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

Percentage Accurate: 74.6% → 86.9%

Time: 27.6s

Precision: binary64

Cost: 5840

Math

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

↓

\[\begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := t_1 + \left(a + 1\right)\\ t_3 := \frac{x + \frac{y \cdot z}{t}}{t_2}\\ \mathbf{if}\;t_3 \leq -\infty:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + t_1\right)\right)}\\ \mathbf{elif}\;t_3 \leq -1 \cdot 10^{-282}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq 0:\\ \;\;\;\;\frac{t}{y} \cdot \frac{x + \frac{y}{\frac{t}{z}}}{b}\\ \mathbf{elif}\;t_3 \leq 4 \cdot 10^{+242}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{t_2}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

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))
        (t_2 (+ t_1 (+ a 1.0)))
        (t_3 (/ (+ x (/ (* y z) t)) t_2)))
   (if (<= t_3 (- INFINITY))
     (/ (* y z) (* t (+ 1.0 (+ a t_1))))
     (if (<= t_3 -1e-282)
       t_3
       (if (<= t_3 0.0)
         (* (/ t y) (/ (+ x (/ y (/ t z))) b))
         (if (<= t_3 4e+242) (/ (+ x (* (* y z) (/ 1.0 t))) t_2) (/ 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;
	double t_2 = t_1 + (a + 1.0);
	double t_3 = (x + ((y * z) / t)) / t_2;
	double tmp;
	if (t_3 <= -((double) INFINITY)) {
		tmp = (y * z) / (t * (1.0 + (a + t_1)));
	} else if (t_3 <= -1e-282) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (t / y) * ((x + (y / (t / z))) / b);
	} else if (t_3 <= 4e+242) {
		tmp = (x + ((y * z) * (1.0 / t))) / t_2;
	} 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;
	double t_2 = t_1 + (a + 1.0);
	double t_3 = (x + ((y * z) / t)) / t_2;
	double tmp;
	if (t_3 <= -Double.POSITIVE_INFINITY) {
		tmp = (y * z) / (t * (1.0 + (a + t_1)));
	} else if (t_3 <= -1e-282) {
		tmp = t_3;
	} else if (t_3 <= 0.0) {
		tmp = (t / y) * ((x + (y / (t / z))) / b);
	} else if (t_3 <= 4e+242) {
		tmp = (x + ((y * z) * (1.0 / t))) / t_2;
	} 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
	t_2 = t_1 + (a + 1.0)
	t_3 = (x + ((y * z) / t)) / t_2
	tmp = 0
	if t_3 <= -math.inf:
		tmp = (y * z) / (t * (1.0 + (a + t_1)))
	elif t_3 <= -1e-282:
		tmp = t_3
	elif t_3 <= 0.0:
		tmp = (t / y) * ((x + (y / (t / z))) / b)
	elif t_3 <= 4e+242:
		tmp = (x + ((y * z) * (1.0 / t))) / t_2
	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(y * b) / t)
	t_2 = Float64(t_1 + Float64(a + 1.0))
	t_3 = Float64(Float64(x + Float64(Float64(y * z) / t)) / t_2)
	tmp = 0.0
	if (t_3 <= Float64(-Inf))
		tmp = Float64(Float64(y * z) / Float64(t * Float64(1.0 + Float64(a + t_1))));
	elseif (t_3 <= -1e-282)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = Float64(Float64(t / y) * Float64(Float64(x + Float64(y / Float64(t / z))) / b));
	elseif (t_3 <= 4e+242)
		tmp = Float64(Float64(x + Float64(Float64(y * z) * Float64(1.0 / t))) / t_2);
	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;
	t_2 = t_1 + (a + 1.0);
	t_3 = (x + ((y * z) / t)) / t_2;
	tmp = 0.0;
	if (t_3 <= -Inf)
		tmp = (y * z) / (t * (1.0 + (a + t_1)));
	elseif (t_3 <= -1e-282)
		tmp = t_3;
	elseif (t_3 <= 0.0)
		tmp = (t / y) * ((x + (y / (t / z))) / b);
	elseif (t_3 <= 4e+242)
		tmp = (x + ((y * z) * (1.0 / t))) / t_2;
	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[(y * b), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(a + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, (-Infinity)], N[(N[(y * z), $MachinePrecision] / N[(t * N[(1.0 + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, -1e-282], t$95$3, If[LessEqual[t$95$3, 0.0], N[(N[(t / y), $MachinePrecision] * N[(N[(x + N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 4e+242], N[(N[(x + N[(N[(y * z), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision], N[(z / b), $MachinePrecision]]]]]]]]

Target

Original	74.6%
Target	79.5%
Herbie	86.9%

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

Derivation

1. Split input into 5 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 24.2%

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

   2. Simplified 16.4%

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

      [Start] 24.2	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      *-commutative [=>] 24.2	\[ \frac{x + \frac{\color{blue}{z \cdot y}}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-/l* [=>] 24.2	\[ \frac{x + \color{blue}{\frac{z}{\frac{t}{y}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-*l/ [<=] 16.4	\[ \frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + \color{blue}{\frac{y}{t} \cdot b}} \]

   3. Taylor expanded in x around 0 86.8%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < -1e-282

   1. Initial program 99.8%

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

   if -1e-282 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 0.0

   1. Initial program 59.0%

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

   2. Taylor expanded in b around inf 65.8%

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

   3. Simplified 76.1%

      \[\leadsto \color{blue}{\frac{t}{y} \cdot \frac{x + \frac{y}{\frac{t}{z}}}{b}} \]
      Step-by-step derivation

      [Start] 65.8	\[ \frac{t \cdot \left(\frac{y \cdot z}{t} + x\right)}{y \cdot b} \]
      times-frac [=>] 76.2	\[ \color{blue}{\frac{t}{y} \cdot \frac{\frac{y \cdot z}{t} + x}{b}} \]
      +-commutative [=>] 76.2	\[ \frac{t}{y} \cdot \frac{\color{blue}{x + \frac{y \cdot z}{t}}}{b} \]
      associate-/l* [=>] 76.1	\[ \frac{t}{y} \cdot \frac{x + \color{blue}{\frac{y}{\frac{t}{z}}}}{b} \]

   if 0.0 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t))) < 4.0000000000000002e242

   1. Initial program 99.6%

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

   2. Applied egg-rr 99.6%

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

      [Start] 99.6	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      clear-num [=>] 99.5	\[ \frac{x + \color{blue}{\frac{1}{\frac{t}{y \cdot z}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-/r/ [=>] 99.6	\[ \frac{x + \color{blue}{\frac{1}{t} \cdot \left(y \cdot z\right)}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]

   if 4.0000000000000002e242 < (/.f64 (+.f64 x (/.f64 (*.f64 y z) t)) (+.f64 (+.f64 a 1) (/.f64 (*.f64 y b) t)))

   1. Initial program 7.9%

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

   2. Simplified 21.8%

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

      [Start] 7.9	\[ \frac{x + \frac{y \cdot z}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      *-commutative [=>] 7.9	\[ \frac{x + \frac{\color{blue}{z \cdot y}}{t}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-/l* [=>] 19.7	\[ \frac{x + \color{blue}{\frac{z}{\frac{t}{y}}}}{\left(a + 1\right) + \frac{y \cdot b}{t}} \]
      associate-*l/ [<=] 21.8	\[ \frac{x + \frac{z}{\frac{t}{y}}}{\left(a + 1\right) + \color{blue}{\frac{y}{t} \cdot b}} \]

   3. Taylor expanded in t around 0 78.9%

      \[\leadsto \color{blue}{\frac{z}{b}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -\infty:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + \frac{y \cdot b}{t}\right)\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq -1 \cdot 10^{-282}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 0:\\ \;\;\;\;\frac{t}{y} \cdot \frac{x + \frac{y}{\frac{t}{z}}}{b}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)} \leq 4 \cdot 10^{+242}:\\ \;\;\;\;\frac{x + \left(y \cdot z\right) \cdot \frac{1}{t}}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	86.9%
Cost	5712

\[\begin{array}{l} t_1 := \frac{y \cdot b}{t}\\ t_2 := \frac{x + \frac{y \cdot z}{t}}{t_1 + \left(a + 1\right)}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y \cdot z}{t \cdot \left(1 + \left(a + t_1\right)\right)}\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-282}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;\frac{t}{y} \cdot \frac{x + \frac{y}{\frac{t}{z}}}{b}\\ \mathbf{elif}\;t_2 \leq 4 \cdot 10^{+242}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 2
Accuracy	50.4%
Cost	2024

\[\begin{array}{l} t_1 := x + \frac{y \cdot z}{t}\\ t_2 := \frac{t_1}{a}\\ t_3 := \frac{x}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ t_4 := \frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+188}:\\ \;\;\;\;\frac{y}{\frac{t}{z} \cdot \left(a + 1\right)}\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{+111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.86 \cdot 10^{-154}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-231}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{-299}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 10^{-110}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1550000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+139}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \end{array} \]

Alternative 3
Accuracy	50.2%
Cost	2024

\[\begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ t_2 := x + \frac{y \cdot z}{t}\\ t_3 := \frac{t_2}{a}\\ \mathbf{if}\;a \leq -6.2 \cdot 10^{+188}:\\ \;\;\;\;\frac{y}{\frac{t}{z} \cdot \left(a + 1\right)}\\ \mathbf{elif}\;a \leq -6 \cdot 10^{+111}:\\ \;\;\;\;\frac{x}{\frac{y \cdot b}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{+28}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.6 \cdot 10^{-230}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 9.1 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.4 \cdot 10^{-110}:\\ \;\;\;\;\frac{x}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{elif}\;a \leq 1550000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+65}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a}\\ \end{array} \]

Alternative 4
Accuracy	42.0%
Cost	1900

\[\begin{array}{l} t_1 := \frac{y}{t} \cdot \frac{z}{a}\\ t_2 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -4.7 \cdot 10^{+188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.95 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq -1.15 \cdot 10^{-40}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-229}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.6 \cdot 10^{-126}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-15}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+139}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+210}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{+280}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 5
Accuracy	53.8%
Cost	1760

\[\begin{array}{l} t_1 := \frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ t_2 := \frac{x + \frac{y}{\frac{t}{z}}}{a}\\ t_3 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.35 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-231}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{-97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1400000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4.1 \cdot 10^{+65}:\\ \;\;\;\;\frac{t_3}{a}\\ \mathbf{elif}\;a \leq 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Accuracy	50.6%
Cost	1633

\[\begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a}\\ t_2 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-41}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-231}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 8.8 \cdot 10^{-125}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1500000 \lor \neg \left(a \leq 1.4 \cdot 10^{+44}\right) \land a \leq 7.2 \cdot 10^{+140}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	50.5%
Cost	1632

\[\begin{array}{l} t_1 := \frac{x + \frac{y}{\frac{t}{z}}}{a}\\ t_2 := x + \frac{y \cdot z}{t}\\ \mathbf{if}\;a \leq -1.4 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{-40}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-229}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4 \cdot 10^{-126}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-97}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 64000:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+44}:\\ \;\;\;\;\frac{t_2}{a}\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+139}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	81.1%
Cost	1353

\[\begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-18} \lor \neg \left(t \leq 2.9 \cdot 10^{-160}\right):\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]

Alternative 9
Accuracy	80.6%
Cost	1352

\[\begin{array}{l} \mathbf{if}\;t \leq -1.58 \cdot 10^{-226}:\\ \;\;\;\;\frac{x + \frac{y \cdot z}{t}}{\frac{y}{\frac{t}{b}} + \left(a + 1\right)}\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-160}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{b \cdot \frac{y}{t} + \left(a + 1\right)}\\ \end{array} \]

Alternative 10
Accuracy	55.0%
Cost	972

\[\begin{array}{l} t_1 := \frac{x}{a + 1}\\ \mathbf{if}\;t \leq -1.3 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-49}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+72}:\\ \;\;\;\;\frac{y}{\frac{t}{z} \cdot \left(a + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Accuracy	69.9%
Cost	969

\[\begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{-19} \lor \neg \left(t \leq 6.9 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t}{z}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]

Alternative 12
Accuracy	69.6%
Cost	969

\[\begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{-18} \lor \neg \left(t \leq 2.9 \cdot 10^{-123}\right):\\ \;\;\;\;\frac{x + z \cdot \frac{y}{t}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]

Alternative 13
Accuracy	69.5%
Cost	969

\[\begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-19} \lor \neg \left(t \leq 7.2 \cdot 10^{-123}\right):\\ \;\;\;\;\frac{x + \frac{z}{\frac{t}{y}}}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b} + \frac{x \cdot t}{y \cdot b}\\ \end{array} \]

Alternative 14
Accuracy	42.1%
Cost	721

\[\begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+96}:\\ \;\;\;\;\frac{x}{a}\\ \mathbf{elif}\;a \leq 1950000000000 \lor \neg \left(a \leq 2.5 \cdot 10^{+46}\right) \land a \leq 3.6 \cdot 10^{+140}:\\ \;\;\;\;\frac{z}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a}\\ \end{array} \]

Alternative 15
Accuracy	56.5%
Cost	585

\[\begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-17} \lor \neg \left(t \leq 6.4 \cdot 10^{-41}\right):\\ \;\;\;\;\frac{x}{a + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{b}\\ \end{array} \]

Alternative 16
Accuracy	25.6%
Cost	192

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

Reproduce

herbie shell --seed 2023160 
(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))))