/ [<=] 38.9	\[ \left(x + z \cdot \frac{y}{t}\right) \cdot \left(1 \cdot \frac{1}{a + \left(1 + \color{blue}{\frac{y}{t} \cdot b}\right)}\right) \]
      *-commutative [=>] 38.9	\[ \left(x + z \cdot \frac{y}{t}\right) \cdot \left(1 \cdot \frac{1}{a + \left(1 + \color{blue}{b \cdot \frac{y}{t}}\right)}\right) \]

   4. Taylor expanded in x around 0 37.6%

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

   5. Simplified 79.2%

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

      [Start] 37.6	\[ \frac{y \cdot z}{t \cdot \left(\frac{y \cdot b}{t} + \left(1 + a\right)\right)} \]
      times-frac [=>] 79.2	\[ \color{blue}{\frac{y}{t} \cdot \frac{z}{\frac{y \cdot b}{t} + \left(1 + a\right)}} \]

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -1.9999999999999999e-280

   1. Initial program 99.3%

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

   if -1.9999999999999999e-280 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.9999999999999997e253

   1. Initial program 83.7%

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

   2. Simplified 84.2%

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

      [Start] 83.7	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-/l* [=>] 80.4	\[ \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-+l+ [=>] 80.4	\[ \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{a + \left(1 + \frac{y \cdot b}{t}\right)}} \]
      *-commutative [=>] 80.4	\[ \frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{\color{blue}{b \cdot y}}{t}\right)} \]
      associate-/l* [=>] 84.2	\[ \frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \color{blue}{\frac{b}{\frac{t}{y}}}\right)} \]

   if 4.9999999999999997e253 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 9.2%

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

   2. Simplified 23.8%

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

      [Start] 9.2	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-/l* [=>] 18.2	\[ \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-+l+ [=>] 18.2	\[ \frac{x + \frac{y}{\frac{t}{z}}}{\color{blue}{a + \left(1 + \frac{y \cdot b}{t}\right)}} \]
      *-commutative [=>] 18.2	\[ \frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{\color{blue}{b \cdot y}}{t}\right)} \]
      associate-/l* [=>] 23.8	\[ \frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \color{blue}{\frac{b}{\frac{t}{y}}}\right)} \]

   3. Taylor expanded in y around inf 73.2%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y}{t} \cdot \frac{z}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -2 \cdot 10^{-280}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 5 \cdot 10^{+253}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	80.7%
Cost	1617

\[\begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-155}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-171} \lor \neg \left(t \leq 6.5 \cdot 10^{-115}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \end{array} \]

Alternative 2
Accuracy	80.7%
Cost	1616

\[\begin{array}{l} t_1 := x + \frac{y}{\frac{t}{z}}\\ t_2 := \frac{t_1}{a + \left(1 + \frac{y}{\frac{t}{b}}\right)}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-155}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-172}:\\ \;\;\;\;\frac{t_1}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-117}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Accuracy	65.4%
Cost	1488

\[\begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ t_2 := \frac{x}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+36}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-116}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-22}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Accuracy	54.0%
Cost	1236

\[\begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-106}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 6.7 \cdot 10^{-22}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{+80}:\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Accuracy	54.1%
Cost	1104

\[\begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-109}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-82}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{1 + \frac{y \cdot b}{t}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Accuracy	59.3%
Cost	1104

\[\begin{array}{l} t_1 := \frac{z + \frac{x \cdot t}{y}}{b}\\ t_2 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{-82}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Accuracy	59.4%
Cost	1104

\[\begin{array}{l} t_1 := \frac{z + \frac{x \cdot t}{y}}{b}\\ t_2 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -5.9 \cdot 10^{+38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-80}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Accuracy	59.3%
Cost	1104

\[\begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-114}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-82}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-15}:\\ \;\;\;\;\frac{z + \frac{x \cdot t}{y}}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	42.2%
Cost	984

\[\begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+70}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -8.8 \cdot 10^{-36}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 10^{-286}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 10^{-64}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1620000000000:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 10
Accuracy	42.1%
Cost	984

\[\begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+75}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-35}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-287}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-64}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-14}:\\ \;\;\;\;x - x \cdot a\\ \mathbf{elif}\;a \leq 1900000000000:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 11
Accuracy	64.7%
Cost	969

\[\begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+36} \lor \neg \left(t \leq 1.9 \cdot 10^{-106}\right):\\ \;\;\;\;\frac{x}{a + \left(1 + b \cdot \frac{y}{t}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]

Alternative 12
Accuracy	64.7%
Cost	969

\[\begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+36} \lor \neg \left(t \leq 3.2 \cdot 10^{-106}\right):\\ \;\;\;\;\frac{x}{a + \left(1 + \frac{b}{\frac{t}{y}}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]

Alternative 13
Accuracy	54.7%
Cost	585

\[\begin{array}{l} \mathbf{if}\;t \leq -6.8 \cdot 10^{+36} \lor \neg \left(t \leq 5.4 \cdot 10^{-106}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 14
Accuracy	42.2%
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -0.0032:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 400:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 15
Accuracy	20.5%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023137 
(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))))